title: Kiruna

text: Mining plays a major role as a source of national income and employment for Kiruna and the surrounding region. As with most of Northern Sweden the area is rich with Magnetite which is mined to produce various Iron ore products which are then transported by rail to Narvik port in Norway to be shipped to customers around the world.


title: Kiruna

text: Large-scale mining in Kiruna started in the 19th century right around the time the major Swedish mining company LKAB was founded in 1890.


title: Kiruna

text: In winter, the Icehotel in nearby Jukkasjärvi and the northern lights attract tourists. The long and certain snow cover, which generally lasts from October to May, and frozen lakes and rivers facilitate cross-country and alpine skiing, dog sledding and snowmobiling. There is ice climbing in the mountains and ice skating on lakes or rivers. The annual Snow Festival is held over the last weekend of January and includes scooter jumping, reindeer racing and an ice sculpture contest.


title: Parallel (geometry)

text: In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. "Parallel curves" are curves that do not touch each other or intersect and keep a fixed minimum distance. In three-dimensional Euclidean space, a line and a plane that do not share a point are also said to be parallel. However, two noncoplanar lines are called "skew lines".


title: Parallel (geometry)

text: Parallel lines are the subject of Euclid's parallel postulate. Parallelism is primarily a property of affine geometries and Euclidean geometry is a special instance of this type of geometry.


title: Parallel (geometry)

text: In some other geometries, such as hyperbolic geometry, lines can have analogous properties that are referred to as parallelism.


title: Parallel (geometry)

text: The parallel symbol is formula_1. For example, formula_2 indicates that line "AB" is parallel to line "CD".


title: Parallel (geometry)

text: In the Unicode character set, the "parallel" and "not parallel" signs have codepoints U+2225 (∥) and U+2226 (∦), respectively. In addition, U+22D5 (⋕) represents the relation "equal and parallel to".


title: Parallel (geometry)

text: The same symbol is used for a binary function in electrical engineering (the parallel operator). It is distinct from the double-vertical-line brackets that indicate a norm, as well as from the logical or operator (codice_1) in several programming languages.


title: Parallel (geometry)

text: Given parallel straight lines "l" and "m" in Euclidean space, the following properties are equivalent:


title: Parallel (geometry)

text: Since these are equivalent properties, any one of them could be taken as the definition of parallel lines in Euclidean space, but the first and third properties involve measurement, and so, are "more complicated" than the second. Thus, the second property is the one usually chosen as the defining property of parallel lines in Euclidean geometry. The other properties are then consequences of Euclid's Parallel Postulate. Another property that also involves measurement is that lines parallel to each other have the same gradient (slope).


title: Parallel (geometry)

text: The definition of parallel lines as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements. Alternative definitions were discussed by other Greeks, often as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis.


title: Parallel (geometry)

text: At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools. The traditional treatment of geometry was being pressured to change by the new developments in projective geometry and non-Euclidean geometry, so several new textbooks for the teaching of geometry were written at this time. A major difference between these reform texts, both between themselves and between them and Euclid, is the treatment of parallel lines. These reform texts were not without their critics and one of them, Charles Dodgson (a.k.a. Lewis Carroll), wrote a play, "Euclid and His Modern Rivals", in which these texts are lambasted.


title: Parallel (geometry)

text: One of the early reform textbooks was James Maurice Wilson's "Elementary Geometry" of 1868. Wilson based his definition of parallel lines on the primitive notion of "direction". According to Wilhelm Killing the idea may be traced back to Leibniz. Wilson, without defining direction since it is a primitive, uses the term in other definitions such as his sixth definition, "Two straight lines that meet one another have different directions, and the difference of their directions is the "angle" between them." In definition 15 he introduces parallel lines in this way; "Straight lines which have the "same direction", but are not parts of the same straight line, are called "parallel lines"." Augustus De Morgan reviewed this text and declared it a failure, primarily on the basis of this definition and the way Wilson used it to prove things about parallel lines. Dodgson also devotes a large section of his play (Act II, Scene VI § 1) to denouncing Wilson's treatment of parallels. Wilson edited this concept out of the third and higher editions of his text.


title: Parallel (geometry)

text: Other properties, proposed by other reformers, used as replacements for the definition of parallel lines, did not fare much better. The main difficulty, as pointed out by Dodgson, was that to use them in this way required additional axioms to be added to the system. The equidistant line definition of Posidonius, expounded by Francis Cuthbertson in his 1874 text "Euclidean Geometry" suffers from the problem that the points that are found at a fixed given distance on one side of a straight line must be shown to form a straight line. This can not be proved and must be assumed to be true. The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, "The Elements of Geometry, simplified and explained" requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.


title: Parallel (geometry)

text: Because parallel lines in a Euclidean plane are equidistant there is a unique distance between the two parallel lines. Given the equations of two non-vertical, non-horizontal parallel lines,


title: Parallel (geometry)

text: the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope "m", a common perpendicular would have slope −1/"m" and we can take the line with equation "y" = −"x"/"m" as a common perpendicular. Solve the linear systems


title: Parallel (geometry)

text: These formulas still give the correct point coordinates even if the parallel lines are horizontal (i.e., "m" = 0). The distance between the points is


title: Parallel (geometry)

text: When the lines are given by the general form of the equation of a line (horizontal and vertical lines are included):


title: Parallel (geometry)

text: Two lines in the same three-dimensional space that do not intersect need not be parallel. Only if they are in a common plane are they called parallel; otherwise they are called skew lines.


title: Parallel (geometry)

text: Two distinct lines "l" and "m" in three-dimensional space are parallel if and only if the distance from a point "P" on line "m" to the nearest point on line "l" is independent of the location of "P" on line "m". This never holds for skew lines.


title: Parallel (geometry)

text: A line "m" and a plane "q" in three-dimensional space, the line not lying in that plane, are parallel if and only if they do not intersect.


title: Parallel (geometry)

text: Equivalently, they are parallel if and only if the distance from a point "P" on line "m" to the nearest point in plane "q" is independent of the location of "P" on line "m".


title: Parallel (geometry)

text: Similar to the fact that parallel lines must be located in the same plane, parallel planes must be situated in the same three-dimensional space and contain no point in common.


title: Parallel (geometry)

text: Two distinct planes "q" and "r" are parallel if and only if the distance from a point "P" in plane "q" to the nearest point in plane "r" is independent of the location of "P" in plane "q". This will never hold if the two planes are not in the same three-dimensional space.


title: Parallel (geometry)

text: In non-Euclidean geometry, it is more common to talk about geodesics than (straight) lines. A geodesic is the shortest path between two points in a given geometry. In physics this may be interpreted as the path that a particle follows if no force is applied to it. In non-Euclidean geometry (elliptic or hyperbolic geometry) the three Euclidean properties mentioned above are not equivalent and only the second one (Line m is in the same plane as line l but does not intersect l) is useful in non-Euclidean geometries, since it involves no measurements. In general geometry the three properties above give three different types of curves, equidistant curves, parallel geodesics and geodesics sharing a common perpendicular, respectively.


title: Parallel (geometry)

text: While in Euclidean geometry two geodesics can either intersect or be parallel, in hyperbolic geometry, there are three possibilities. Two geodesics belonging to the same plane can either be:


title: Parallel (geometry)

text: In the literature "ultra parallel" geodesics are often called "non-intersecting". "Geodesics intersecting at infinity" are called "limiting parallel".


title: Parallel (geometry)

text: As in the illustration through a point "a" not on line "l" there are two limiting parallel lines, one for each direction ideal point of line l. They separate the lines intersecting line l and those that are ultra parallel to line "l".


title: Parallel (geometry)

text: Ultra parallel lines have single common perpendicular (ultraparallel theorem), and diverge on both sides of this common perpendicular.


title: Parallel (geometry)

text: In spherical geometry, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Thus, there are no parallel geodesics to a given geodesic, as all geodesics intersect. Equidistant curves on the sphere are called parallels of latitude analogous to the latitude lines on a globe. Parallels of latitude can be generated by the intersection of the sphere with a plane parallel to a plane through the center of the sphere.


title: Parallel (geometry)

text: In this case, parallelism is a transitive relation. However, in case "l" = "n", the superimposed lines are "not" considered parallel in Euclidean geometry. The binary relation between parallel lines is evidently a symmetric relation. According to Euclid's tenets, parallelism is "not" a reflexive relation and thus "fails" to be an equivalence relation. Nevertheless, in affine geometry a pencil of parallel lines is taken as an equivalence class in the set of lines where parallelism is an equivalence relation.


title: Parallel (geometry)

text: To this end, Emil Artin (1957) adopted a definition of parallelism where two lines are parallel if they have all or none of their points in common.


title: Parallel (geometry)

text: Then a line "is" parallel to itself so that the reflexive and transitive properties belong to this type of parallelism, creating an equivalence relation on the set of lines. In the study of incidence geometry, this variant of parallelism is used in the affine plane.


title: Focus on the Family

text: Focus on the Family (FOTF or FotF) is a fundamentalist Protestant organization founded in 1977 in Southern California by James Dobson, based in Colorado Springs, Colorado. The group is one of a number of evangelical parachurch organizations that rose to prominence in the 1980s. As of the 2017 tax filing year, Focus on the Family declared itself to be a church, "primarily to protect the confidentiality of our donors." Traditionally, entities considered churches have been ones that have regular worship services and congregants.


title: Focus on the Family

text: It most prominently lobbies against LGBT rights — including those related to marriage, adoption, and parenting — labeling it a "particularly evil lie of Satan". Focus on the Family has been criticized by psychiatrists, psychologists, and social scientists for misrepresenting their research in order to bolster its religious ideology and political agenda, as well as for their anti-LGBT views. The organization also seeks to change public policy in the areas of sex education, creationism, abortion, state-sponsored school prayer, gambling, drugs, and enforcement of their interpretation of proper gender roles.


title: Focus on the Family

text: The core promotional activities of the organization include the flagship daily radio broadcast hosted by its president Jim Daly together with co-host Focus VP John Fuller. Focus also provides free resources in line with the group's views, and publishes books, magazines, videos, and audio recordings.


