title: Ejaculation

text: Ejaculation usually begins during the first or second contraction of orgasm. For most men, the first ejection of semen occurs during the second contraction, while the second is typically the largest expelling 40% or more of total semen discharge. After this peak, the magnitude of semen the penis emits diminishes as the contractions begin to lessen in intensity. The muscle contractions of the orgasm can continue after ejaculation with no additional semen discharge occurring. A small sample study of seven men showed an average of 7 spurts of semen followed by an average of 10 more contractions with no semen expelled. This study also found a high correlation between number of spurts of semen and total ejaculate volume, i.e., larger semen volumes resulted from additional pulses of semen rather than larger individual spurts.


title: Ejaculation

text: Alfred Kinsey measured the distance of ejaculation, in "some hundreds" of men. In three-quarters of men tested, ejaculate "is propelled with so little force that the liquid is not carried more than a minute distance beyond the tip of the penis." In contrast to those test subjects, Kinsey noted "In other males the semen may be propelled from a matter of some inches to a foot or two, or even as far as five or six and (rarely) eight feet". Masters and Johnson report ejaculation distance to be no greater than . During the series of contractions that accompany ejaculation, semen is propelled from the urethra at , close to .


title: Ejaculation

text: Most men experience a refractory period immediately following an orgasm, during which time they are unable to achieve another erection, and a longer period again before they are capable of achieving another ejaculation. During this time a male feels a deep and often pleasurable sense of relaxation, usually felt in the groin and thighs. The duration of the refractory period varies considerably, even for a given individual. Age affects the recovery time, with younger men typically recovering faster than older men, though not universally so.


title: Ejaculation

text: Whereas some men may have refractory periods of 15 minutes or more, some men are able to experience sexual arousal immediately after ejaculation. A short recovery period may allow partners to continue sexual play relatively uninterrupted by ejaculation. Some men may experience their penis becoming hypersensitive to stimulation after ejaculation, which can make sexual stimulation unpleasant even while they may be sexually aroused.


title: Ejaculation

text: There are men who are able to achieve multiple orgasms, with or without the typical sequence of ejaculation and refractory period. Some of those men report not noticing refractory periods, or are able to maintain erection by "sustaining sexual activity with a full erection until they passed their refractory time for orgasm when they proceeded to have a second or third orgasm".


title: Ejaculation

text: The force and amount of semen that will be ejected during an ejaculation will vary widely between men and may contain between 0.1 and 10 milliliters (by way of comparison, note that a teaspoon is 5 ml and a tablespoon holds 15 ml). Adult semen volume is affected by the time that has passed since the previous ejaculation; larger semen volumes are seen with greater durations of abstinence. The duration of the stimulation leading up to the ejaculation can affect the volume. Abnormally low semen volume is known as hypospermia and abnormally high semen volume is known as hyperspermia. One of the possible underlying causes of low volume or complete lack of semen is ejaculatory duct obstruction. It is normal for the amount of semen to diminish with age.


title: Ejaculation

text: The number of sperm in an ejaculation also varies widely, depending on many factors, including the time since the last ejaculation, age, stress levels, and testosterone. Greater lengths of sexual stimulation immediately preceding ejaculation can result in higher concentrations of sperm. An unusually low sperm count, not the same as low semen volume, is known as oligospermia, and the absence of any sperm from the semen is termed azoospermia.


title: Ejaculation

text: The first ejaculation in males often occurs about 12 months after the onset of puberty, generally through masturbation or nocturnal emission (wet dreams). This first semen volume is small. The typical ejaculation over the following three months produces less than 1 ml of semen. The semen produced during early puberty is also typically clear. After ejaculation this early semen remains jellylike and, unlike semen from mature males, fails to liquefy. A summary of semen development is shown in Table 1.


title: Ejaculation

text: Most first ejaculations (90%) lack sperm. Of the few early ejaculations that do contain sperm, the majority of sperm (97%) lack motion. The remaining sperm (3%) have abnormal motion.


title: Ejaculation

text: As the male proceeds through puberty, the semen develops mature characteristics with increasing quantities of normal sperm. Semen produced 12 to 14 months after the first ejaculation liquefies after a short period of time. Within 24 months of the first ejaculation, the semen volume and the quantity and characteristics of the sperm match that of adult male semen.


title: Ejaculation

text: There is a central pattern generator in the spinal cord, made up of groups of spinal interneurons, that is involved in the rhythmic response of ejaculation. This is known as the "spinal generator for ejaculation".


title: Ejaculation

text: To map the neuronal activation of the brain during the ejaculatory response, researchers have studied the expression of c-Fos, a proto-oncogene expressed in neurons in response to stimulation by hormones and neurotransmitters. Expression of c-Fos in the following areas has been observed:


title: Ejaculation

text: Although uncommon, some men can achieve ejaculations during masturbation without any manual stimulation. Such men usually do it by tensing and flexing their abdominal and buttocks muscles along with vigorous fantasising. Others may do it by relaxing the area around the penis, which may result in harder erections especially when hyperaroused.


title: Ejaculation

text: Perineum pressing results in an ejaculation which is purposefully held back by pressing on either the perineum or the urethra to force the seminal fluid to remain inside. In such a scenario, the seminal fluid stays inside the body and goes to the bladder. Some people do this to avoid making a mess by keeping all the semen inside. As a medical condition, it is called retrograde ejaculation.


title: Ejaculation

text: For most men, no detrimental health effects have been determined from ejaculation itself or from frequent ejaculations, though sexual activity in general can have health or psychological consequences. A small fraction of men have a disease called postorgasmic illness syndrome (POIS), which causes severe muscle pain throughout the body and other symptoms immediately following ejaculation. The symptoms last for up to a week. Some doctors speculate that the frequency of POIS "in the population may be greater than has been reported in the academic literature", and that many POIS sufferers are undiagnosed.


title: Ejaculation

text: It is not clear whether frequent ejaculation has any effect on the risk of prostate cancer. Two large studies examining the issue were "Ejaculation Frequency and Subsequent Risk of Prostate Cancer" and "Sexual Factors and Prostate Cancer". These suggest that frequent ejaculation after puberty offers some reduction of the risk of prostate cancer. The US study involving 29,342 US men aged 46 to 81 years suggested that "high ejaculation frequency was related to decreased risk of total prostate cancer". An Australian study involving 1,079 men with prostate cancer and 1,259 healthy men found that "there is evidence that the more frequently men ejaculate between the ages of 20 and 50, the less likely they are to develop prostate cancer":


title: Ejaculation

text: In mammals and birds, multiple ejaculation is commonplace. During copulation, the two sides of a short-beaked echidna's penis are used sequentially. Alternating between the two sides allows for persistent stimulation to induce ejaculation without impeding the refractory period.


title: Ejaculation

text: In stallions, ejaculation is accompanied by a motion of the tail known as "tail flagging". When a male wolf ejaculates, his final pelvic thrust may be slightly prolonged. A male rhesus monkey usually ejaculates less than 15 seconds after sexual penetration. The first report and footage of spontaneous ejaculation in an aquatic mammal was recorded in a wild Indo-Pacific bottlenose dolphin near Mikura Island, Japan, in 2012.


title: Ejaculation

text: In horses, sheep, and cattle, ejaculation occurs within a few seconds, but in boars, it can last for five to thirty minutes. Ejaculation in boars is stimulated when the spiral-shaped penis interlocks with the female's cervix. A mature boar can produce of semen during one ejaculation. In llamas and alpacas, ejaculation occurs continuously during copulation.


title: Ejaculation

text: The semen of male dogs is ejaculated in three separate phases. The last phase of a male canine’s ejaculation occurs during the copulatory tie, and contains mostly prostatic fluid.


title: Alexandra Grant

text: Alexandra Annette Grant (born April 4, 1973) is an American visual artist who examines language and written texts through painting, drawing, sculpture, video, and other media. She uses language and exchanges with writers as a source for much of that work. Grant examines the process of writing and ideas based in linguistic theory as it connects to art and creates visual images inspired by text and collaborative group installations based on that process. She is based in Los Angeles.


title: Alexandra Grant

text: Grant was born in Fairview Park, Ohio. Her father was a Scottish geology professor and her mother an American political science


title: Alexandra Grant

text: professor, foreign-service diplomat, and educational administrator based in Africa and the Middle East. Her parents, who both spent time in Africa, divorced when she was young and she lived with her mother, who was based in Mexico City. In Mexico City, she attended a British school that was made up of a multi-national student body. When she was 11 years old, Grant attended a boarding school, the Thomas Jefferson School, in St. Louis, Missouri for a year. Shortly thereafter, she moved with her mother to Paris, where she attended the International School of Paris. From these experiences in various locations in Europe and the Middle East, Grant is multi-lingual, and speaks English, Spanish, and French.


title: Alexandra Grant

text: In 1990, Grant graduated High School from Phillips Exeter Academy, an exclusive private boarding school in Exeter, New Hampshire.


title: Alexandra Grant

text: In 1995, Grant graduated from Swarthmore College with a BA in history and studio art. In 2000, Grant graduated from San Francisco's California College of the Arts with an MFA in drawing and painting.


title: Alexandra Grant

text: In 2007, Grant had her first solo exhibition at the Museum of Contemporary Art (MOCA) in Los Angeles, curated by Alma Ruiz. A catalog from the exhibition features Grant's large-scale works on paper, an essay on Grant's work by Ruiz, and an essay that inspired Grant by the French writer and philosopher Hélène Cixous.


title: Alexandra Grant

text: Grant's work has been described as a "radical collaboration", that is, work made in collaboration with the text and work of other writers and artists, and is often participatory and ongoing. The longest exchange has been with the pioneering writer of hypertext fiction, Michael Joyce. The paintings and sculpture based on Joyce's texts (using them as scores or scripts to interpret rather than follow) have been the subject of at least three series: the "Ladder Quartet" (shown at MOCA in 2007), the "Six Portals" (shown at Honor Fraser gallery in 2008), and "Bodies" (shown at Honor Fraser gallery in 2010).