title: Focus on the Family

text: The organization also produces programs for targeted audiences, such as "Adventures in Odyssey" and "Ribbits!" for children, and dramas.


title: Focus on the Family

text: From 1977 to 2003, James Dobson served as the sole leader of the organization. In 2003, Donald P. Hodel became president and chief executive officer, tasked with the day-to-day operations. Dobson remained chairman of the board of directors, with chiefly creative and speaking duties. In March 2005, Hodel retired and Jim Daly, formerly the Vice President in charge of Focus on the Family's International Division, assumed the role of president and chief executive officer.


title: Focus on the Family

text: In November 2008, the organization announced that it was eliminating 202 jobs, representing 18 percent of its workforce. The organization also cut its budget from $160 million in fiscal 2008 to $138 million for fiscal 2009.


title: Focus on the Family

text: In February 2009, Dobson resigned his chairmanship. He left Focus on the Family in early 2010, and subsequently founded Family Talk as a non-profit organization and launched a new broadcast that began airing nationally on May 3, 2010. He is no longer affiliated with Focus on the Family.


title: Focus on the Family

text: On June 23, 2017, Vice President Mike Pence attended the organization's 40th anniversary celebration; at the event, he praised founder James Dobson, stated that President Donald Trump is an ally of the organization, and added that the Trump administration supports its goals (including the abolition of Planned Parenthood). Pence's attendance at the event, along with Focus on the Family's stances on LGBT rights, was criticized by the Human Rights Campaign.


title: Focus on the Family

text: In its IRS Form 990 for Tax Year 2015, dated October 26, 2017, Focus on the Family for the first time declared itself a "church, convention of churches or association of churches", claiming that it was no longer required to file the IRS disclosure form and that the sources and disposition of its $89 million budget were "Not for public inspection". Tax attorney Gail Harmon, who advises nonprofit organizations on tax law, said she found the declaration "shocking", noting that "There's nothing about them that meets the traditional definition of what a church is. They don't have a congregation, they don't have the rites of various parts of a person's life." A spokesperson for the organization stated that it changed its status "primarily to protect the confidentiality of our donors". By 2020, the organization would have offices in 14 countries and partnerships in 60 countries, for an international presence in 74 countries.


title: Focus on the Family

text: Focus on the Family's Wait No More ministry works with adoption agencies, church leaders and ministry partners to recruit families to adopt children from foster care. In Colorado, the number of children waiting for adoption dropped from about 800 to 350, due in-part to the efforts of Wait No More. Focus on the Family's efforts to encourage adoption among Christian families is part of a larger effort by Evangelicals to, in their perception, live out what they see as the "biblical mandate" to help children.


title: Focus on the Family

text: Focus on the Family's Option Ultrasound Program (OUP) provides grants to crisis pregnancy centers to pay the cost of ultrasound machines or sonography training. Focus on the Family began OUP in 2004 with the goal of convincing women not to have abortions. FOTF officials said that ultrasound services help a woman better understand her pregnancy and baby's development, creating an important "bonding opportunity" between "mother and unborn child".


title: Focus on the Family

text: A study released in February 2012 shows that ultrasounds do not have a direct impact on an abortion decision. In 2011, FOTF announced that they would like to talk with pro-choice groups like Planned Parenthood to work towards the shared goal of making abortion less common. Rep. Michele Bachmann (R-Minn.) introduced a sonogram bill in 2011 and, citing Focus on the Family, told Congress that "78 percent of women who see and hear the fetal heartbeat choose life." She was later corrected by Focus on the Family, which released a statement saying they did not release such data.


title: Focus on the Family

text: Boundless.org is Focus on the Family's website for young adults featuring articles, a blog, a podcast, and a conference. The website covers topics such as singleness, dating, relationships, popular culture, career, and sex.


title: Focus on the Family

text: Pluggedin is a Focus on the Family publication and associated website created for families that reviews magazines, films, books, music, and TV shows.


title: Focus on the Family

text: The Day of Dialogue was a student event which took place April 16. Since 2018 the event is no longer marked on a single date, or organized nationally. Founders described the goal of the event, created in opposition to the anti-bullying and anti-homophobic Day of Silence, as "encouraging honest and respectful conversation among students about God's design for sexuality." It was previously known as the "Day of Truth" and was founded by the Alliance Defense Fund in 2005. In 2007, Exodus International began supporting the Day of Truth, an event created by Alliance Defending Freedom (ADF) in 2005 that challenges homosexuality. In 2009, the ADF announced they had passed on their leadership role for the event to Exodus. In October 2010, Exodus announced they would no longer support the event. President Alan Chambers stated they realised they needed to "equip kids to live out biblical tolerance and grace while treating their neighbors as they'd like to be treated, whether they agree with them or not", adding that the Day of Truth was becoming too divisive. Chambers said that Exodus had not changed its position on homosexuality, rather they were reevaluating how to best communicate their message. Focus on the Family subsequently took leadership of the event, and renamed it the Day of Dialogue.


title: Focus on the Family

text: The National Day of Prayer Task Force is an American evangelical conservative Christian non-profit organization which organizes, coordinates, and presides over Evangelical Christian religious observances each year on the National Day of Prayer. The website of the NDP Task Force states that "its business affairs are separate" from those of Focus on the Family, but also that "between 1990 and 1993, Focus on the Family did provide grants in support of the NDP Task Force" and that "Focus on the Family is compensated for services rendered." Shirley Dobson, wife of James Dobson, was chairwoman of the NDP Task Force from 1991 until 2016, when Anne Graham Lotz, daughter of evangelist Billy Graham, assumed the post.


title: Focus on the Family

text: Radio Theatre is a program run by Focus on the Family that makes both original and adapted radio dramas. Much of the staff involved with Adventures in Odyssey is also involved with Radio Theatre such as Paul McCusker.


title: Focus on the Family

text: They have made adaptations of many novels including "Les Miserables" and "Anne of Green Gables" as well as an adaptation of the complete Chronicles of Narnia. Radio Theatre often hires famous actors to be a part of their adaptations such as Andy Serkis.


title: Focus on the Family

text: Focus on the Family formed Love Won Out, an ex-gay ministry in 1998. In 2009, it was sold to Exodus International.


title: Focus on the Family

text: Focus on the Family's 501(c)(3) status prevents them from advocating any individual political candidate. FOTF also has an affiliated group, Family Policy Alliance, though the two groups are legally separate. As a 501(c)(4) social welfare group, Family Policy Alliance has fewer political lobbying restrictions. FOTF's revenue in 2012 was US$90.5 million, and that of Family Policy Alliance (formerly CitizenLink) was US$8 million.


title: Focus on the Family

text: Focus on the Family maintains a strong stand against abortion, and provides grant funding and medical training to assist crisis pregnancy centers (CPCs; also known as pregnancy resource centers) in obtaining ultrasound machines. According to the organization, this funding, which has allowed CPCs to provide pregnant women with live sonogram images of the developing fetus, has led directly to the birth of over 1500 babies who would have otherwise been aborted. The organization has been staunchly opposed to public funding for elective abortions.


title: Focus on the Family

text: Focus on the Family has been a prominent supporter of the pseudoscience of intelligent design, publishing pro-intelligent design articles in its "Citizen" magazine and selling intelligent design videos on its website. Focus on the Family co-published the intelligent design videotape "Unlocking the Mystery of Life" with the Discovery Institute, hub of the intelligent design movement.


title: Focus on the Family

text: In New Zealand, Focus on the Family supported a Citizens Initiated Referendum on the repeal of section 59 of the Crimes Act 1961, which placed limits on the physical disciplining of children.


title: Focus on the Family

text: Focus on the Family Singapore came under criticism in October 2014 over allegations of sexism and promoting gender stereotypes during their workshops on managing relationships for junior college students. The workshop received a complaint from both a Hwa Chong Junior College student, as well as negative feedback from the college management as being 'ineffective' and stopped before the end of the year.


title: Focus on the Family

text: Following the 2022 U.S. Supreme Court decision to overturn "Roe v. Wade", Focus on the Family published an article on its "Daily Citizen" site urging conservative Christians to engage in a "cultural civil war" against "radical abortion laws" implemented in left-leaning states. This added to speculation that political violence similar to the January 6th attacks could be accepted or encouraged on the grounds of opposing abortion rights.


title: Focus on the Family

text: In the 2008 United States presidential election, Focus on the Family shifted from supporting Mike Huckabee, to not supporting any candidate, to accepting the Republican ticket once Sarah Palin was added. Prior to the election, a television and letter campaign was launched predicting terrorist attacks in four U.S. cities and equating the U.S. with Nazi Germany. This publicity was condemned by the Anti Defamation League. Within a month before the general election, Focus on the Family began distributing a 16-page letter titled "Letter from 2012 in Obama's America", which describes an imagined American future in which "many of our freedoms have been taken away by a liberal Supreme Court of the United States and a majority of Democrats in both the House of Representatives and the Senate." According to "USA Today", the letter "is part of an escalation in rhetoric from Christian right activists" trying to paint Democratic Party presidential nominee Senator Barack Obama in a negative light.


title: Focus on the Family

text: Focus on the Family Action supported Senator Saxby Chambliss (R-Ga.) in his successful December 2, 2008, runoff election win. The organization, according to the "Colorado Independent", donated $35,310 in radio ads to the Chambliss runoff campaign effort. As the "Independent" reports, the Focus-sponsored ads were aired in about a dozen Georgia markets. The commercials were produced in the weeks after Focus laid off 202 employees, some 20 percent of its workforce, because of the national economic crisis.


title: Focus on the Family

text: Dobson spoke at the 2004 rally against gay marriage called Mayday for Marriage. It was here for the first time that he endorsed a presidential candidate, George W. Bush. Here he denounced the Supreme Court rulings in favor of gay rights, and he urged rally participants to get out and vote so that the battle against gay rights could be won in the Senate.


title: Focus on the Family

text: In an interview with "Christianity Today", Dobson also explained that he was not in favor of civil unions. He stated that civil unions are just same-sex marriage under a different name. The main priority of the opposing same-sex marriage movement is to define marriage on the federal level as between a man and a woman and combat the passage of civil unions later.


title: Focus on the Family

text: Civil rights advocacy groups identify Focus on the Family as a major opponent of gay rights. The Southern Poverty Law Center, a civil rights and hate group monitoring organization, described Focus on the Family as one of a "dozen major groups [which] help drive the religious right's anti-gay crusade". The SPLC does not list Focus on the Family as a hate group, however, since it opposes homosexuality "on strictly Biblical grounds".


title: Focus on the Family

text: Focus on the Family is a member of ProtectMarriage.com, a coalition formed to sponsor California Proposition 8, a ballot initiative to restrict marriage to opposite-sex couples, which passed in 2008, but was subsequently struck down as being unconstitutional by a federal court in "Perry v. Schwarzenegger".


title: Focus on the Family

text: Social scientists have criticized Focus on the Family for misrepresenting their research in order to bolster its own perspective. Researcher Judith Stacey, whose work was used by Focus on the Family to claim that gays and lesbians do not make good parents, said that the claim was "a direct misrepresentation of the research". She elaborated, "Whenever you hear Focus on the Family, legislators or lawyers say, 'Studies prove that children do better in families with a mother and a father,' they are referring to studies which compare two-parent heterosexual households to single-parent households. The studies they are talking about do not cite research on families headed by gay and lesbian couples." FOTF claimed that Stacey's allegation was without merit and that their position is that the best interests of children are served when there is a father and a mother. "We haven't said anything about sexual orientation", said Glenn Stanton.


title: Focus on the Family

text: James Dobson cited the research of Kyle Pruett and Carol Gilligan in a "Time" magazine guest article in the service of a claim that two women cannot raise a child; upon finding out that her work had been used in this way, Gilligan wrote a letter to Dobson asking him to apologize and to cease and desist from citing her work, describing herself as "mortified to learn that you had distorted my work ... Not only did you take my research out of context, you did so without my knowledge to support discriminatory goals that I do not agree with ... there is nothing in my research that would lead you to draw the stated conclusions you did in the "Time" article." Pruett wrote a similar letter, in which he said that Dobson "cherry-picked a phrase to shore up highly (in my view) discriminatory purposes. This practice is condemned in real science, common though it may be in pseudo-science circles. There is nothing in my longitudinal research or any of my writings to support such conclusions", and asked that FOTF not cite him again without permission.


title: Focus on the Family

text: After Elizabeth Saewyc's research on teen suicide was used by Focus on the Family to promote conversion therapy she said that "the research has been hijacked for somebody's political purposes or ideological purposes and that's worrisome", and that research in fact linked the suicide rate among LGBT teens to harassment, discrimination, and closeting. Other scientists who have criticized Focus on the Family for misrepresenting their findings include Robert Spitzer, Gary Remafedi, and Angela Phillips.


title: Focus on the Family

text: In 2010, Focus on the Family bought ad time during Super Bowl XLIV to air a commercial featuring Heisman Trophy winning Florida Gators quarterback Tim Tebow and his mother, Pam. In the ad, Pam described Tim as a "miracle baby" who "almost didn't make it into this world", and further elaborated that "with all our family's been through, we have to be tough" (after which Pam was promptly tackled by Tim). The ad directed viewers to the organization's website.


title: Focus on the Family

text: Women's rights groups asked CBS not to air the then-unseen ad, arguing that it was divisive. Planned Parenthood released a video response of its own featuring fellow NFL player Sean James. The claim that Tebow's family chose not to perform an abortion was also widely criticized; critics felt that the claim was implausible because it would be unlikely for doctors to recommend the procedure because abortion is illegal in the Philippines. CBS's decision to run the ad was also criticized for deviating from its past policy to reject advocacy-type ads during the Super Bowl, including ads by left-leaning groups such as PETA, MoveOn.org and the United Church of Christ (which wanted to run an ad that was pro-same-sex marriage). However, CBS stated that "we have for some time moderated our approach to advocacy submissions after it became apparent that our stance did not reflect public sentiment or industry norms on the issue."


title: Focus on the Family

text: Focus on the Family produced another commercial which ran during the second quarter of the January 14, 2012 Denver Broncos-New England Patriots AFC Divisional Playoff broadcast on CBS, featuring children reciting the Bible verse John 3:16. The ad did not generate nearly the amount of controversy that surrounded the Super Bowl commercial. It did gain some national media attention, and president Jim Daly stated in a press release that its purpose was to "help everyone understand some numbers are more important than the ones on the scoreboard."


title: Focus on the Family

text: In 2008, Dobson's "Focus on the Family" program was nominated for induction into the National Radio Hall of Fame. Nominations were made by the 157 members of the Hall of Fame and voting on inductees was handed over to the public using online voting. The nomination drew the ire of gay rights activists, who launched efforts to have the program removed from the nominee list and to vote for other nominees to prevent "Focus" from winning. However, on July 18, 2008, it was announced that the program had won and would be inducted into the Radio Hall of Fame in a ceremony on November 8, 2008. Truth Wins Out, a gay rights group, protested the ceremony with over 300 protesters.


title: Focus on the Family

text: The Focus on the Family headquarters is a four building, complex located off of Interstate 25 in northern Colorado Springs, Colorado, with its own ZIP Code (80995). The buildings consist of the Administration building, International building, Welcome Center and Operations building (currently unused), and totals 526,070 square feet.


title: Focus on the Family

text: Focus on the Family moved to its current headquarters from Pomona, California, in 1991, with 1,200 employees. In 2002, the number of employees peaked at 1,400. By September 2011, after years of layoffs, they had 650 employees remaining. Christopher Ott of "Salon" said in 1998 that the FOTF campus has "handsome new brick buildings, professional landscaping and even its own traffic signs" and that "The buildings and grounds are well-maintained and comfortable. If there is any ostentatious or corrupt influence here, it is nowhere in sight."


title: Suma Kanakala

text: Suma Kanakala (née Pallassana Paachuveettil; was born on 22 March 1974) she is an Indian television presenter, actress, and television producer who predominantly works in Telugu television. She is best known for hosting ETV's "Star Mahila"a Telugu TV game show, which is the longest-running TV game show in India and ran for almost 1215 years (until 2021).


title: Suma Kanakala

text: Suma was born on 22 March 1975 in her native hometown of Palakkad, Kerala, India. Her parents are Pullot Narayanan Kutty Nair and Pallassana Paachuveettil Vimala, who were in Secunderabad, Andhra Pradesh (now in Telangana), India for a very long time because of the father's government job transfer over there. Their only daughter Suma was born 10 years later after her parents’ marriage as the only child for them. As a six-month old baby, she along with her parents flew to Secunderabad where she was brought up near Lalaguda & Mettuguda railways. She married Tollywood actor, Rajeev Kanakala on 10 February 1999. That’s why she’s known as Suma Kanakala in the Tollywood industry, otherwise Kerala culture would take up mother surname as well as their property to their children. They have two children- one son named Roshan Karthik Kanakala (b. 2000) & Snehanaswini Kanakala (b. 2005). In addition to her mother tongue of Malayalam, she is fluent in Telugu, Hindi, Tamil, and English.


title: Suma Kanakala

text: A presenter aged 16, she has hosted many Telugu film audio launches, film awards and functions. She is a Malayali from Kerala, but speaks Telugu fluently. She has acted in various serial and telefilms since 1995, her breakthrough came with the boom in satellite channels. "Swayamvaram", "Anveshitha", "Geethanjali", and "Ravoyi Chandamama" were her major serials. She didn't have any interest in working in films. Kanakala's flagship show is "Star Mahila" on ETV, which attracted many female audiences. She created a record by this show becoming one of the longest running women game show in India. Her versatility is evident in Panchavataram on TV9. "Cash" on ETV and Start music on MAA TV are her current prime time shows. Kanakala started her own production house named K. Suma Rajeev Creations on 26 December 2012 and has produced a show named "Lakku Kikku" which is telecast on Zee Telugu. She also worked in a show named "Genes" on ETV. Her "Kevvu Keka" on MAA TV with co-star Mano and produced by K. Suma Rajeev Creations. Kanakala also sang "Suya Suya" song from the 2017 Telugu film "Winner". She is well known for her spontaneous and humorous remarks during her shows.


title: Branford Marsalis

text: Branford Marsalis (born August 26, 1960) is an American saxophonist, composer, and bandleader. While primarily known for his work in jazz as the leader of the Branford Marsalis Quartet, he also performs frequently as a soloist with classical ensembles and has led the group Buckshot LeFonque. From 1992 to 1995 he led the Tonight Show Band.


title: Branford Marsalis

text: Marsalis was born on August 26, 1960, in Breaux Bridge, Louisiana, and raised in New Orleans. He is the son of Dolores (née Ferdinand), a jazz singer and substitute teacher, and Ellis Louis Marsalis, Jr., a pianist and music professor. His brothers Jason Marsalis, Wynton Marsalis, and Delfeayo Marsalis are also jazz musicians.


title: Branford Marsalis

text: In mid-1980, while still a Berklee College of Music student, Marsalis toured Europe playing alto and baritone saxophone in a large ensemble led by drummer Art Blakey. Other big band experiences with Lionel Hampton and Clark Terry followed over the next year, and by the end of 1981 Marsalis, on alto saxophone, had joined his brother Wynton in Blakey's Jazz Messengers. Other performances with his brother, including a 1981 Japanese tour with Herbie Hancock, led to the formation of his brother Wynton's first quintet, where Marsalis shifted his emphasis to soprano and tenor saxophones. He continued to work with Wynton until 1985, a period that also saw the release of his own first recording, "Scenes in the City", as well as guest appearances with other artists including Miles Davis and Dizzy Gillespie.


title: Branford Marsalis

text: In 1985, he joined Sting, singer and bassist of rock band the Police, on his first solo project, "The Dream of the Blue Turtles", alongside jazz and session musicians Omar Hakim on drums, Darryl Jones on the bass and Kenny Kirkland on keyboards. He became a regular in Sting's line-up both in the studio and live up until the release of "Brand New Day" in 1999.


title: Branford Marsalis

text: In 1986, Marsalis formed the Branford Marsalis Quartet with pianist Kirkland, drummer Jeff "Tain" Watts and bass player Robert Hurst. That year, they released their first album, "Royal Garden Blues". That lineup of the quartet would go on to release four more albums, the last of which, "I Heard You Twice the First Time" (1992), won the Grammy Award for Best Instrumental Jazz Album, Individual or Group.