title: Alexandra Grant

text: In 2008 she participated in Edgar Arceneaux’s Watts House Project, a non profit group that aimed to renovate houses across the Watts Towers, in Los Angeles. Each of the households who agreed to participate in the project was appointed a team of an artist and an architect to remodel their homes. The initial plan for Grant’s “Love House” was to build a large construction of her brands’ logo (LOVE) over the house. However, years passed with no major constructions taking place to any of the houses and a dispute with the IRS and the Watts House project in general, has prevented it to come to fruition. Grant resigned from the projects’ board but is still raising funds in order to complete the “Love House”.


title: Alexandra Grant

text: In 2013, Grant collaborated on twin series of exhibitions with Cixous, based on the latter's book "Philippines". The "Forêt Intérieure/Interior Forest” exhibition first took place at 18th Street Arts Center in Santa Monica, and at Mains d’Oeuvres in Saint-Ouen, France. Participants joined Grant in creating large-scale drawings of Cixous's novel, which touched on many themes including telepathy in Cixous and the work of Jacques Derrida and Sigmund Freud. Grant and Cixous spoke about their telepathic relationship in 2013 as part of a conversation from Mains d’Oeuvres to Nottingham Contemporary in 2016. 18th Street Arts Center published the “Forêt Intérieure/Interior Forest” to thank the many participants in the project, a catalog which includes photographs of both exhibitions, and essays by Cixous, Grant, curator Pilar Tompkins Rivas, Robert Nashak, and a transcription of Grant's 2013 conversation with Cixous.


title: Alexandra Grant

text: In 2013, Grant continued this work in the series called “Century of the Self". The first exhibition was “Drawn to Language" at USC's The Fisher Museum in 2013, followed by a show at Lora Reynold's Gallery in Austin, TX in 2014, at the 2015 Venice Biennial in an exhibition called “We Must Risk Delight: 20 Artists from Los Angeles” and in a two-person exhibition with Steve Roden at the Pasadena Museum of California Art that was called “These Carnations Defy Language.” These works were inspired by the documentary film "Century of the Self" by BBC documentarian Adam Curtis.


title: Alexandra Grant

text: In 2015, Grant exhibited her work in a painting called “Antigone 3000” inspired by the Greek myth, and specifically a phrase in Sophocles's play where Antigone confronts her uncle Creon—the king—and says, “I was born to love not to hate.” Works from Antigone 3000 have been shown at the Barnsdall Art Center, when Grant won the City of Los Angeles Mid-Career Artist Award (COLA) in 2015 and most recently in 2017 at the Los Angeles County Museum of Art (LACMA) as part of the exhibition “L.A. Exuberance: Recent Gifts by Artists.”


title: Alexandra Grant

text: In 2017, Grant wrote the text for "Antigone is me" with her sister, Florence Grant, which is meant to capture the ancient Greek myth Antigone in a contemporary scene. The exhibit was a community-based project installation held at The Eastern Star Gallery at The Archer School for Girls in Los Angeles.


title: Alexandra Grant

text: Grant has worked as a professor. From 2009 to 2011, she was an adjunct professor at Art Center College of Design (Pasadena, CA). In 2010, Grant taught an MFA seminar at Cal State Northridge and from 2013 to 2014 was a mentor in the Pacific Northwest College of Art's Distance MFA program. In 2015, Grant was an MFA program mentor at Syracuse University, and co-taught a course with Isabelle Lutterodt at Ashesi University in Accra, Ghana.


title: Alexandra Grant

text: In 2015, as part of a residency at the Bemis Center for Contemporary Art in Omaha, Nebraska, Grant directed a documentary film called "Taking Lena Home". The film was about returning a stolen tombstone to rural Nebraska.


title: Alexandra Grant

text: In 2009, Grant met actor Keanu Reeves at a social event. This led to "Ode to Happiness", published by Gerhard Steidl in early 2011, Grant's first collaboration with Reeves. It was Grant's first artist book and Reeves's first book as a writer.


title: Alexandra Grant

text: In 2016, Grant and Reeves reunited for their second collaboration, "Shadows", a book and suite of photographic images printed by Steidl in Germany. The photographs were exhibited at ACME Gallery in Los Angeles, and Ochi Gallery in Sun Valley, ID. As part of the release of the book, Grant did a collaboration with artist Alia Raza for "Issue" magazine that featured fashion and shadows.


title: Alexandra Grant

text: In 2017 Grant, alongside designer Jessica Fleischmann and Keanu Reeves, established a small publishing company called X Artists Books, sometimes abbreviated XAB. In November 2019, Grant and Reeves appeared as a couple on the red carpet of the LACMA Art + Film Gala, prompting media coverage of their romantic relationship. Grant's friend Jennifer Tilly said they had been dating "for several years". Grant and Reeves had already been photographed as a couple in Switzerland attending the UNAIDS gala in June 2016, and several other times afterward.


title: Golden ratio

text: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities formula_2 and formula_3 with formula_4,


title: Golden ratio

text: where the Greek letter phi ( or formula_5) denotes the golden ratio. The constant formula_6 satisfies the quadratic equation formula_7 and is an irrational number with a value of


title: Golden ratio

text: The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.


title: Golden ratio

text: Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of formula_6—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.


title: Golden ratio

text: Some 20th-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing it to be aesthetically pleasing. These uses often appear in the form of a golden rectangle.


title: Golden ratio

text: One method for finding formula_6's closed form starts with the left fraction. Simplifying the fraction and substituting the reciprocal formula_13,


title: Golden ratio

text: Because formula_6 is a ratio between positive quantities, formula_6 is necessarily the positive root. The negative root is in fact the negative inverse formula_17, which shares many properties with the golden ratio.


title: Golden ratio

text: Ancient Greek mathematicians first studied the golden ratio because of its frequent appearance in geometry; the division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. According to one story, 5th-century BC mathematician Hippasus discovered that the golden ratio was neither a whole number nor a fraction (an irrational number), surprising Pythagoreans. Euclid's "Elements" () provides several propositions and their proofs employing the golden ratio, and contains its first known definition which proceeds as follows:


title: Golden ratio

text: The golden ratio was studied peripherally over the next millennium. Abu Kamil (c. 850–930) employed it in his geometric calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry problems but did not observe that it was connected to the Fibonacci numbers.


title: Golden ratio

text: Luca Pacioli named his book "Divina proportione" (1509) after the ratio; the book, largely plagiarized from Piero della Francesca, explored its properties including its appearance in some of the Platonic solids. Leonardo da Vinci, who illustrated Pacioli's book, called the ratio the "sectio aurea" ('golden section'). Though it is often said that Pacioli advocated the golden ratio's application to yield pleasing, harmonious proportions, Livio points out that the interpretation has been traced to an error in 1799, and that Pacioli actually advocated the Vitruvian system of rational proportions. Pacioli also saw Catholic religious significance in the ratio, which led to his work's title. 16th-century mathematicians such as Rafael Bombelli solved geometric problems using the ratio.


title: Golden ratio

text: German mathematician Simon Jacob (d. 1564) noted that consecutive Fibonacci numbers converge to the golden ratio; this was rediscovered by Johannes Kepler in 1608. The first known decimal approximation of the (inverse) golden ratio was stated as "about formula_18" in 1597 by Michael Maestlin of the University of Tübingen in a letter to Kepler, his former student. The same year, Kepler wrote to Maestlin of the Kepler triangle, which combines the golden ratio with the Pythagorean theorem. Kepler said of these:


title: Golden ratio

text: 18th-century mathematicians Abraham de Moivre, Nicolaus I Bernoulli, and Leonhard Euler used a golden ratio-based formula which finds the value of a Fibonacci number based on its placement in the sequence; in 1843, this was rediscovered by Jacques Philippe Marie Binet, for whom it was named "Binet's formula". Martin Ohm first used the German term "goldener Schnitt" ('golden section') to describe the ratio in 1835. James Sully used the equivalent English term in 1875.


title: Golden ratio

text: By 1910, inventor Mark Barr began using the Greek letter Phi as a symbol for the golden ratio. It has also been represented by tau the first letter of the ancient Greek τομή ('cut' or 'section').


title: Golden ratio

text: The zome construction system, developed by Steve Baer in the late 1960s, is based on the symmetry system of the icosahedron/dodecahedron, and uses the golden ratio ubiquitously. Between 1973 and 1974, Roger Penrose developed Penrose tiling, a pattern related to the golden ratio both in the ratio of areas of its two rhombic tiles and in their relative frequency within the pattern. This gained in interest after Dan Shechtman's Nobel-winning 1982 discovery of quasicrystals with icosahedral symmetry, which were soon afterward explained through analogies to the Penrose tiling.


title: Golden ratio

text: If we call the whole formula_19 and the longer part formula_20 then the second statement above becomes


title: Golden ratio

text: To say that the golden ratio formula_6 is rational means that formula_6 is a fraction formula_23 where formula_19 and formula_25 are integers. We may take formula_23 to be in lowest terms and formula_19 and formula_25 to be positive. But if formula_23 is in lowest terms, then the equally valued formula_30 is in still lower terms. That is a contradiction that follows from the assumption that formula_6 is rational.


title: Golden ratio

text: Another short proof – perhaps more commonly known – of the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. If formula_32 is rational, then formula_33 is also rational, which is a contradiction if it is already known that the square root of all non-square natural numbers are irrational.


title: Golden ratio

text: The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial


title: Golden ratio

text: which has roots formula_36 and formula_37 As the root of a quadratic polynomial, the golden ratio is a constructible number.


title: Golden ratio

text: The absolute value of this quantity corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, formula_39).