title: Branford Marsalis

text: In 1988, Marsalis co-starred in the Spike Lee film "School Daze", also rendering several horn-blowing interludes for the music in the film. His witty comments have pegged him to many memorable one-liners in the film. In 1989, Marsalis played a 30-second cover of "Lift Every Voice and Sing" over the opening logos of Lee's film "Do the Right Thing".


title: Branford Marsalis

text: Between 1990 and 1994, Branford played with the Grateful Dead numerous times, and appeared on their 1990 live album "Without a Net".


title: Branford Marsalis

text: In 1992, Marsalis became the leader of the Tonight Show Band on the newly launched "The Tonight Show with Jay Leno", after Jay Leno replaced Johnny Carson. Initially, Marsalis turned down the offer, but later reconsidered and accepted the position. He brought with him the three other members of the Branford Marsalis Quartet, who became the Tonight Show Band's pianist, drummer and bass player, respectively.


title: Branford Marsalis

text: In 1994, Marsalis formed the group Buckshot LeFonque (named after a pseudonym once used by Cannonball Adderley), a jazz group with elements of rock and hip-hop. That year, they released their first album, "Buckshot LeFonque", which was mostly produced by DJ Premier.


title: Branford Marsalis

text: In 1994, Marsalis appeared on the Red Hot Organization's compilation CD, "". The album, meant to raise awareness of the AIDS epidemic in African American society, was named Album of the Year by "Time".


title: Branford Marsalis

text: In 1995, Marsalis left "The Tonight Show", having become unhappy in the role: he disliked that he was supposed to always show enthusiasm, even for jokes he thought were unfunny. He was succeeded as bandleader by guitarist Kevin Eubanks. In a well-publicized interview soon after leaving, Marsalis said, "The job of musical director I found out later was just to kiss the ass of the host, and I ain't no ass kisser." He also complained that when he did not laugh or smile, some viewers' perception was, "Oh, he’s surly. He hates his boss." When the interviewer asked if Marsalis did hate Leno, Marsalis responded, "Oh, I despised him." He later stated that he did not hate Leno, and that this was a sarcastic response to what he considered "a ridiculous question".


title: Branford Marsalis

text: In 1997, bassist Eric Revis replaced Hurst in the Branford Marsalis Quartet. Kirkland died the following year, and was replaced by pianist Joey Calderazzo. The Branford Marsalis Quartet has since toured and recorded extensively. For two decades Marsalis was associated with Columbia, where he served as creative consultant and producer for jazz recordings between 1997 and 2001, including signing saxophonist David S. Ware for two albums.


title: Branford Marsalis

text: In 2002, Marsalis founded his own label, Marsalis Music. Its catalogue includes Claudia Acuña, Harry Connick Jr., Doug Wamble, Miguel Zenón, in addition to albums by members of the Marsalis family.


title: Branford Marsalis

text: Marsalis has also become involved in college education, with appointments at Michigan State University (1996–2000), San Francisco State University (2000–2002), and North Carolina Central University (2005–present). After Hurricane Katrina in 2005, Marsalis and Harry Connick, Jr., working with the local Habitat for Humanity, created Musicians Village in New Orleans, with the Ellis Marsalis Center for Music the centerpiece.


title: Branford Marsalis

text: Under the direction of conductor Gil Jardim, Branford Marsalis and members of the Philharmonia Brasileira toured the United States in the fall of 2008, performing works by Brazilian composer Heitor Villa-Lobos, arranged for solo saxophone and orchestra. This project commemorated the 50th Anniversary of the revered Brazilian composer s death.


title: Branford Marsalis

text: Marsalis and the members of his quartet joined the North Carolina Symphony for "American Spectrum", released in February 2009 by Sweden's BIS Records. The album showcases Marsalis and the orchestra performing a range of American music by Michael Daugherty, John Williams, Ned Rorem and Christopher Rouse, while being conducted by Grant Llewellyn.


title: Branford Marsalis

text: On July 14, 2010, Marsalis made his debut with the New York Philharmonic on Central Park's Great Lawn. Led by conductor Andrey Boreyko, Marsalis and the New York Philharmonic performed Glazunov's "Concerto for Alto Saxophone" and Schuloff's "Hot-Sonate for Alto Saxophone and Orchestra." Boreyko, Marsalis and the Philharmonic performed the same program again in Vail, CO later that month and four more times at Avery Fisher Hall in New York, NY the following February.


title: Branford Marsalis

text: In June 2011, after working together for over 10 years in a band setting, Branford Marsalis and Joey Calderazzo released their first duo album titled "Songs of Mirth and Melancholy", on Branford's label, Marsalis Music. Their first public performance was at the 2011 TD Toronto Jazz Festival.


title: Branford Marsalis

text: In 2012, Branford Marsalis released "Four MFs Playin' Tunes" on deluxe 180-gram high definition vinyl, prior to Record Store Day 2012 on April 21, 2012. This is the first recording of the Branford Marsalis Quartet with drummer Justin Faulkner, who joined the band in 2009, and was the first vinyl release from Marsalis Music. The album was named Apple iTunes Best of 2012 Instrumental Jazz Album of the Year.


title: Branford Marsalis

text: Marsalis performed "The Star-Spangled Banner" on Wednesday, September 5, 2012, at the Democratic National Convention in Charlotte.


title: Branford Marsalis

text: In 2019 Marsalis released "The Secret Between the Shadow and the Soul", which he recorded in Australia with his quartet. Marsalis, commenting on the longevity of his band and their approach said, ahead of the album's release: '“Staying together allows us to play adventurous, sophisticated music and sound good. Lack of familiarity leads to defensive playing, playing not to make a mistake. I like playing sophisticated music, and I couldn’t create this music with people I don’t know.”


title: Branford Marsalis

text: Marsalis lives in Durham, North Carolina with his wife Nicole and their two daughters. He was raised Catholic.


title: Primitive root modulo n

text: In modular arithmetic, a number is a primitive root modulo  if every number coprime to is congruent to a power of modulo . That is, is a "primitive root modulo"  if for every integer coprime to , there is some integer for which ≡ (mod ). Such a value is called the index or discrete logarithm of to the base modulo . So is a "primitive root modulo"  if and only if is a generator of the multiplicative group of integers modulo.


title: Primitive root modulo n

text: Gauss defined primitive roots in Article 57 of the "Disquisitiones Arithmeticae" (1801), where he credited Euler with coining the term. In Article 56 he stated that Lambert and Euler knew of them, but he was the first to rigorously demonstrate that primitive roots exist for a prime . In fact, the "Disquisitiones" contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive.


title: Primitive root modulo n

text: Here we see that the period of 3 modulo 7 is 6. The remainders in the period, which are 3, 2, 6, 4, 5, 1, form a rearrangement of all nonzero remainders modulo 7, implying that 3 is indeed a primitive root modulo 7. This derives from the fact that a sequence ( modulo ) always repeats after some value of , since modulo  produces a finite number of values. If is a primitive root modulo  and is prime, then the period of repetition is Permutations created in this way (and their circular shifts) have been shown to be Costas arrays.


title: Primitive root modulo n

text: If is a positive integer, the integers from 0 to that are coprime to (or equivalently, the congruence classes coprime to ) form a group, with multiplication modulo as the operation; it is denoted by formula_2, and is called the group of units modulo , or the group of primitive classes modulo . As explained in the article multiplicative group of integers modulo, this multiplicative group (formula_2) is cyclic if and only if is equal to 2, 4, , or 2 where is a power of an odd prime number. When (and only when) this group formula_2 is cyclic, a generator of this cyclic group is called a primitive root modulo (or in fuller language primitive root of unity modulo , emphasizing its role as a fundamental solution of the roots of unity polynomial equations X − 1 in the ring formula_2), or simply a primitive element of formula_2.


title: Primitive root modulo n

text: When formula_2 is non-cyclic, such primitive elements mod do not exist. Instead, each prime component of has its own sub-primitive roots (see in the examples below).


title: Primitive root modulo n

text: For any (whether or not formula_2 is cyclic), the order of formula_2 is given by Euler's totient function () . And then, Euler's theorem says that for every coprime to ; the lowest power of that is congruent to 1 modulo is called the multiplicative order of modulo . In particular, for to be a primitive root modulo , () has to be the smallest power of that is congruent to 1 modulo .


title: Primitive root modulo n

text: For example, if then the elements of formula_2 are the congruence classes {1, 3, 5, 9, 11, 13}; there are of them. Here is a table of their powers modulo 14:


title: Primitive root modulo n

text: The order of 1 is 1, the orders of 3 and 5 are 6, the orders of 9 and 11 are 3, and the order of 13 is 2. Thus, 3 and 5 are the primitive roots modulo 14.


title: Primitive root modulo n

text: For a second example let The elements of formula_2 are the congruence classes {1, 2, 4, 7, 8, 11, 13, 14}; there are of them.


title: Primitive root modulo n

text: Since there is no number whose order is 8, there are no primitive roots modulo 15. Indeed, , where is the Carmichael function.


title: Primitive root modulo n

text: Gauss proved that for any prime number (with the sole exception of the product of its primitive roots is congruent to 1 modulo .


title: Primitive root modulo n

text: He also proved that for any prime number , the sum of its primitive roots is congruent to ( − 1) modulo , where is the Möbius function.


title: Primitive root modulo n

text: Artin's conjecture on primitive roots states that a given integer that is neither a perfect square nor −1 is a primitive root modulo infinitely many primes.


title: Primitive root modulo n

text: No simple general formula to compute primitive roots modulo is known. There are however methods to locate a primitive root that are faster than simply trying out all candidates. If the multiplicative order (its exponent) of a number modulo is equal to formula_22 (the order of formula_2), then it is a primitive root. In fact the converse is true: If is a primitive root modulo , then the multiplicative order of is formula_24 We can use this to test a candidate to see if it is primitive.