title: Golden ratio

text: The conjugate and the defining quadratic polynomial relationship lead to decimal values that have their fractional part in common with formula_6:


title: Golden ratio

text: The sequence of powers of formula_6 contains these values formula_42 formula_43 formula_44 formula_45 more generally,


title: Golden ratio

text: As a result, one can easily decompose any power of formula_6 into a multiple of formula_6 and a constant. The multiple and the constant are always adjacent Fibonacci numbers. This leads to another property of the positive powers of formula_6:


title: Golden ratio

text: The formula formula_51 can be expanded recursively to obtain a continued fraction for the golden ratio:


title: Golden ratio

text: The convergents of these continued fractions formula_52 formula_52 formula_54 formula_55 formula_56 formula_57 ... or formula_58 formula_59 formula_60 formula_61 formula_62 are ratios of successive Fibonacci numbers. The consistently small terms in its continued fraction explain why the approximants converge so slowly. This makes the golden ratio an extreme case of the Hurwitz inequality for Diophantine approximations, which states that for every irrational formula_63, there are infinitely many distinct fractions formula_64 such that,


title: Golden ratio

text: This means that the constant formula_66 cannot be improved without excluding the golden ratio. It is, in fact, the smallest number that must be excluded to generate closer approximations of such Lagrange numbers.


title: Golden ratio

text: Fibonacci numbers and Lucas numbers have an intricate relationship with the golden ratio. In the Fibonacci sequence, each number is equal to the sum of the preceding two, starting with the base sequence formula_69:


title: Golden ratio

text: The sequence of Lucas numbers (not to be confused with the generalized Lucas sequences, of which this is part) is like the Fibonacci sequence, in-which each term is the sum of the previous two, however instead starts with formula_70:


title: Golden ratio

text: Exceptionally, the golden ratio is equal to the limit of the ratios of successive terms in the Fibonacci sequence and sequence of Lucas numbers:


title: Golden ratio

text: In other words, if a Fibonacci and Lucas number is divided by its immediate predecessor in the sequence, the quotient approximates formula_6.


title: Golden ratio

text: These approximations are alternately lower and higher than formula_74 and converge to formula_6 as the Fibonacci and Lucas numbers increase.


title: Golden ratio

text: Combining both formulas above, one obtains a formula for formula_76 that involves both Fibonacci and Lucas numbers:


title: Golden ratio

text: Between Fibonacci and Lucas numbers one can deduce formula_77 which simplifies to express the limit of the quotient of Lucas numbers by Fibonacci numbers as equal to the square root of five:


title: Golden ratio

text: Consecutive Fibonacci numbers can also be used to obtain a similar formula for the golden ratio, here by infinite summation:


title: Golden ratio

text: In particular, the powers of formula_6 themselves round to Lucas numbers (in order, except for the first two powers, formula_85 and formula_6, are in reverse order):


title: Golden ratio

text: Rooted in their interconnecting relationship with the golden ratio is the notion that the sum of "third" consecutive Fibonacci numbers equals a Lucas number, that is formula_88; and, importantly, that formula_89.


title: Golden ratio

text: Both the Fibonacci sequence and the sequence of Lucas numbers can be used to generate approximate forms of the golden spiral (which is a special form of a logarithmic spiral) using quarter-circles with radii from these sequences, differing only slightly from the "true" golden logarithmic spiral. "Fibonacci spiral" is generally the term used for spirals that approximate golden spirals using Fibonacci number-sequenced squares and quarter-circles.


title: Golden ratio

text: The golden ratio features prominently in geometry. For example, it is intrinsically involved in the internal symmetry of the pentagon, and extends to form part of the coordinates of the vertices of a regular dodecahedron, as well as those of a 5-cell. It features in the Kepler triangle and Penrose tilings too, as well as in various other polytopes.


title: Golden ratio

text: Application examples you can see in the articles Pentagon with a given side length, Decagon with given circumcircle and Decagon with a given side length.


title: Golden ratio

text: Both of the above displayed different algorithms produce geometric constructions that determine two aligned line segments where the ratio of the longer one to the shorter one is the golden ratio.


title: Golden ratio

text: When two angles that make a full circle have measures in the golden ratio, the smaller is called the "golden angle", with measure formula_123


title: Golden ratio

text: This angle occurs in patterns of plant growth as the optimal spacing of leaf shoots around plant stems so that successive leaves do not block sunlight from the leaves below them.


title: Golden ratio

text: Logarithmic spirals are self-similar spirals where distances covered per turn are in geometric progression. Importantly, isosceles golden triangles can be encased by a golden logarithmic spiral, such that successive turns of a spiral generate new golden triangles inside. This special case of logarithmic spirals is called the "golden spiral", and it exhibits continuous growth in golden ratio. That is, for every formula_125 turn, there is a growth factor of formula_6. As mentioned above, these "golden spirals" can be approximated by quarter-circles generated from Fibonacci and Lucas number-sized squares that are tiled together. In their exact form, they can be described by the polar equation with formula_127:


title: Golden ratio

text: Golden spirals can be symmetrically placed inside pentagons and pentagrams as well, such that fractal copies of the underlying geometry are reproduced at all scales.


title: Golden ratio

text: George Odom found a construction for formula_6 involving an equilateral triangle: if an equilateral triangle is inscribed in a circle and the line segment joining the midpoints of two sides is produced to intersect the circle in either of two points, then these three points are in golden proportion.


title: Golden ratio

text: The "Kepler triangle", named after Johannes Kepler, is the unique right triangle with sides in geometric progression:


title: Golden ratio

text: The Kepler triangle can also be understood as the right triangle formed by three squares whose areas are also in golden geometric progression formula_135.


title: Golden ratio

text: Fittingly, the Pythagorean means for formula_136 are precisely formula_137, formula_6, and formula_139. It is from these ratios that we are able to geometrically express the fundamental defining quadratic polynomial for formula_6 with the Pythagorean theorem; that is, formula_7.


title: Golden ratio

text: The inradius of an isosceles triangle is greatest when the triangle is composed of two mirror Kepler triangles, such that their bases lie on the same line. Also, the isosceles triangle of given perimeter with the largest possible semicircle is one from two mirrored Kepler triangles.


title: Golden ratio

text: A "golden triangle" is characterized as an isosceles formula_143 with the property that bisecting the angle formula_144 produces new acute and obtuse isosceles triangles formula_145 and formula_146 that are similar to the original, as well as in leg to base length ratios of formula_147 and formula_148, respectively.


title: Golden ratio

text: The acute isosceles triangle is sometimes called a "sublime triangle", and the ratio of its base to its equal-length sides is formula_6. Its apex angle formula_150 is equal to:


title: Golden ratio

text: Both base angles of the isosceles golden triangle equal formula_151 degrees each, since the sum of the angles of a triangle must equal formula_152 degrees. It is the only triangle to have its three angles in formula_153 ratio. A regular pentagram contains five acute sublime triangles, and a regular decagon contains ten, as each two vertices connected to the center form acute golden triangles.


title: Golden ratio

text: The obtuse isosceles triangle is sometimes called a "golden gnomon", and the ratio of its base to its other sides is the reciprocal of the golden ratio, formula_154. The measure of its apex angle formula_155 is:


title: Golden ratio

text: Its two base angles equal formula_156 each. It is the only triangle whose internal angles are in formula_157 ratio. Its base angles, being equal to formula_156, are the same measure as that of the acute golden triangle's apex angle. Five golden gnomons can be created from adjacent sides of a pentagon whose non-coincident vertices are joined by a diagonal of the pentagon.


title: Golden ratio

text: Appropriately, the ratio of the area of the obtuse golden gnomon to that of the acute sublime triangle is in formula_159 golden ratio. Bisecting a base angle inside a sublime triangle produces a golden gnomon, and another a sublime triangle. Bisecting the apex angle of a golden gnomon in formula_160 ratio produces two new golden triangles, too. Golden triangles that are decomposed further like this into pairs of isosceles and obtuse golden triangles are known as "Robinson triangles."


title: Golden ratio

text: The golden ratio proportions the adjacent side lengths of a "golden rectangle" in formula_159 ratio. Stacking golden rectangles produces golden rectangles anew, and removing or adding squares from golden rectangles leaves rectangles still proportioned in formula_6 ratio. They can be generated by "golden spirals", through successive Fibonacci and Lucas number-sized squares and quarter circles. They feature prominently in the icosahedron as well as in the dodecahedron (see section below for more detail).


title: Golden ratio

text: A "golden rhombus" is a rhombus whose diagonals are in proportion to the golden ratio, most commonly formula_159. For a rhombus of such proportions, its acute angle and obtuse angles are:


title: Golden ratio

text: The lengths of its short and long diagonals formula_164 and formula_165, in terms of side length formula_2 are:


title: Golden ratio

text: These geometric values can be calculated from their Cartesian coordinates, which also can be given using formulas involving formula_6. The coordinates of the dodecahedron are displayed on the figure above, while those of the icosahedron are the cyclic permutations of:


title: Golden ratio

text: Sets of three golden rectangles intersect perpendicularly inside dodecahedra and icosahedra, forming Borromean rings. In dodecahedra, pairs of opposing vertices in golden rectangles meet the centers of pentagonal faces, and in icosahedra, they meet at its vertices. In all, the three golden rectangles contain formula_172 vertices of the icosahedron, or equivalently, intersect the centers of formula_172 of the dodecahedron's faces.


title: Golden ratio

text: A cube can be inscribed in a regular dodecahedron, with some of the diagonals of the pentagonal faces of the dodecahedron serving as the cube's edges; therefore, the edge lengths are in the golden ratio. The cube's volume is formula_174 times that of the dodecahedron's. In fact, golden rectangles inside a dodecahedron are in golden proportions to an inscribed cube, such that edges of a cube and the long edges of a golden rectangle are themselves in formula_175 ratio. On the other hand, the octahedron, which is the dual polyhedron of the cube, can inscribe an icosahedron, such that an icosahedron's formula_172 vertices touch the formula_172 edges of an octahedron at points that divide its edges in golden ratio.