title: Primitive root modulo n

text: For formula_25 first, compute formula_26 Then determine the different prime factors of formula_22, say , ..., . Finally, compute


title: Primitive root modulo n

text: using a fast algorithm for modular exponentiation such as exponentiation by squaring. A number for which these results are all different from 1 is a primitive root.


title: Primitive root modulo n

text: since, in general, a cyclic group with elements has formula_30 generators, with being the integers coprime to , which generate .


title: Primitive root modulo n

text: For prime , this equals formula_31, and since formula_32 the generators are very common among {2, ..., −1} and thus it is relatively easy to find one.


title: Primitive root modulo n

text: If is a primitive root modulo , then is also a primitive root modulo all powers unless ≡ 1 (mod ); in that case, + is.


title: Primitive root modulo n

text: If is a primitive root modulo , then either or + (whichever one is odd) is a primitive root modulo 2.


title: Primitive root modulo n

text: Finding primitive roots modulo is also equivalent to finding the roots of the ( − 1)st cyclotomic polynomial modulo .


title: Primitive root modulo n

text: Fridlander (1949) and Salié (1950) proved that there is a positive constant such that for infinitely many primes


title: Primitive root modulo n

text: It can be proved in an elementary manner that for any positive integer there are infinitely many primes such that < <


title: Primitive root modulo n

text: A primitive root modulo is often used in pseudorandom number generators and cryptography, including the Diffie–Hellman key exchange scheme. Sound diffusers have been based on number-theoretic concepts such as primitive roots and quadratic residues.


title: Primitive root modulo n

text: The "Disquisitiones Arithmeticae" has been translated from Gauss's Ciceronian Latin into English and German. The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes.


title: K31

text: The Karabiner Modell 1931 (K. 31/Kar. 31/Mq. 31) is a magazine-fed, straight-pull bolt-action rifle. It was the standard issue rifle of the Swiss armed forces from 1933 until 1958 though examples remained in service into the 1970s. It has a 6-round removable magazine, and is chambered for the 7.5×55mm Swiss "Gewehrpatrone 1911" or GP 11, a cartridge with ballistic qualities similar to the 7.62×51mm NATO/.308 Winchester cartridge. Each rifle included a 6-round detachable box magazine with matching stamped serial number. A stripper clip can be used to load the magazine from the top of the receiver.


title: K31

text: The Karabiner Modell 1931 replaced both the Model 1911 rifle and carbine and was gradually replaced by the Stgw 57 from 1958 onwards.


title: K31

text: Although the K. 31/Kar. 31 is a straight-pull carbine broadly based on previous Swiss "Schmidt–Rubin" service rifles and carbines, the K. 31/Kar. 31 was not designed by Colonel Rudolf Schmidt (1832–1898) as he was not alive in 1931 to do so.


title: K31

text: Mechanical engineer Eduard Rubin (1846–1920) was the designer of the 7.5×55mm Swiss ammunition previous Swiss service rifles and the K. 31/Kar. 31 are chambered for.


title: K31

text: The Karabiner Modell 31 was a new design by the Eidgenössische Waffenfabrik in Bern, Switzerland under Colonel Adolf Furrer (1873–1958). The first 200 K. 31/Kar. 31s were made in May 1931 for troop trials (serials 500,001 – 500,200), thus the model number of 1931.


title: K31

text: Compared to the previous Schmidt–Rubin series Model 1911 rifle and carbine, the Karabiner Modell 31 bolt and receiver were significantly shortened, allowing for a rifle length barrel and sight radius, without increasing the overall length of the Model 1911 carbine, moving the rear sight element closer to the eye, and cutting in half the amount of time for the firing pin to strike the cartridge after the trigger was pulled.


title: K31

text: The Karabiner Modell 31 barrel has 4 rifling grooves and a rifling twist rate. The action itself is only connected to the stock by two screws, one attaching to the recoil lug, with the second attaching to the tang. This allowed the Swiss to eliminate the aluminium barrel mounting collar used in the Schmidt-Rubin series. The trigger was also redesigned.


title: K31

text: Karabiner Modell 31s are noted for their excellent accuracy and quality for a service rifle. The Swiss armed forces considered individual marksmanship to be of utmost importance. Therefore, the K. 31/Kar. 31 was made to tight tolerances and excellent overall craftsmanship.


title: K31

text: According to the Swiss Military manual for the Karabiner Modell 31 using standard issue 7.5×55mm Swiss GP 11 ball ammunition in a fixed mounting the expected accuracy of fire at a range of is (R) in the horizontal (windage) axis and (R) in the vertical (elevation) axis.


title: K31

text: R at a range means the closest 50% of the shot group will all be within a circle of the mentioned diameter at that distance. The employed circular error probable method cannot be converted and is not comparable to US military methods for determining rifle accuracy. For reference a 1 minute of arc (MOA) circle at has a diameter of and at has a diameter of . When the R results are doubled the hit probability increases to 93.7%.


title: K31

text: The Karabiner Modell 31 is noted for its straight-pull bolt action, meaning that the bolt handle is pulled directly rearward to unlock the action and eject the spent cartridge case in one motion, and then pushing the bolt handle forward again to chamber a new cartridge, cock the striker, and lock the action, rather than being manually turned and pulled back and forth, as in contemporary bolt action service rifles, like the German Karabiner 98k, or the British Lee–Enfield Rifle No. 4. A straight-pull bolt action reduces the range of motion by the shooter, with the goal of increasing the rifle's rate of fire.


title: K31

text: Unlike the previous Schmidt–Rubin series of rifles, the K. 31/Kar. 31's locking lugs lock up immediately behind the chamber. This forward positioning of the locking lugs affords several advantages. The entire action is strengthened as the lugs lock into the much thicker forward part of the receiver. Lock-up is also more precise.


title: K31

text: The cocking piece doubles as a safety and is attached at the rear of the bolt sleeve assembly and secures the firing pin. When the cocking piece ending in a cocking ring is pulled rearward and turned horizontal, the cocking piece sear can be placed in a recessed safety slot in the bolt plug. This slot is shorter than the firing slot so the firing pin cannot protrude past the face of the bolt cylinder. Any contact with the cartridge primer is thus prevented. The safe mode also prevents the action from being cycled hence preventing the bolt from accidental opening. The operating ring is quite large, making it easy to operate with gloves. When the operating ring is in the vertical position and pulled back by cycling the action or cocking it by hand the action is ready to fire.


title: K31

text: The Karabiner Modell 31 feeds from a detachable box magazine machined to match the cartridge for which the rifle was being chambered, that can hold up to 6 rifle cartridges. The magazine release button is an integral part of the magazine.


title: K31

text: For reloading the K. 31/Kar. 31 box magazine was normally not exchanged for another magazine but a unique formed phenolic resin embedded paper stripper clip with a tinned metal edge holding six rounds was used. Whereas most chargers or stripper clips only held the rounds at the end of the cartridge cases, the K. 31/Kar. 31 charger nearly covers the entire cartridge. The charger has a guide slot wide enough for a gloved thumb to force rounds down and into the magazine in one smooth motion. The chargers or stripper clips have to be manually removed before the bolt can be closed.


title: K31

text: When the last cartridge from the magazine is fired, the follower comes up automatically during cycling locking the bolt open and preventing it from closing reminding the user the K. 31/Kar. 31 needs to be reloaded.


title: K31

text: The Karabiner Modell 31 has a two-stage trigger with a noticeable long take up before the trigger engages the sear. This feature aids in preventing premature firing during stressful (combat) situations.


title: K31

text: The standard iron sights on a Karabiner Modell 31 are open sights that can be adjusted for both windage and elevation and have a sight radius of . The rear sight is graduated from in increments. The sight line can be adjusted with a front sight adjustment tool. Moving the front post horizontally results in a shift at . To adjust the average height of the point of impact 5 front posts ranging from height in increments are available. The change in impact height from one front sight to the next is at .


title: K31

text: The standard K. 31/Kar. 31 iron sight line elevation concept is somewhat unconventional and designed for center hold (point of aim = point of impact) at the and meter settings with GP11 ammunition. Starting at and more distant ranges the shooter should aim below the bottom of the target, so that the front sight's post is just out of the way. The 6 o'clock hold is intended for target shooting at , meaning the sight line is designed to let GP11 ammunition hit over the point of aim on a diameter bulls eye the Swiss military and shooting clubs used for sighting in the K. 31/Kar. 31, marksmanship training and competitions. A 6 o'clock hold is only good for a known target size at a known distance and will not hold zero without user adjustment if these factors are varied. Combined with GP11 ammunition the and settings can alternatively be used as center holds for and .


title: K31

text: As the Swiss have a militia army where soldiers sometimes keep their service rifles for a lifetime and also compete with their service rifle. Many aftermarket sights were available: Waffenfabrik Bern made the "S" and "K" (Klammer) diopter sights, Wyss makes the "W" diopter and Furter, Haemmerli and Gruenig & Elmiger made special windage and elevation fine-correctors, Sahli and many other made elevation fine correctors and these days a company by the name of Swiss Products in the United States makes a clamp-on diopter which was recently approved for use at official Swiss shooting matches.


title: K31

text: During its production run there were several modifications tested, rejected and made to the K. 31/Kar. 31.


title: K31

text: Karabiner Modell 31s were issued with slings, muzzle caps, knife-type detachable bayonets, cleaning kits and carrying pouches for stripper clips.


title: K31

text: The telescopic sights of these models were made by Kern and mounted on production Karabiner Modell 31s chosen for their accuracy offset on the left side of the receiver enabling the shooter to use the standard iron sight line.


title: K31

text: In the 1950s an elaborate modified variant of the Karabiner Modell 31 was developed for designated marksman/sniper use. This rifle was not issued as a Model 31 variant, but as the Zielfernrohr-Karabiner 55 (Zf. Kar. 55) Sniper Rifle. It featured a more powerful 3.5×23 telescopic sight made by Kern adjustable for bullet drop from in increments. The bullet drop compensation (BDC) adjustment turret is free spinning under grease friction. Like the standard K. 31/Kar. 31 iron sight line elevation concept the BDC adjustment of the telescopic sight is somewhat unconventional and designed for center hold (point of aim = point of impact) at the settings with GP11 ammunition. At more distant ranges the shooter should aim below the bottom of the target for a 6 o'clock hold, so that the reticle's post is just out of the way. The windage adjustment turret of the telescopic sight features more conventional click adjustments. Each full windage increment corresponds to a horizontal displacement of , i.e. the width of a man at (1.5 mil/1.5 ‰). The full increments are themselves subdivided into six at (0.25 mil/0.25 ‰) clicks.