title: Golden ratio

text: Other polyhedra are related to the dodecahedron and icosahedron or their symmetries, and therefore have corresponding relations to the golden ratio. These include the compound of five cubes, compound of five octahedra, compound of five tetrahedra, the compound of ten tetrahedra, rhombic triacontahedron, icosidodecahedron, truncated icosahedron, truncated dodecahedron, and rhombicosidodecahedron, rhombic enneacontahedron, and Kepler-Poinsot polyhedra, and rhombic hexecontahedron. In four dimensions, the dodecahedron and icosahedron appear as faces of the 120-cell and 600-cell, which again have dimensions related to the golden ratio.


title: Golden ratio

text: The golden ratio's "decimal expansion" can be calculated via root-finding methods, such as Newton's method or Halley's method, on the equation formula_178 or on formula_179 (to compute formula_66 first). The time needed to compute formula_19 digits of the golden ratio using Newton's method is essentially formula_182, where formula_183 is the time complexity of multiplying two formula_19-digit numbers. This is considerably faster than known algorithms for formula_185 and formula_186. An easily programmed alternative using only integer arithmetic is to calculate two large consecutive Fibonacci numbers and divide them. The ratio of Fibonacci numbers formula_187 and formula_188 each over formula_189 digits, yields over formula_190 significant digits of the golden ratio. The decimal expansion of the golden ratio formula_6 has been calculated to an accuracy of ten trillion digits.


title: Golden ratio

text: The golden ratio and inverse golden ratio formula_192 have a set of symmetries that preserve and interrelate them. They are both preserved by the fractional linear transformations formula_193 – this fact corresponds to the identity and the definition quadratic equation.


title: Golden ratio

text: Further, they are interchanged by the three maps formula_194 – they are reciprocals, symmetric about formula_195 and (projectively) symmetric about formula_196 More deeply, these maps form a subgroup of the modular group formula_197 isomorphic to the symmetric group on formula_198 letters, formula_199 corresponding to the stabilizer of the set formula_200 of formula_198 standard points on the projective line, and the symmetries correspond to the quotient map formula_202 – the subgroup formula_203 consisting of the identity and the formula_198-cycles, in cycle notation formula_205 fixes the two numbers, while the formula_206-cycles formula_207 interchange these, thus realizing the map.


title: Golden ratio

text: In the complex plane, the fifth roots of unity formula_208 (for an integer formula_209) satisfying formula_210 are the vertices of a pentagon. They do not form a ring of quadratic integers, however the sum of any fifth root of unity and its complex conjugate, formula_211 "is" a quadratic integer, an element of formula_212 Specifically,


title: Golden ratio

text: For the gamma function formula_214, the only solutions to the equation formula_215 are formula_216 and formula_217.


title: Golden ratio

text: When the golden ratio is used as the base of a numeral system (see golden ratio base, sometimes dubbed "phinary" or formula_6"-nary"), quadratic integers in the ring formula_219 – that is, numbers of the form formula_220 for formula_221 – have terminating representations, but rational fractions have non-terminating representations.


title: Golden ratio

text: The golden ratio also appears in hyperbolic geometry, as the maximum distance from a point on one side of an ideal triangle to the closer of the other two sides: this distance, the side length of the equilateral triangle formed by the points of tangency of a circle inscribed within the ideal triangle, is formula_222


title: Golden ratio

text: where formula_224 and formula_225 in the continued fraction should be evaluated as formula_226. The function formula_227 is invariant under formula_228, a congruence subgroup of the modular group. Also for positive real numbers formula_229 and formula_230 then


title: Golden ratio

text: The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."


title: Golden ratio

text: Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's "Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture.


title: Golden ratio

text: In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. Le Corbusier's 1927 Villa Stein in Garches exemplified the Modulor system's application. The villa's rectangular ground plan, elevation, and inner structure closely approximate golden rectangles.


title: Golden ratio

text: Another Swiss architect, Mario Botta, bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio, the golden ratio is the proportion between the central section and the side sections of the house.


title: Golden ratio

text: Leonardo da Vinci's illustrations of polyhedra in Pacioli's "Divina proportione" have led some to speculate that he incorporated the golden ratio in his paintings. But the suggestion that his "Mona Lisa", for example, employs golden ratio proportions, is not supported by Leonardo's own writings. Similarly, although Leonardo's "Vitruvian Man" is often shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.


title: Golden ratio

text: Salvador Dalí, influenced by the works of Matila Ghyka, explicitly used the golden ratio in his masterpiece, "The Sacrament of the Last Supper". The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.


title: Golden ratio

text: A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is formula_232 with averages for individual artists ranging from formula_233 (Goya) to formula_234 (Bellini). On the other hand, Pablo Tosto listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and formula_235 proportions, and others with proportions like formula_236 formula_237 formula_238 and formula_239


title: Golden ratio

text: There was a time when deviations from the truly beautiful page proportions formula_240 formula_241 and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter.


title: Golden ratio

text: According to some sources, the golden ratio is used in everyday design, for example in the proportions of playing cards, postcards, posters, light switch plates, and widescreen televisions.


title: Golden ratio

text: The aspect ratio (width to height ratio) of the flag of Togo was intended to be the golden ratio, according to its designer.


title: Golden ratio

text: Ernő Lendvai analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale, though other music scholars reject that analysis. French composer Erik Satie used the golden ratio in several of his pieces, including "Sonneries de la Rose+Croix". The golden ratio is also apparent in the organization of the sections in the music of Debussy's "Reflets dans l'eau (Reflections in Water)", from "Images" (1st series, 1905), in which "the sequence of keys is marked out by the intervals and and the main climax sits at the phi position".


title: Golden ratio

text: The musicologist Roy Howat has observed that the formal boundaries of Debussy's "La Mer" correspond exactly to the golden section. Trezise finds the intrinsic evidence "remarkable", but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.


title: Golden ratio

text: Music theorists including Hans Zender and Heinz Bohlen have experimented with the 833 cents scale, a musical scale based on using the golden ratio as its fundamental musical interval. When measured in cents, a logarithmic scale for musical intervals, the golden ratio is approximately 833.09 cents.


title: Golden ratio

text: Johannes Kepler wrote that "the image of man and woman stems from the divine proportion. In my opinion, the propagation of plants and the progenitive acts of animals are in the same ratio".


title: Golden ratio

text: The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argued from these patterns in nature that the golden ratio was a universal law. Zeising wrote in 1854 of a universal orthogenetic law of "striving for beauty and completeness in the realms of both nature and art".


title: Golden ratio

text: However, some have argued that many apparent manifestations of the golden ratio in nature, especially in regard to animal dimensions, are fictitious.


title: Golden ratio

text: The quasi-one-dimensional Ising ferromagnet CoNbO (cobalt niobate) has 8 predicted excitation states (with E symmetry), that when probed with neutron scattering, showed its lowest two were in golden ratio. Specifically, these quantum phase transitions during spin excitation, which occur at near absolute zero temperature, showed pairs of kinks in its ordered-phase to spin-flips in its paramagnetic phase; revealing, just below its critical field, a spin dynamics with sharp modes at low energies approaching the golden mean.


title: Golden ratio

text: There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution (see, for example, "Thomson problem" or "Tammes problem"). However, a useful approximation results from dividing the sphere into parallel bands of equal surface area and placing one node in each band at longitudes spaced by a golden section of the circle, i.e. formula_242 This method was used to arrange the 1500 mirrors of the student-participatory satellite Starshine-3.


title: Golden ratio

text: The Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu) has been analyzed by pyramidologists as having a doubled Kepler triangle as its cross-section. If this theory were true, the golden ratio would describe the ratio of distances from the midpoint of one of the sides of the pyramid to its apex, and from the same midpoint to the center of the pyramid's base. However, imprecision in measurement caused in part by the removal of the outer surface of the pyramid makes it impossible to distinguish this theory from other numerical theories of the proportions of the pyramid, based on pi or on whole-number ratios. The consensus of modern scholars is that this pyramid's proportions are not based on the golden ratio, because such a basis would be inconsistent both with what is known about Egyptian mathematics from the time of construction of the pyramid, and with Egyptian theories of architecture and proportion used in their other works.


title: Golden ratio

text: The Parthenon's façade (c. 432 BC) as well as elements of its façade and elsewhere are said by some to be circumscribed by golden rectangles. Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, Keith Devlin says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation." Midhat J. Gazalé affirms that "It was not until Euclid ... that the golden ratio's mathematical properties were studied."


title: Golden ratio

text: From measurements of 15 temples, 18 monumental tombs, 8 sarcophagi, and 58 grave stelae from the fifth century BC to the second century AD, one researcher concluded that the golden ratio was totally absent from Greek architecture of the classical fifth century BC, and almost absent during the following six centuries.


title: Golden ratio

text: Later sources like Vitruvius (first century BC) exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.


title: Golden ratio

text: The Section d'Or ('Golden Section') was a collective of painters, sculptors, poets and critics associated with Cubism and Orphism. Active from 1911 to around 1914, they adopted the name both to highlight that Cubism represented the continuation of a grand tradition, rather than being an isolated movement, and in homage to the mathematical harmony associated with Georges Seurat. (Several authors have claimed that Seurat employed the golden ratio in his paintings, but Seurat’s writings and paintings suggest that he employed simple whole-number ratios and any approximation of the golden ratio was coincidental.) The Cubists observed in its harmonies, geometric structuring of motion and form, "the primacy of idea over nature", "an absolute scientific clarity of conception". However, despite this general interest in mathematical harmony, whether the paintings featured in the celebrated 1912 "Salon de la Section d'Or" exhibition used the golden ratio in any compositions is more difficult to determine. Livio, for example, claims that they did not, and Marcel Duchamp said as much in an interview. On the other hand, an analysis suggests that Juan Gris made use of the golden ratio in composing works that were likely, but not definitively, shown at the exhibition. Art historian Daniel Robbins has argued that in addition to referencing the mathematical term, the exhibition's name also refers to the earlier "Bandeaux d'Or" group, with which Albert Gleizes and other former members of the Abbaye de Créteil had been involved.


title: Golden ratio

text: Piet Mondrian has been said to have used the golden section extensively in his geometrical paintings, though other experts (including critic Yve-Alain Bois) have discredited these claims.


title: Sofia Coppola

text: Sofia Carmina Coppola (; born May 14, 1971) is an American filmmaker and actress. The youngest child and only daughter of filmmakers Eleanor and Francis Ford Coppola, she made her film debut as an infant in her father's acclaimed crime drama film "The Godfather" (1972). Coppola later appeared in several music videos, as well as a supporting role in "Peggy Sue Got Married" (1986). Coppola then portrayed Mary Corleone, the daughter of Michael Corleone, in "The Godfather Part III" (1990). She then turned her attention to filmmaking.


title: Sofia Coppola

text: Coppola made her feature-length directorial debut with the coming-of-age drama "The Virgin Suicides" (1999). It was the first of her collaborations with actress Kirsten Dunst. In 2004, Coppola received the Academy Award for Best Original Screenplay for the comedy-drama "Lost in Translation" and became the third woman to be nominated for an Academy Award for Best Director. In 2006, Coppola directed the historical drama "Marie Antoinette", starring Dunst as the title character. In 2010, with the drama "Somewhere", Coppola became the first American woman (and fourth American filmmaker) to win the Golden Lion, the top prize at the Venice Film Festival. In 2013, she directed the satirical crime film "The Bling Ring", based on the crime ring of the same name which drew from the Vanity Fair article "The Suspects Wore Louboutins" by Nancy Jo Sales about the real group of burglarizing teens who were "motivated by vanity and worship." The film premiered at the Cannes Film Festival.


title: Sofia Coppola

text: In 2015, Coppola released the Christmas musical comedy special "A Very Murray Christmas", starring Bill Murray, on Netflix. It earned her a nomination for the Primetime Emmy Award for Outstanding Television Movie. At the 2017 Cannes Film Festival, she won Best Director for her work on the drama film "The Beguiled", becoming the second woman in the festival's history to win the award. Her latest film, "On the Rocks", received a limited theatrical release in October 2020 by A24 as well as a streaming release on Apple TV+.


title: Sofia Coppola

text: Coppola was born in New York City on May 14, 1971, the youngest child and only daughter of documentarian Eleanor ("née" Neil) and filmmaker Francis Ford Coppola. She is of Italian descent (Lucanian and Neapolitan) by her father's side and was raised on her parents' farm in Rutherford, California. Coppola graduated from St. Helena High School in 1989. She later attended Mills College and the California Institute of the Arts. At 15, Coppola interned with Chanel. After dropping out of college, Coppola started a clothing line called Milkfed, which is now sold exclusively in Japan. Among her extensive Hollywood family are her aunt Talia Shire, and her first cousins Nicolas Cage and Jason Schwartzman. Coppola had many varying interests growing up, including fashion, photography, music, and design, and did not initially intend to become a filmmaker. However, after making her first short film "Lick the Star" in 1998, she realized it "brought together all the things [she] loved," and decided to continue her directing pursuits.


title: Sofia Coppola

text: Coppola's acting career, marked by frequent criticisms of nepotism and negative reviews, began while she was an infant, as she made background appearances in seven of her father's films. The best known of these is her appearance in "The Godfather" as the infant Michael Francis Rizzi, in the baptism scene. Coppola also acted in her father's films "The Outsiders" (1983), in a scene where Matt Dillon, Tommy Howell, and Ralph Macchio are eating at a Dairy Queen; "Rumble Fish" (1983); "The Cotton Club" (1984); and "Peggy Sue Got Married" (1986), in which she portrayed Kathleen Turner's sister Nancy. "Frankenweenie" (1984) was the first film Coppola performed in that was not associated with her father; however, it often goes unnoted due to her stage name "Domino", which she adopted at the time because she thought it was glamorous. A short film entitled "Life Without Zoe" (1989), released as part of a tripartite anthology film "New York Stories", was co-written by a teenage Coppola and her father; her father also directed the film.


title: Sofia Coppola

text: During the nineties, she appeared in several music videos, including the ones for Sonic Youth's song "Mildred Pierce" from the Goo album, "Sometimes Salvation" by The Black Crowes, and The Chemical Brothers' "Elektrobank", directed by her then partner Spike Jonze (who also appears in the video).


title: Sofia Coppola

text: Coppola returned to her father's "Godfather" trilogy in both the second and third "Godfather" films, playing an immigrant child in "The Godfather Part II" and playing Michael Corleone's daughter in "The Godfather Part III" after the originally-cast actress, Winona Ryder, dropped out of the film at the last minute due to nervous exhaustion. It has been suggested that Coppola's performance in "The Godfather Part III" damaged Francis Ford Coppola's career and ruined Sofia's before it had even begun. Coppola has said that she never really wanted to act and only did it to help out when her father asked her to. It has also been suggested that Sofia's role in the film may have contributed to its box office performance, which started strongly and then went into decline. Coppola herself worried that she had only been given the role because she was the director's daughter, and the role placed a strain on her during the time of shooting that her mother observed in a series of diaries she wrote for "Vogue" during the filming. Coppola later stated that she was not hurt by the criticism from her work in the film because she never especially wanted an acting career.


title: Sofia Coppola

text: After she was critically panned for her performance in "The Godfather Part III" (for which she was named "Worst Supporting Actress" and "Worst New Star" at the 1990 Golden Raspberry Awards), Coppola largely ended her acting career; however, she did appear in the independent film "Inside Monkey Zetterland" (1992), as well as in the backgrounds of films by her friends and family (for example, she appeared as Saché, one of Queen Padmé Amidala's five handmaidens, in George Lucas' 1999 film ""). Coppola also appeared in several 1990s music videos: The Black Crowes' "Sometimes Salvation"; Sonic Youth's "Mildred Pierce"; Madonna's "Deeper and Deeper"; The Chemical Brothers' "Elektrobank", which was directed by her then-husband Spike Jonze; and later Phoenix's "Funky Squaredance".


title: Sofia Coppola

text: In 2022, Coppola guest starred as herself with her husband Thomas Mars and fellow director Jim Jarmusch in a 2022 episode of the horror comedy series "What We Do in the Shadows".


title: Sofia Coppola

text: Coppola's first short film was "Lick the Star" (1998). It played many times on the Independent Film Channel. She made her feature film directing debut with "The Virgin Suicides" (1999); it received critical acclaim upon its premiere in North America at the 2000 Sundance Film Festival and was released later that year.


title: Sofia Coppola

text: Coppola's second feature was "Lost in Translation" (2003). Coppola won the Academy Award for her original screenplay and three Golden Globe Awards including Best Picture Musical or Comedy. After Lina Wertmüller and Jane Campion, Coppola became the third female director to be nominated for an Academy Award for Directing and the second to win the Original Screenplay award, after Campion in 1994 (Wertmüller was also nominated). Her win for the best original screenplay in 2003 made her a third-generation Oscar winner. Coppola was the second woman, after Edith Head, to be nominated for three Oscars in one night. In 2004, Coppola was invited to join the Academy of Motion Picture Arts and Sciences.


title: Sofia Coppola

text: Her third film was the biopic "Marie Antoinette" (2006), adapted from the biography by British historian Antonia Fraser. Kirsten Dunst plays the title character, who marries King Louis XVI, played by Jason Schwartzman, Coppola's cousin. It debuted at the 2006 Cannes Film Festival where, despite boos in the audience, it received a standing ovation. Though critics were divided at the time of its release, it has since received more critical acclaim in the years that followed.


title: Sofia Coppola

text: Coppola's fourth film was "Somewhere" (2010), filmed at Chateau Marmont. The plot focuses on a "bad boy" actor Marco (portrayed by Stephen Dorff) who is forced to reevaluate his life when his daughter Cleo (played by Elle Fanning) arrives unexpectedly. The relationship between Marco and Cleo was loosely based on Coppola's own relationship with her father. The film won the prestigious Golden Lion at the Venice Film Festival. In November 2010, Coppola was interviewed by Joel Coen, who professed his admiration of her work, at the DGA screening of "Somewhere" in New York City.


title: Sofia Coppola

text: Coppola's next film, "The Bling Ring" (2013), was based on actual events centered around the Bling Ring, a group of California teenagers who burgled the homes of several celebrities over 2008 and 2009, stealing around $3 million in cash and belongings. Emma Watson, Taissa Farmiga, Leslie Mann, Israel Broussard, Katie Chang, and Claire Julien starred in the film, which opened the "Un Certain Regard" section of the 2013 Cannes Film Festival.


title: Sofia Coppola

text: An announcement in mid-December 2013 stated that American Zoetrope had successfully attained the screen rights for the memoir "Fairyland: A Memoir of My Father" and that Coppola would adapt the book with Andrew Durham. Coppola would also produce the film with her brother Roman.


title: Sofia Coppola

text: In March 2014, it was reported that Coppola was in negotiations to direct a live-action adaptation of "The Little Mermaid" from a script by Caroline Thompson. Coppola wanted to shoot her version underwater, and although she later admitted that such a prospect was unrealistic, test footage was shot. In June 2015, it was announced Coppola had dropped out of the film due to creative differences.


title: Sofia Coppola

text: Coppola collaborated again with her "Lost in Translation" star Bill Murray on "A Very Murray Christmas", which starred Murray and was co-written by herself, Murray and Mitch Glazer. The film, an homage to classic Christmas-themed variety shows, was released in December 2015 on Netflix.


title: Sofia Coppola

text: Coppola directed "The Beguiled" (2017), a remake of the 1971 eponymous Southern Gothic film, starring Nicole Kidman, Elle Fanning, and Kirsten Dunst. The film premiered at the 2017 Cannes Film Festival, where Coppola became the second woman (and the first American woman) to win the Best Director award.