title: K31

text: The Zf. Kar. 55 only has four small parts in common (the cocking piece, the firing pin, the firing pin spring, and the extractor) with the Karabiner Modell 31. The telescopic sight mounts are an integral part of the receiver. The 3.5×23 telescopic sight features an integral quick release mount that connects to the mounts on the left side of the receiver. The entire action of the Zf. Kar. 55 is tilted at an angle of approximately 15 degrees to provide room for the unimpaired loading and ejecting cartridges with the telescopic sight mounted. The tilting of the action and magazine also provided a centered position of the telescopic sight over the action and stock at the cost of widening the rifle somewhat. The barrel fitted to the Zf. Kar. 55 is heavier than the one on the Karabiner Modell 31 and is fitted with a muzzle brake. The Zf. Kar. 55 also has a half-stock with a checkered pistol grip instead of a semi-pistol grip and an underfolding integrated bipod. A total of 4,150 Zf. Kar. 55s where manufactured.


title: K31

text: The poor condition of many stocks was caused mostly by the wearing of crampons [ice-cleats that project not only from the sole but the sides of the heels] worn over hobnail boots and rifle drills that were common. The military habit of stacking rifles in threes - often in the snow - also contributes to the 'ragged' appearance of the end of the butt. Postwar beech stocks are more affected than the older walnut ones. Walnut stocks - the material of choice prior to 1946 - were treated with linseed oil and later beech stocks got a shellac protective layer that easily dissolves in alcohol for (arsenal) repairs.


title: K31

text: As of 2010, the Swiss arsenals are long sold out and the rifles now available for sale from military surplus vendors in countries around the world are ex-Swiss-civilian owned rifles. The stocks are usually in average condition, but the barrel and bolt assembly are usually in very good condition because the Swiss used a special gun grease known as "Waffenfett" instead of gun cleaning oil, and the issued ammunition was non-corrosive. Some K. 31/Kar. 31s can be found with "trooper tags" underneath the steel butt plate at the rear end of the stock, showing its former Swiss government user. Many collectors of the K. 31/Kar. 31 recovered a small tag of plasticized paper containing the military unit, name and address and pension number of the Swiss citizen to whom the rifle was issued. In some cases, collectors have used the information to contact the previous users, and have recounted the details of those encounters on a variety of collector's web forums.


title: K31

text: Karabiner Modell 31s are noted for their excellent accuracy and quality for a service rifle. The Swiss armed forces considered individual marksmanship to be of utmost importance. Therefore, the K. 31/Kar. 31 was made to tight tolerances and excellent overall craftsmanship.


title: K31

text: The Swiss Military manual for the Karabiner Modell 31 using standard issue 7.5×55mm Swiss GP 11 ball ammunition in a fixed mounting mentions the expected accuracy of fire at various ranges.


title: K31

text: The following table lists accuracy statistics for typical in service K31 rifles firing 7.5×55mm Swiss GP 11 service ammunition. The statistics were computed under the 1930s era Swiss method for determining accuracy, which is more complex than Western methods which usually involve firing a group of shots and then measuring the overall diameter of the group. The Swiss method differs in that after a group of shots is fired into the target from a machine rest hits on the outer part of the target are disregarded, while only half of the hits on the inner part of the circles are counted (50% or R), which significantly reduces the overall diameter of the groups. The vertical and horizontal measurements of the reduced groups are then used to measure accuracy. This circular error probable method used by the Swiss and other European militaries cannot be converted and is not comparable to US military methods for determining rifle accuracy. When the R results are doubled the hit probability increases to 93.7%.


title: K31

text: For reference a 1 minute of arc (MOA) circle at has a diameter of and at has a diameter of . The radius of a circle is half its diameter.


title: K31

text: In Switzerland, the Karabiner Modell 31 is like other (ex) Swiss service rifles used for target shooting matches. Recreational practice with guns is a popular form of recreation, and is encouraged by the government, particularly for the members of the militia. Typical Swiss rifle shooting "(Eidgenössisches Feldschiessen)" is done with an (ex) Swiss service rifle at a range of , prone. For this the standard iron sights can be replaced by target shooting diopter and globe sight sighting lines. In other countries the K. 31/Kar. 31 can often be used in vintage military service rifle matches. Clamp-on sighting options for competition diopter style sights and telescopic sights make it easier to mount more precise aiming means than the standard factory tangent iron sights on the receiver. Many competition shooters are able to achieve 1 MOA shooting groups with unmodified K. 31/Kar. 31s with the factory tangent iron sight line.


title: K31

text: To celebrate its introduction in the Swiss armed forces a small commemorative batch of Karabiner Modell 31s was produced 80 years later.


title: K31

text: In rare instances, the locking lugs of some K. 31/Kar. 31 rifles can develop cracks that can be visually determined by the naked eye or with the help of a loupe. Rifles with substandard locking lugs should be immediately be withdrawn from shooting and professionally repaired to prevent dangerous situations.


The 2022 United States Senate election in Maryland was held on November 8, 2022, to elect a member of the United States Senate to represent Maryland. The Democratic and Republican primaries were held on July 19, 2022.


title: 2022 United States Senate election in Maryland

text: Incumbent Democratic Senator Chris Van Hollen was first elected in 2016 with 60.9% of the vote, winning the seat of retiring incumbent Barbara Mikulski. He ran for a second term against Chris Chaffee, the Republican nominee.


title: Memory management unit

text: A memory management unit (MMU), sometimes called paged memory management unit (PMMU), is a computer hardware unit having all memory references passed through itself, primarily performing the translation of virtual memory addresses to physical addresses.


title: Memory management unit

text: An MMU effectively performs virtual memory management, handling at the same time memory protection, cache control, bus arbitration and, in simpler computer architectures (especially 8-bit systems), bank switching.


title: Memory management unit

text: Modern MMUs typically divide the virtual address space (the range of addresses used by the processor) into pages, each having a size which is a power of 2, usually a few kilobytes, but they may be much larger. The bottom bits of the address (the offset within a page) are left unchanged. The upper address bits are the virtual page numbers.


title: Memory management unit

text: Most MMUs use an in-memory table of items called a "page table", containing one "page table entry" (PTE) per page, to map virtual page numbers to physical page numbers in main memory. An associative cache of PTEs is called a translation lookaside buffer (TLB) and is used to avoid the necessity of accessing the main memory every time a virtual address is mapped. Other MMUs may have a private array of memory or registers that hold a set of page table entries. The physical page number is combined with the page offset to give the complete physical address.


title: Memory management unit

text: A PTE may also include information about whether the page has been written to (the "dirty bit"), when it was last used (the "accessed bit," for a least recently used (LRU) page replacement algorithm), what kind of processes (user mode or supervisor mode) may read and write it, and whether it should be cached.


title: Memory management unit

text: Sometimes, a PTE prohibits access to a virtual page, perhaps because no physical random-access memory (RAM) has been allocated to that virtual page. In this case, the MMU signals a page fault to the CPU. The operating system (OS) then handles the situation, perhaps by trying to find a spare frame of RAM and set up a new PTE to map it to the requested virtual address. If no RAM is free, it may be necessary to choose an existing page (known as a "victim"), using some replacement algorithm, and save it to disk (a process called "paging"). With some MMUs, there can also be a shortage of PTEs, in which case the OS will have to free one for the new mapping.


title: Memory management unit

text: The MMU may also generate illegal access error conditions or invalid page faults upon illegal or non-existing memory accesses, respectively, leading to segmentation fault or bus error conditions when handled by the operating system.


title: Memory management unit

text: In some cases, a page fault may indicate a software bug, which can be prevented by using memory protection as one of key benefits of an MMU: an operating system can use it to protect against errant programs by disallowing access to memory that a particular program should not have access to. Typically, an operating system assigns each program its own virtual address space.


title: Memory management unit

text: An MMU also mitigates the problem of fragmentation of memory. After blocks of memory have been allocated and freed, the free memory may become fragmented (discontinuous) so that the largest contiguous block of free memory may be much smaller than the total amount. With virtual memory, a contiguous range of virtual addresses can be mapped to several non-contiguous blocks of physical memory; this non-contiguous allocation is one of the benefits of paging.


title: Memory management unit

text: In some early microprocessor designs, memory management was performed by a separate integrated circuit such as the VLSI Technology VI475 (1986), the Motorola 68851 (1984) used with the Motorola 68020 CPU in the Macintosh II, or the Z8010 and Z8015 (1985) used with the Zilog Z8000 family of processors. Later microprocessors (such as the Motorola 68030 and the Zilog Z280) placed the MMU together with the CPU on the same integrated circuit, as did the Intel 80286 and later x86 microprocessors.


title: Memory management unit

text: While this article concentrates on modern MMUs, commonly based on pages, early systems used a similar concept for base-limit addressing that further developed into segmentation. Those are occasionally also present on modern architectures. The x86 architecture provided segmentation, rather than paging, in the 80286, and provides both paging and segmentation in the 80386 and later processors (although the use of segmentation is not available in 64-bit operation).


title: Memory management unit

text: Most modern systems divide memory into pages that are in size, often with the capability to use so called huge pages of or in size (often both variants are possible). Page translations are cached in a translation lookaside buffer (TLB). Some systems, mainly older RISC designs, trap into the OS when a page translation is not found in the TLB. Most systems use a hardware-based tree walker. Most systems allow the MMU to be disabled, but some disable the MMU when trapping into OS code.


title: Memory management unit

text: VAX pages are 512 bytes, which is very small. An OS may treat multiple pages as if they were a single larger page. For example, Linux on VAX groups eight pages together. Thus, the system is viewed as having pages. The VAX divides memory into four fixed-purpose regions, each in size. They are:


title: Memory management unit

text: Page tables are big linear arrays. Normally, this would be very wasteful when addresses are used at both ends of the possible range, but the page table for applications is itself stored in the kernel's paged memory. Thus, there is effectively a two-level tree, allowing applications to have sparse memory layout without wasting a lot of space on unused page table entries. The VAX MMU is notable for lacking an accessed bit. OSes which implement paging must find some way to emulate the accessed bit if they are to operate efficiently. Typically, the OS will periodically unmap pages so that page-not-present faults can be used to let the OS set an accessed bit.


title: Memory management unit

text: ARM architecture-based application processors implement an MMU defined by ARM's virtual memory system architecture. The current architecture defines PTEs for describing and pages, sections and super-sections; legacy versions also defined a tiny page. ARM uses a two-level page table if using and pages, or just a one-level page table for sections and sections.


title: Memory management unit

text: TLB updates are performed automatically by page table walking hardware. PTEs include read/write access permission based on privilege, cacheability information, an NX bit, and a non-secure bit.


title: Memory management unit

text: The IBM System/360 Model 67, which was introduced Aug. 1965, included an MMU called a dynamic address translation (DAT) box. It has the unusual feature of storing accessed and dirty bits outside of the page table (along with the four bit protection key for all S/360 processors). They refer to physical memory rather than virtual memory, and are accessed by special-purpose instructions. This reduces overhead for the OS, which would otherwise need to propagate accessed and dirty bits from the page tables to a more physically oriented data structure. This makes OS-level virtualization, later called paravirtualization, easier.


title: Memory management unit

text: Starting in August, 1972, the IBM System/370 has a similar MMU, although it initially supported only a 24-bit virtual address space rather than the 32-bit virtual address space of the System/360 Model 67. It also stores the accessed and dirty bits outside the page table. In early 1983, the System/370-XA architecture expanded the virtual address space to 31 bits, and in 2000, the 64-bit z/Architecture was introduced, with the address space expanded to 64 bits; those continue to store the accessed and dirty bits outside the page table.


title: Memory management unit

text: The DEC Alpha processor divides memory into pages. After a TLB miss, low-level firmware machine code (here called PALcode) walks a three-level tree-structured page table. Addresses are broken down as follows: 21 bits unused, 10 bits to index the root level of the tree, 10 bits to index the middle level of the tree, 10 bits to index the leaf level of the tree, and 13 bits that pass through to the physical address without modification. Full read/write/execute permission bits are supported.


title: Memory management unit

text: The MIPS architecture supports one to 64 entries in the TLB. The number of TLB entries is configurable at CPU configuration before synthesis. TLB entries are dual. Each TLB entry maps a virtual page number (VPN2) to either one of two page frame numbers (PFN0 or PFN1), depending on the least significant bit of the virtual address that is not part of the page mask. This bit and the page mask bits are not stored in the VPN2. Each TLB entry has its own page size, which can be any value from to in multiples of four. Each PFN in a TLB entry has a caching attribute, a dirty and a valid status bit. A VPN2 has a global status bit and an OS assigned ID which participates in the virtual address TLB entry match, if the global status bit is set to zero. A PFN stores the physical address without the page mask bits.


title: Memory management unit

text: A TLB refill exception is generated when there are no entries in the TLB that match the mapped virtual address. A TLB invalid exception is generated when there is a match but the entry is marked invalid. A TLB modified exception is generated when a store instruction references a mapped address and the matching entry's dirty status is not set. If a TLB exception occurs when processing a TLB exception, a double fault TLB exception, it is dispatched to its own exception handler.


title: Memory management unit

text: MIPS32 and MIPS32r2 support 32 bits of virtual address space and up to 36 bits of physical address space. MIPS64 supports up to 64 bits of virtual address space and up to 59 bits of physical address space.


title: Memory management unit

text: The original Sun 1 is a single-board computer built around the Motorola 68000 microprocessor and introduced in 1982. It includes the original Sun 1 memory management unit that provides address translation, memory protection, memory sharing and memory allocation for multiple processes running on the CPU. All access of the CPU to private on-board RAM, external Multibus memory, on-board I/O and the Multibus I/O runs through the MMU, where address translation and protection are done in a uniform fashion. The MMU is implemented in hardware on the CPU board.


title: Memory management unit

text: The MMU consists of a context register, a segment map and a page map. Virtual addresses from the CPU are translated into intermediate addresses by the segment map, which in turn are translated into physical addresses by the page map. The page size is and the segment size is which gives 16 pages per segment. Up to 16 contexts can be mapped concurrently. The maximum logical address space for a context is or The maximum physical address that can be mapped simultaneously is also


title: Memory management unit

text: The context register is important in a multitasking operating system because it allows the CPU to switch between processes without reloading all the translation state information. The 4-bit context register can switch between 16 sections of the segment map under supervisor control, which allows 16 contexts to be mapped concurrently. Each context has its own virtual address space. Sharing of virtual address space and inter-context communications can be provided by writing the same values in to the segment or page maps of different contexts. Additional contexts can be handled by treating the segment map as a context cache and replacing out-of-date contexts on a least-recently used basis.


title: Memory management unit

text: The context register makes no distinction between user and supervisor states. Interrupts and traps do not switch contexts, which requires that all valid interrupt vectors always be mapped in page 0 of context, as well as the valid supervisor stack.


title: Memory management unit

text: In PowerPC G1, G2, G3, and G4 pages are normally After a TLB miss, the standard PowerPC MMU begins two simultaneous lookups. One lookup attempts to match the address with one of four or eight data block address translation (DBAT) registers, or four or eight instruction block address translation registers (IBAT), as appropriate. The BAT registers can map linear chunks of memory as large as and are normally used by an OS to map large portions of the address space for the OS kernel's own use. If the BAT lookup succeeds, the other lookup is halted and ignored.


title: Memory management unit

text: The other lookup, not directly supported by all processors in this family, is via a so-called "inverted page table," which acts as a hashed off-chip extension of the TLB. First, the top four bits of the address are used to select one of 16 segment registers. Then 24 bits from the segment register replace those four bits, producing a 52-bit address. The use of segment registers allows multiple processes to share the same hash table.


title: Memory management unit

text: The 52-bit address is hashed, then used as an index into the off-chip table. There, a group of eight-page table entries is scanned for one that matches. If none match due to excessive hash collisions, the processor tries again with a slightly different hash function. If this, too, fails, the CPU traps into OS (with MMU disabled) so that the problem may be resolved. The OS needs to discard an entry from the hash table to make space for a new entry. The OS may generate the new entry from a more-normal tree-like page table or from per-mapping data structures which are likely to be slower and more space-efficient. Support for no-execute control is in the segment registers, leading to granularity.


title: Memory management unit

text: A major problem with this design is poor cache locality caused by the hash function. Tree-based designs avoid this by placing the page table entries for adjacent pages in adjacent locations. An operating system running on the PowerPC may minimize the size of the hash table to reduce this problem.


title: Memory management unit

text: It is also somewhat slow to remove the page table entries of a process. The OS may avoid reusing segment values to delay facing this, or it may elect to suffer the waste of memory associated with per-process hash tables. G1 chips do not search for page table entries, but they do generate the hash, with the expectation that an OS will search the standard hash table via software. The OS can write to the TLB. G2, G3, and early G4 chips use hardware to search the hash table. The latest chips allow the OS to choose either method. On chips that make this optional or do not support it at all, the OS may choose to use a tree-based page table exclusively.


title: Memory management unit

text: The x86 architecture has evolved over a very long time while maintaining full software compatibility, even for OS code. Thus, the MMU is extremely complex, with many different possible operating modes. Normal operation of the traditional 80386 CPU and its successors (IA-32) is described here.


title: Memory management unit

text: The CPU primarily divides memory into pages. Segment registers, fundamental to the older 8088 and 80286 MMU designs, are not used in modern OSes, with one major exception: access to thread-specific data for applications or CPU-specific data for OS kernels, which is done with explicit use of the FS and GS segment registers. All memory access involves a segment register, chosen according to the code being executed. The segment register acts as an index into a table, which provides an offset to be added to the virtual address. Except when using FS or GS, the OS ensures that the offset will be zero.


title: Memory management unit

text: After the offset is added, the address is masked to be no larger than 32 bits. The result may be looked up via a tree-structured page table, with the bits of the address being split as follows: 10 bits for the branch of the tree, 10 bits for the leaves of the branch, and the 12 lowest bits being directly copied to the result. Some operating systems, such as OpenBSD with its W^X feature, and Linux with the Exec Shield or PaX patches, may also limit the length of the code segment, as specified by the CS register, to disallow execution of code in modifiable regions of the address space.


title: Memory management unit

text: Minor revisions of the MMU introduced with the Pentium have allowed very large pages by skipping the bottom level of the tree (this leaves 10 bits for indexing the first level of page hierarchy with the remaining 10+12 bits being directly copied to the result). Minor revisions of the MMU introduced with the Pentium Pro introduced the physical address extension (PAE) feature, enabling 36-bit physical addresses with 2+9+9 bits for three-level page tables and 12 lowest bits being directly copied to the result. Large pages () are also available by skipping the bottom level of the tree (resulting in 2+9 bits for two-level table hierarchy and the remaining 9+12 lowest bits copied directly). In addition, the page attribute table allowed specification of cacheability by looking up a few high bits in a small on-CPU table.


title: Memory management unit

text: No-execute support was originally only provided on a per-segment basis, making it very awkward to use. More recent x86 chips provide a per-page no-execute bit in the PAE mode. The W^X, Exec Shield, and PaX mechanisms described above emulate per-page non-execute support on machines x86 processors lacking the NX bit by setting the length of the code segment, with a performance loss and a reduction in the available address space.


title: Memory management unit

text: x86-64 is a 64-bit extension of x86 that almost entirely removes segmentation in favor of the flat memory model used by almost all operating systems for the 386 or newer processors. In long mode, all segment offsets are ignored, except for the FS and GS segments. When used with pages, the page table tree has four levels instead of three.


title: Memory management unit

text: The virtual addresses are divided as follows: 16 bits unused, nine bits each for four tree levels (for a total of 36 bits), and the 12 lowest bits directly copied to the result. With pages, there are only three levels of page table, for a total of 27 bits used in paging and 21 bits of offset. Some newer CPUs also support a page with two levels of paging and of offset.