title: Sofia Coppola

text: Coppola again worked with Bill Murray on the film", On the Rocks", starring Murray and Rashida Jones.


title: Sofia Coppola

text: Coppola was first drawn to the story after reading the book by Jeffrey Eugenides in 1995, at the recommendation of musician Thurston Moore. Coppola said she felt the novel's author understood the teenage experience. She has also said that if not for the book, she may not have had a career in film. Specifically, Coppola has highlighted the representation of teenagers "lazing around," a situation she connected with but felt was not seen very much in films in any relatable way. The story's theme of loss was a personal connection for Coppola in light of the 1986 death of her oldest brother in a boating accident, though she stated that she did not immediately realize this connection. Coppola secured the rights to the novel without her father's help, and adapted the screenplay herself. The low-budget film drew praise from critics, and represented the point at which Coppola broke out of her father's shadow as a filmmaker in her own right. She credits the start of her career to the Cannes festival after the film premiered there.


title: Sofia Coppola

text: Coppola shot "Lost in Translation" in 27 days, with a small crew, working without permits. Scenes were filmed impromptu on the street, while scenes shot at the Park Hyatt Hotel allowed the crew to use its corridors between two and three in the morning without disturbing guests.


title: Sofia Coppola

text: The film received positive reception and acclaim, as well as controversy due the film's usage "of Japan as an exotic and bizarre landscape for its American protagonists". The group Asian Mediawatch lobbied against the film's Academy Award nominations, stating "The film has no meaningful Japanese roles, nor is there any significant dialogue between the main characters and the Japanese. Such portrayals perpetuate negative stereotypes and attitudes that are harmful to Asian Americans in the US, where a significant minority of Americans already have negative attitudes towards Asians." Coppola responded to these allegations in an interview for "The Independent", "I can see why people might think that, but I know I'm not racist. I think if everything's based on truth, you can make fun, have a little laugh, but also be respectful of a culture. I just love Tokyo, and I'm not mean-spirited...Even on our daily call sheets, they would mix up the 'rs' and the 'ls' – all that was from experience, it's not made up. I guess someone has misunderstood my intentions. It bugs me, because I know I'm not racist."


title: Sofia Coppola

text: "Marie Antoinette" was shot on location at the Château de Versailles. Coppola herself has claimed that she was initially drawn towards the character of Marie Antoinette as an innocent and caring character who found herself in a situation outside of her control, and that rather than creating a historical representation, she wanted to create a more intimate look into the world of the heroine. The film's style is not that of a traditional biopic, and instead utilizes "hit songs and incongruous dialogue".


title: Sofia Coppola

text: "Somewhere" depicts a newly famous actor (Stephen Dorff) recuperating from a minor injury whose wealth, fame, and professional experiences cannot allevaite the existential crisis he is experiencing, as he is forced to care for his 11-year-old daughter in the absence of his wife. The film premiered at the 67th Venice International Film Festival, and opened in the rest of Italy, on September 3, 2010. The festival jury unanimously awarded the film the Golden Lion prize for the best overall film. Quentin Tarantino, president of the jury, said the film "grew and grew in our hearts, in our minds, in our affections" after the first screening. The film would continue to receive critical acclaim, especially from notable film critic Roger Ebert of the "Chicago Sun-Times" who praised the detail in the portrait of Johnny Marco, writing, "Coppola is a fascinating director. She sees, and we see exactly what she sees. There is little attempt here to observe a plot. All the attention is on the handful of characters, on Johnny."


title: Sofia Coppola

text: "The Bling Ring" premiered at the 2013 Cannes Film Festival. It was inspired by a "Vanity Fair" feature on the real-life criminals depicted in the film, whom Coppola described as "products of our growing reality TV culture". The film received generally positive reviews, with many praising its style and performances, while some felt that the film glamorized the crimes in the story and failed to make an assertive message about them through the narrative; "Coppola neither makes a case for her characters nor places them inside of some kind of moral or critical framework; they simply pass through the frame, listing off name brands and staring at their phones,".


title: Sofia Coppola

text: The film is based on the 1966 book of the same name by author Thomas P. Cullinan about a wounded Union soldier in a Mississippi seminary during the American Civil War, and was made for under $10 million. The film exhibited elements of the thriller genre, another departure for Coppola.


title: Sofia Coppola

text: Coppola cited her intrigue with the South as part of the story's intrigue. Coppola has said that she "wanted the film to represent an exaggerated version of all the ways women were traditionally raised there just to be lovely and cater to men—the manners of that whole world, and how they change when the men go away". Coppola has cited "Gone with the Wind" as her inspiration for creating a film that was relatable despite its position within a different era.


title: Sofia Coppola

text: The film faced a wave of controversy and division, including accusations of 'whitewashing' the original story after she chose to both remove the supporting role of a black female slave from the film, as well as to choose Kirsten Dunst to portray a character who was biracial in the original novel. Coppola also faced criticism for minimizing the story of the people experiencing actual hardship in favor of depicting, albeit authentically, the lavish lifestyle of her protagonists, thus minimizing the importance of a weighty topic. Coppola responded to these allegations by citing the presence of young girls among her moviegoing audience. "The Beguiled" is not the only of Coppola's films to be accused of exposing the sociocultural affordances of her own childhood.


title: Sofia Coppola

text: Coppola described her version of the film as a reinterpretation, rather than a remake, of Don Siegel's 1971 adaption of the same book. Coppola wanted to tell the story of the male soldier entering into a classically southern and female environment from the point of view of the women and represent what that was like for them. Coppola thought that the earlier version made the characters out to be crazy caricatures and did not allow the viewer to know them.


title: Sofia Coppola

text: While some critics claim that Coppola intended "The Beguiled" as a feminist work, Coppola explained that she is not in favor of that labeling. Though she has said she is happy if others see the film in this way, she sees it as a film, rather, that possesses a female perspective—an important distinction. "The Beguiled" was also made as a contrast to "The Bling Ring", and Coppola has explained that


title: Sofia Coppola

text: she needed to correct that film's harsh Los Angeles aesthetic with something more beautiful and poetic.


title: Sofia Coppola

text: Coppola's next film, "On the Rocks", tells the story of a daughter and father, played by Rashida Jones and Bill Murray respectively, as they explore New York together in an attempt to mend their fractured relationship. It was released in a limited theatrical release on October 2, 2020, by A24 and was released for digital streaming on October 23, 2020, by Apple TV+. It received positive reviews from critics, who praised Coppola's screenplay and direction, and noted it as lighter than her previous films. Some critics stated that the film "isn't destined to achieve the same kind of iconic status as some of Coppola's previous work".


title: Sofia Coppola

text: Coppola arrived at a career in filmmaking with a background by means of acting, modeling, and design, all of which have influenced her directorial work. Her background in fashion, especially, has played a large part in the aesthetic tones of her films and has heightened the roles of design and style in her work. Her upbringing in a Hollywood family has also greatly influenced her work, as well as her public reception and image, and she has always had to fight accusations surrounding her background of privilege. After both winning an Oscar for "Lost in Translation" and showing "The Beguiled", Coppola was accused by some critics of displaying the social and cultural privileges of her own childhood.


title: Sofia Coppola

text: Coppola has described some of her influences as coming from her own work, with each film actively influencing the next. She points to Jeffrey Eugenides's book "The Virgin Suicides", which was the inspiration for her first film of the same name, as the reason for her career in film.


title: Sofia Coppola

text: Coppola has had to deal with sexism in the industry, and her quintessentially feminine work has been dismissed as decorative and insubstantial. Coppola has said that she is proud of the more "girly" aspects of her work and that she feels that she has a feminine point of view that she is happy to project. She has cited her upbringing around so many strong men as a possible reason for her strong connection to femininity. She has been open about her experiences with sexism in the industry and has cited them as a reason she favors working in the independent realm. Coppola has also said that big budget productions hinder her creative freedom, and so she prefers to work on films she can control. She has also criticized big studio production for its focus on business rather than art.


title: Sofia Coppola

text: Coppola has cited her own perceptions of gaps in the film industry as her own inspiration, explaining that she has always made the films that she herself would have wanted to see as a younger person. She has described this younger demographic of girls as deprived of high-quality videography and as disrespected as an audience. She has also said that she likes making films for a young audience because she perceives them as smarter and more sophisticated than they are often given credit for.


title: Sofia Coppola

text: Zoetrope, Francis Ford Coppola's production company, has backed all of her films. Her family ties have proven to hold both pros and cons, which she has articulated. Though she learned from her father and is proud of her family, she has said she is happy to have carved her own way. Coppola has also said that she is aware of her hard work and is grateful for her film education and that her connections in the film industry were helpful because of the lack of female directors. She said that she did what she could and is confident that her work is her own. After Francis Ford Coppola did not assist her in securing the rights to the Jeffrey Eugenides novel "The Virgin Suicides", which her 1999 film was based on, much of the criticism surrounding her familial benefits subsided. Coppola usually involves her father in her projects. She has said that she likes being independent but respects him and his suggestions, though in the end always makes the choice she feels is right for a given movie. Coppola professed a love for being behind the camera and is not upset by the divisive reactions to some of her films. She has said that she "would rather do something that some people really connect to and some people reject" and that she never wants to make something that is just mediocre.


title: Sofia Coppola

text: Reviews of Coppola's works often included "implied, gendered language" which undermine the body of the critics' arguments, as argued by Todd Kennedy in his article for "Film Criticism" titled "Off with Hollywood's Head: Sofia Coppola as Feminine Auteur". Kennedy cites multiple reviews of Coppola's work which rely upon allegations of her work as "sugarcoated" and flippant; "[the] implication is that Coppola 1) as a woman, only has the ability to make films because of her economic privilege, 2) only has whatever talent she does possess because of her all-powerful director/father, and 3) because her movies are feminine, can only produce pretty films that 'lack depth'".


title: Sofia Coppola

text: Her style of films is described as "slow-moving portraits with bittersweet emotional palettes". Coppola likes to use visuals to convey what the characters are feeling at any given moment. Coppola's films often deal with melancholy stories with a dreamy aesthetic. Her films' aesthetics are influenced by her background in fashion with floral motifs and female beauty at the forefront of the films' set design and mise-en-scene. Coppola's films' focus on protagonists in life transitions and crises in their lives. Her characters feel stranded in their environments and alone even in the midst of other people. Visually portraying the experiences of these characters is one of Coppola's specialties.


title: Sofia Coppola

text: Coppola's films often deal with themes of loneliness, wealth, privilege, isolation, youth, femininity, and adolescence in America. Her works utilize the "feminine gaze" and demonstrate a knowledge of feminist film theory, such as Laura Mulvey's "Visual Pleasure and Narrative Cinema".


title: Sofia Coppola

text: In the mid-1990s, Coppola and her best friend Zoe Cassavetes helmed the short-lived series Comedy Central series "Hi Octane", which spotlit performers in underground music. The show was cancelled after four episodes.


title: Sofia Coppola

text: In December 2008, Coppola's first commercial premiered during an episode of "Gossip Girl". The advertisement she directed for the Christian Dior fragrance "Miss Dior Chérie", shot in France with model Maryna Linchuk, was very well received and continues to be popular on YouTube.


title: Sofia Coppola

text: In May 2020, it was announced Coppola would write and direct an adaptation of "The Custom of the Country" by Edith Wharton for Apple TV+.


title: Sofia Coppola

text: At the beginning of the 1990s, Coppola was often featured in girl-oriented magazines like "Seventeen" and "YM". In 1994, she co-founded the clothing line "Milk Fed" in Japan, with her friend Stephanie Hayman in cooperation with Sonic Youth's Kim Gordon. In 2001, the fashion designer Marc Jacobs chose the actress/director to be the "face" of his house's fragrance. The campaign involved photographs of Coppola shot by photographer Jürgen Teller. The July 2013 issue of "Elle" featured photographs shot by Coppola of Paris Hilton at Hilton's Beverly Hills mansion (Both model and house appear in "The Bling Ring").


title: Sofia Coppola

text: In 2017, before Coppola started pre-production on "The Beguiled", she was asked by Italian state broadcaster Rai Com from All'Opera to direct their latest production of "La Traviata. La traviata" is a three act opera by Giuseppe Verdi set to an Italian libretto by Francesca Maria Piave. This Coppola-directed production was filmed for broadcast in Germany and France by Arte/ZDF, using multiple state-of-the art 4k cameras and up to 100 microphones. Coppola said in an interview she "could not turn down the project" with designer and fashion icon Valentino Garavani designing the costumes for this 15 show run of "La Traviata" (2017). Discussing her modern take on this classic story Coppola says "I wanted to bring out the personal side of the French courtesan, the party girl used to the social scene. It's a very feminine world that I love".


title: Sofia Coppola

text: This was the first stage production Coppola directed. Coppola discusses how Valentino "really motivated me to take a chance and do something that was scary for me and very unfamiliar," and promised a "traditional" production that could nevertheless be appreciated by those who are not opera connoisseurs. Rome Opera House Director Carlo Fuortes said in an interview ticket sales had exceeded 1.2 million euros (1.35 million dollars), a record for the establishment.


title: Sofia Coppola

text: All fifteen shows nearly sold out before opening night. It was the biggest box office success since the Teatro dell'Opera Di Roma opened in 1880.


title: Sofia Coppola

text: In 1992, Coppola met director Spike Jonze; they married in 1999 and divorced in 2003. In an official statement, Coppola's publicist explained that the divorce decision was reached "with sadness". It is widely believed that the main character's husband in "Lost in Translation" is based on Jonze, as Coppola stated after the film's release, "There are elements of Spike there, elements of experiences."


title: Sofia Coppola

text: From 2003 to 2005 Coppola dated filmmaker Quentin Tarantino. They have remained friends since their separation.


title: Sofia Coppola

text: Coppola married musician Thomas Mars on August 27, 2011, at Palazzo Margherita in Bernalda, Italy. They met while producing the soundtrack to "The Virgin Suicides". They have two daughters: Romy (born November 28, 2006), whose name is an homage to Coppola's brother Roman, and Cosima (born May 2010).


title: Sofia Coppola

text: Coppola has maintained a low public profile for her family, aiming for her daughters' lives to be unaffected by her career and travel. When asked if her choices as a parent to keep her children out of the spotlight is a result of her own upbringing, Coppola has explained that she never wants her children to be jaded.


title: Sofia Coppola

text: Coppola's first awards were as an actress winning two Golden Raspberry Awards for her performance in her father's film, "The Godfather Part III" for Worst Supporting Actress and Worst New Star.


title: Sofia Coppola

text: Coppola was nominated for three Academy Awards for her film "Lost in Translation" (2003), in the categories of Best Picture, Best Director, and Best Original Screenplay. She would go on to win for Best Original Screenplay but lost the other two nominations to Peter Jackson's "". Coppola's nomination for Best Director made her the first American woman to be nominated in that category, and the third woman overall, after Lina Wertmüller and Jane Campion. In 2010, Kathryn Bigelow became the fourth woman to be nominated, and the first to win the award. Coppola, however, remains the youngest woman to be nominated in the Best Director category. Coppola's win for Best Original Screenplay (along with her cousin Nicolas Cage's 1996 win for Best Actor) resulted in her family's becoming the second three-generation Oscar-winning family, her grandfather Carmine Coppola and her father Francis Ford Coppola having previously won Oscars. The first family to achieve this feat was the Huston family, for wins by: Walter, John, and Anjelica. For her work on "Lost in Translation", Coppola also won the Best Motion Picture and Best Screenplay Golden Globes, in addition to receiving three BAFTA Award nominations.


title: Sofia Coppola

text: On September 11, 2010, "Somewhere" won the Golden Lion, the top prize at the Venice International Film Festival. Coppola is the first American woman to win the award.


title: Sofia Coppola

text: On May 28, 2017, Coppola was awarded the Best Director Award at the Cannes Film Festival for "The Beguiled", making her the second ever woman (and the first American woman) to win the award.


title: Manhattan Project

text: The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the U.S. Army Corps of Engineers. Nuclear physicist Robert Oppenheimer was the director of the Los Alamos Laboratory that designed the actual bombs. The Army component of the project was designated the Manhattan District as its first headquarters were in Manhattan; the placename gradually superseded the official codename, Development of Substitute Materials, for the entire project. Along the way, the project absorbed its earlier British counterpart, Tube Alloys. The Manhattan Project began modestly in 1939, but grew to employ more than 130,000 people and cost nearly US$2 billion (equivalent to about $ billion in ). Over 90 percent of the cost was for building factories and to produce fissile material, with less than 10 percent for development and production of the weapons. Research and production took place at more than thirty sites across the United States, the United Kingdom, and Canada.


title: Manhattan Project

text: The project led to the development of two types of atomic bombs, both developed concurrently, during the war: a relatively simple gun-type fission weapon and a more complex implosion-type nuclear weapon. The Thin Man gun-type design proved impractical to use with plutonium, so a simpler gun-type called Little Boy was developed that used uranium-235, an isotope that makes up only 0.7 percent of natural uranium. Because it is chemically identical to the most common isotope, uranium-238, and has almost the same mass, separating the two proved difficult. Three methods were employed for uranium enrichment: electromagnetic, gaseous and thermal. Scientists conducted most of this work at the Clinton Engineer Works at Oak Ridge, Tennessee.


title: Manhattan Project

text: In parallel with the work on uranium was an effort to produce plutonium, which researchers at the University of California, Berkeley, discovered in 1940. After the feasibility of the world's first artificial nuclear reactor, the Chicago Pile-1, was demonstrated in 1942 at the Metallurgical Laboratory in the University of Chicago, the project designed the X-10 Graphite Reactor at Oak Ridge and the production reactors at the Hanford Site in Washington state, in which uranium was irradiated and transmuted into plutonium. The plutonium was then chemically separated from the uranium, using the bismuth phosphate process. The Fat Man plutonium implosion-type weapon was developed in a concerted design and development effort by the Los Alamos Laboratory.


title: Manhattan Project

text: The project was also charged with gathering intelligence on the German nuclear weapon project. Through Operation Alsos, Manhattan Project personnel served in Europe, sometimes behind enemy lines, where they gathered nuclear materials and documents, and rounded up German scientists. Despite the Manhattan Project's tight security, Soviet atomic spies successfully penetrated the program.


title: Manhattan Project

text: The first nuclear device ever detonated was an implosion-type bomb during the Trinity test, conducted at New Mexico's Alamogordo Bombing and Gunnery Range on 16 July 1945. Little Boy and Fat Man bombs were used a month later in the atomic bombings of Hiroshima and Nagasaki, respectively, with Manhattan Project personnel serving as bomb assembly technicians and weaponeers on the attack aircraft. In the immediate postwar years, the Manhattan Project conducted weapons testing at Bikini Atoll as part of Operation Crossroads, developed new weapons, promoted the development of the network of national laboratories, supported medical research into radiology and laid the foundations for the nuclear navy. It maintained control over American atomic weapons research and production until the formation of the United States Atomic Energy Commission in January 1947.