title: Memory management unit

text: CPUID can be used to determine if pages are supported. In all three cases, the bits are required to be equal to the 48th bit, or in other words, the low are sign extended to the higher bits. This is done to allow a future expansion of the addressable range, without compromising backwards compatibility. In all levels of the page table, the page table entry includes a no-execute bit.


title: Memory management unit

text: The Burroughs B5000 from 1961 was the first commercial system to support virtual memory (after the Atlas), even though it has no MMU It provides the two functions of an MMU - virtual memory addresses and memory protection - with a different architectural approach.


title: Memory management unit

text: First, in the mapping of virtual memory addresses, instead of needing an MMU, the MCP systems are descriptor-based. Each allocated memory block is given a master descriptor with the properties of the block (i.e., the size, address, and whether present in memory). When a request is made to access the block for reading or writing, the hardware checks its presence via the presence bit (pbit) in the descriptor.


title: Memory management unit

text: A pbit of 1 indicates the presence of the block. In this case, the block can be accessed via the physical address in the descriptor. If the pbit is zero, an interrupt is generated for the MCP (operating system) to make the block present. If the address field is zero, this is the first access to this block, and it is allocated (an init pbit). If the address field is non-zero, it is a disk address of the block, which has previously been rolled out, so the block is fetched from disk and the pbit is set to one and the physical memory address updated to point to the block in memory (another pbit). This makes descriptors equivalent to a page-table entry in an MMU system. System performance can be monitored through the number of pbits. Init pbits indicate initial allocations, but a high level of other pbits indicate that the system may be thrashing.


title: Memory management unit

text: All memory allocation is therefore completely automatic (one of the features of modern systems) and there is no way to allocate blocks other than this mechanism. There are no such calls as malloc or dealloc, since memory blocks are also automatically discarded. The scheme is also lazy, since a block will not be allocated until it is actually referenced. When memory is nearly full, the MCP examines the working set, trying compaction (since the system is segmented, not paged), deallocating read-only segments (such as code-segments which can be restored from their original copy) and, as a last resort, rolling dirty data segments out to disk.


title: Memory management unit

text: Another way the B5000 provides a function of a MMU is in protection. Since all accesses are via the descriptor, the hardware can check that all accesses are within bounds and, in the case of a write, that the process has write permission. The MCP system is inherently secure and thus has no need of an MMU to provide this level of memory protection. Descriptors are read only to user processes and may only be updated by the system (hardware or MCP). (Words whose tag is an odd number are read-only; descriptors have a tag of 5 and code words have a tag of 3.)


title: Memory management unit

text: Blocks can be shared between processes via copy descriptors in the process stack. Thus, some processes may have write permission, whereas others do not. A code segment is read only, thus reentrant and shared between processes. Copy descriptors contain a 20-bit address field giving index of the master descriptor in the master descriptor array. This also implements a very efficient and secure IPC mechanism. Blocks can easily be relocated, since only the master descriptor needs update when a block's status changes.


title: Memory management unit

text: The only other aspect is performance do MMU-based or non-MMU-based systems provide better performance? MCP systems may be implemented on top of standard hardware that does have an MMU (for example, a standard PC). Even if the system implementation uses the MMU in some way, this will not be at all visible at the MCP level.


title: Freaky Friday (1976 film)

text: Freaky Friday is a 1976 American fantasy-comedy film directed by Gary Nelson, with the screenplay written by Mary Rodgers based on her 1972 novel of the same name. The film stars Barbara Harris and Jodie Foster in the lead roles. John Astin, Patsy Kelly, Dick Van Patten, Sorrell Booke and Charlene Tilton are featured in supporting roles. In the film, a mother and her daughter switch their bodies, and they get a taste of each other's lives. The cause of the switch is left unexplained in this film, but occurs on Friday the 13th, when Ellen and Annabel, in different places, say about each other at the same time, "I wish I could switch places with her for just one day." Rodgers added a water skiing subplot to her screenplay.


title: Freaky Friday (1976 film)

text: "Freaky Friday" was released theatrically in the United States on January 21, 1977, by Buena Vista Distribution. The film received positive reviews from critics with praise for Foster and Harris’s performances and was a box office success, grossing $36 million on a $5 million budget. At the 34th Golden Globe Awards, it received three nominations: Best Actress – Comedy or Musical (for both Foster and Harris), and Best Original Song ("I'd Like to Be You for a Day").


title: Freaky Friday (1976 film)

text: Ellen Andrews (Barbara Harris) and her daughter, Annabel (Jodie Foster) constantly quarrel. Following a disagreement on Thursday, before Friday the 13th, Annabel leaves to join a friend at a local diner. In sync, Annabel and Ellen (who is in the family home's kitchen) both wish aloud, "I wish I could switch places with her for just one day." Their wish comes true when their bodies are switched. After a brief scene where they are shocked at seeing their new appearances, both ladies proceed as each other normally would.


title: Freaky Friday (1976 film)

text: Annabel is now a housewife, tending to laundry, car repair, grocery deliveries, carpet cleaners, dry cleaners, her housemaid, and the family Basset hound, Max. As though Annabel did not have her hands full, Bill Andrews (John Astin) coerces her to cook dinner for twenty-five people as his catered dinner party plans fell through. Annabel enlists Boris (Marc McClure), a neighbor on whom she has harbored a crush, to look after her younger brother and help make a chocolate mousse but all three manage to mess everything up, then later saving face by making everything into a smörgåsbord. Annabel does have a bright spot with her brother, Ben, such as getting to have personal discussions with him, when she picks him up from school. He tells her which qualities he envies about Annabel, and is able to share her loathing over the housemaid, who is constantly complaining about Annabel's sloppiness, and then confesses when he tried to be messy to connect with Annabel, the housemaid said he didn't know better and cleaned up after him. Plus, between all the talks, they play baseball which improves their relationship. Annabel later remorses for misjudging Ben and getting a different outlook on him.


title: Freaky Friday (1976 film)

text: Meanwhile Ellen, now a high school student, struggles with marching band, destroys her entire typing class's electric typewriters, exposes her photography class's developing film, and loses a field hockey game. However, Ellen does have one bright point, in a U.S. history class where she accurately recounts the Korean War, having lived through the 1950s as a little girl. In an effort to escape school, Ellen (as Annabel) runs to Bill's office. There, she encounters Bill's new attractive, young, and immodestly dressed secretary. Ellen attempts to intimidate the young woman by sharing how frightening "her mother" is. This effort appeared successful as the secretary adopts more modest clothing, glasses, and an unflattering hairstyle. Ellen (as Annabel) asks Bill for access to his credit card in order to make herself over as her braces were scheduled to be removed that afternoon. Bill approves and chalks up his secretary's awkward appearance to personal problems at home as her son is sick and her husband was wounded in the Vietnam War, causing Ellen to scold herself for not trusting her husband.


title: Freaky Friday (1976 film)

text: The day ends in a comical twist when the mother-daughter pair wishing a new request: to return to themselves. This does happen, although in a different manner than before. They are physically transferred, with Annabel suddenly sitting now behind the wheel of a car with Ben and Boris, with none of them knowing how to drive and attracting the attention of several squad cars. Ellen in turn finds herself water skiing as she (as Annabel) was scheduled to participate in an aquacade. Bill, who has prospective clients at the aquacade, fears unemployment as he sees Ellen flailing helplessly on skis, but her antics amuse the clients so much that Bill wins the account.


title: Freaky Friday (1976 film)

text: With a new understanding of each other's lives, mother and daughter forgive each other. Following the events of Freaky Friday, Annabel begins dating Boris. Bill is playing cards with Ellen, still trying to understand what happened. Ellen and Bill are fine with Boris taking Annabel to a pizzeria for a date, and Annabel surprises Ben by letting him tag along with them. Ben complains that he never gets to do fun stuff like his dad, who is getting ready for a business trip the following Saturday dirt biking with a Japanese motorcycle firm looking to enter the U.S. market, while Bill says Ben should be more appreciative of a worry-free childhood. Ben remarks he would love to spend one Saturday in his dad's shoes, while Bill says the same about Ben, causing Annabel and Ellen to get nervous and suggest that Bill and Ben do not want to switch places, but they simultaneously and indignantly say "Oh, yes, I do!", much to Ellen and Annabel's chagrin.


title: Freaky Friday (1976 film)

text: Neither Barbara Harris nor Jodie Foster did any actual water skiing in the film. In both cases, these scenes were achieved with the use of professional water skiers in long shot on location, and cutaway shots of the actresses in front of a rear projection effect. However, Foster did play field hockey in the film. Parts of the film were shot in Mission Bay, San Diego.


title: Freaky Friday (1976 film)

text: Richard Eder of "The New York Times" wrote, "Toward the end there are some amusing car-chase scenes. Elsewhere the humor is clotted by the feeling that the jokes are chasing the reactions, instead of the other way around." "Variety" wrote that "a promising concept" had been "bungled by a talky, repetitive screenplay and overbroad direction." Roger Ebert gave the film 2.5 stars out of 4 and wrote, "The problems resulting from the switch of identities are fairly predictable, but fun: This is one of the better recent Disney productions." Gene Siskel also gave the film 2.5 stars out of 4 and stated that the two leads "do a serviceable job with mediocre material." Kevin Thomas of the "Los Angeles Times" thought that the movie "has the stuff of a stronger, more sophisticated film but has been processed to fit into the bland, synthetic Disney formula. Even so, both Miss Harris and Miss Foster make the most of their offbeat opportunity." Gary Arnold of "The Washington Post" wrote that the film "suffers from sluggish exposition, mediocre direction and a one-closeup-after-another method of composition advertising the film's eventual retirement to the Disney TV series, but it probably salvages things with juvenile audiences by finishing fast."


title: Freaky Friday (1976 film)

text: "Freaky Friday" has had three different remakes, all produced by the Walt Disney Company: a made-for-television film in 1995 starring Shelley Long and Gaby Hoffmann, a live-action theatrical release in 2003 starring Jamie Lee Curtis and Lindsay Lohan, and a musical version for television starring Cozi Zuehlsdorff and Heidi Blickenstaff.