title: Manhattan Project

text: The discovery of nuclear fission by German chemists Otto Hahn and Fritz Strassmann in 1938, and its theoretical explanation by Lise Meitner and Otto Frisch, made the development of an atomic bomb a theoretical possibility. There were fears that a German atomic bomb project would develop one first, especially among scientists who were refugees from Nazi Germany and other fascist countries. In August 1939, Hungarian-born physicists Leo Szilard and Eugene Wigner drafted the Einstein–Szilard letter, which warned of the potential development of "extremely powerful bombs of a new type". It urged the United States to take steps to acquire stockpiles of uranium ore and accelerate the research of Enrico Fermi and others into nuclear chain reactions. They had it signed by Albert Einstein and delivered to President Franklin D. Roosevelt. Roosevelt called on Lyman Briggs of the National Bureau of Standards to head the Advisory Committee on Uranium to investigate the issues raised by the letter. Briggs held a meeting on 21 October 1939, which was attended by Szilárd, Wigner and Edward Teller. The committee reported back to Roosevelt in November that uranium "would provide a possible source of bombs with a destructiveness vastly greater than anything now known."


title: Manhattan Project

text: In February 1940, the U.S. Navy awarded Columbia University $6,000 in funding, most of which Enrico Fermi and Szilard spent on purchasing graphite. A team of Columbia professors including Fermi, Szilard, Eugene T. Booth and John Dunning created the first nuclear fission reaction in the Americas, verifying the work of Hahn and Strassmann. The same team subsequently built a series of prototype nuclear reactors (or "piles" as Fermi called them) in Pupin Hall at Columbia, but were not yet able to achieve a chain reaction. The Advisory Committee on Uranium became the National Defense Research Committee (NDRC) on Uranium when that organization was formed on 27 June 1940. Briggs proposed spending $167,000 on research into uranium, particularly the uranium-235 isotope, and plutonium, which was discovered in 1940 at the University of California. On 28 June 1941, Roosevelt signed Executive Order 8807, which created the Office of Scientific Research and Development (OSRD), with Vannevar Bush as its director. The office was empowered to engage in large engineering projects in addition to research. The NDRC Committee on Uranium became the S-1 Section of the OSRD; the word "uranium" was dropped for security reasons.


title: Manhattan Project

text: In Britain, Frisch and Rudolf Peierls at the University of Birmingham had made a breakthrough investigating the critical mass of uranium-235 in June 1939. Their calculations indicated that it was within an order of magnitude of , which was small enough to be carried by a bomber of the day. Their March 1940 Frisch–Peierls memorandum initiated the British atomic bomb project and its MAUD Committee, which unanimously recommended pursuing the development of an atomic bomb. In July 1940, Britain had offered to give the United States access to its scientific research, and the Tizard Mission's John Cockcroft briefed American scientists on British developments. He discovered that the American project was smaller than the British, and not as far advanced.


title: Manhattan Project

text: As part of the scientific exchange, the MAUD Committee's findings were conveyed to the United States. One of its members, the Australian physicist Mark Oliphant, flew to the United States in late August 1941 and discovered that data provided by the MAUD Committee had not reached key American physicists. Oliphant then set out to find out why the committee's findings were apparently being ignored. He met with the Uranium Committee and visited Berkeley, California, where he spoke persuasively to Ernest O. Lawrence. Lawrence was sufficiently impressed to commence his own research into uranium. He in turn spoke to James B. Conant, Arthur H. Compton and George B. Pegram. Oliphant's mission was therefore a success; key American physicists were now aware of the potential power of an atomic bomb.


title: Manhattan Project

text: On 9 October 1941, President Roosevelt approved the atomic program after he convened a meeting with Vannevar Bush and Vice President Henry A. Wallace. To control the program, he created a Top Policy Group consisting of himself—although he never attended a meeting—Wallace, Bush, Conant, Secretary of War Henry L. Stimson, and the Chief of Staff of the Army, General George C. Marshall. Roosevelt chose the Army to run the project rather than the Navy, because the Army had more experience with management of large-scale construction projects. He also agreed to coordinate the effort with that of the British, and on 11 October he sent a message to Prime Minister Winston Churchill, suggesting that they correspond on atomic matters.


title: Manhattan Project

text: The S-1 Committee held its meeting on 18 December 1941 "pervaded by an atmosphere of enthusiasm and urgency" in the wake of the attack on Pearl Harbor and the subsequent United States declaration of war upon Japan and then on Germany. Work was proceeding on three different techniques for isotope separation to separate uranium-235 from the more abundant uranium-238. Lawrence and his team at the University of California investigated electromagnetic separation, while Eger Murphree and Jesse Wakefield Beams's team looked into gaseous diffusion at Columbia University, and Philip Abelson directed research into thermal diffusion at the Carnegie Institution of Washington and later the Naval Research Laboratory. Murphree was also the head of an unsuccessful separation project using gas centrifuges.


title: Manhattan Project

text: Meanwhile, there were two lines of research into nuclear reactor technology, with Harold Urey continuing research into heavy water at Columbia, while Arthur Compton brought the scientists working under his supervision from Columbia, California and Princeton University to join his team at the University of Chicago, where he organized the Metallurgical Laboratory in early 1942 to study plutonium and reactors using graphite as a neutron moderator. Briggs, Compton, Lawrence, Murphree, and Urey met on 23 May 1942, to finalize the S-1 Committee recommendations, which called for all five technologies to be pursued. This was approved by Bush, Conant, and Brigadier General Wilhelm D. Styer, the chief of staff of Major General Brehon B. Somervell's Services of Supply, who had been designated the Army's representative on nuclear matters. Bush and Conant then took the recommendation to the Top Policy Group with a budget proposal for $54 million for construction by the United States Army Corps of Engineers, $31 million for research and development by OSRD and $5 million for contingencies in fiscal year 1943. The Top Policy Group in turn sent it on 17 June 1942, to the President, who approved it by writing "OK FDR" on the document.


title: Manhattan Project

text: Compton asked theoretical physicist J. Robert Oppenheimer of the University of California to take over research into fast neutron calculations—the key to calculations of critical mass and weapon detonation—from Gregory Breit, who had quit on 18 May 1942 because of concerns over lax operational security. John H. Manley, a physicist at the Metallurgical Laboratory, was assigned to assist Oppenheimer by contacting and coordinating experimental physics groups scattered across the country. Oppenheimer and Robert Serber of the University of Illinois examined the problems of neutron diffusion—how neutrons moved in a nuclear chain reaction—and hydrodynamics—how the explosion produced by a chain reaction might behave. To review this work and the general theory of fission reactions, Oppenheimer and Fermi convened meetings at the University of Chicago in June and at the University of California in July 1942 with theoretical physicists Hans Bethe, John Van Vleck, Edward Teller, Emil Konopinski, Robert Serber, Stan Frankel, and Eldred C. (Carlyle) Nelson, the latter three former students of Oppenheimer, and experimental physicists Emilio Segrè, Felix Bloch, Franco Rasetti, John Henry Manley, and Edwin McMillan. They tentatively confirmed that a fission bomb was theoretically possible.


title: Manhattan Project

text: There were still many unknown factors. The properties of pure uranium-235 were relatively unknown, as were those of plutonium, an element that had only been discovered in February 1941 by Glenn Seaborg and his team. The scientists at the (July 1942) Berkeley conference envisioned creating plutonium in nuclear reactors where uranium-238 atoms absorbed neutrons that had been emitted from fissioning uranium-235 atoms. At this point no reactor had been built, and only tiny quantities of plutonium were available from cyclotrons at institutions such as Washington University in St. Louis. Even by December 1943, only two milligrams had been produced. There were many ways of arranging the fissile material into a critical mass. The simplest was shooting a "cylindrical plug" into a sphere of "active material" with a "tamper"—dense material that would focus neutrons inward and keep the reacting mass together to increase its efficiency. They also explored designs involving spheroids, a primitive form of "implosion" suggested by Richard C. Tolman, and the possibility of autocatalytic methods, which would increase the efficiency of the bomb as it exploded.


title: Manhattan Project

text: Considering the idea of the fission bomb theoretically settled—at least until more experimental data was available—the 1942 Berkeley conference then turned in a different direction. Edward Teller pushed for discussion of a more powerful bomb: the "super", now usually referred to as a "hydrogen bomb", which would use the explosive force of a detonating fission bomb to ignite a nuclear fusion reaction in deuterium and tritium. Teller proposed scheme after scheme, but Bethe refused each one. The fusion idea was put aside to concentrate on producing fission bombs. Teller also raised the speculative possibility that an atomic bomb might "ignite" the atmosphere because of a hypothetical fusion reaction of nitrogen nuclei. Bethe calculated that it could not happen, and a report co-authored by Teller showed that "no self-propagating chain of nuclear reactions is likely to be started." In Serber's account, Oppenheimer mentioned the possibility of this scenario to Arthur Compton, who "didn't have enough sense to shut up about it. It somehow got into a document that went to Washington" and was "never laid to rest".


title: Manhattan Project

text: The Chief of Engineers, Major General Eugene Reybold, selected Colonel James C. Marshall to head the Army's part of the project in June 1942. Marshall created a liaison office in Washington, D.C., but established his temporary headquarters on the 18th floor of 270 Broadway in New York, where he could draw on administrative support from the Corps of Engineers' North Atlantic Division. It was close to the Manhattan office of Stone & Webster, the principal project contractor, and to Columbia University. He had permission to draw on his former command, the Syracuse District, for staff, and he started with Lieutenant Colonel Kenneth Nichols, who became his deputy.


title: Manhattan Project

text: Because most of his task involved construction, Marshall worked in cooperation with the head of the Corps of Engineers Construction Division, Major General Thomas M. Robbins, and his deputy, Colonel Leslie Groves. Reybold, Somervell, and Styer decided to call the project "Development of Substitute Materials", but Groves felt that this would draw attention. Since engineer districts normally carried the name of the city where they were located, Marshall and Groves agreed to name the Army's component of the project the Manhattan District. This became official on 13 August when Reybold issued the order creating the new district. Informally, it was known as the Manhattan Engineer District, or MED. Unlike other districts, it had no geographic boundaries, and Marshall had the authority of a division engineer. Development of Substitute Materials remained as the official codename of the project as a whole, but was supplanted over time by "Manhattan".