question: when did the us take over wake island

answers: July 4, 1898

answers: January 17, 1899

title: Wake Island (film)

text: Japan. A map is shown with a voiceover giving a brief history of the United States military on Wake Island to November 1941. U.S. Marine Corps Major Geoffrey Caton departs Pearl Harbor naval base in Hawaii aboard the Pan American Clipper to take over command on Wake Island. A military contractor, Mr. McClosky, is also going there. The two clash during the flight. Upon arrival, Caton inspects the island and identifies Privates Randall and Doyle as troublemakers. He has them dig a large slit trench by hand. McClosky has a construction contract for large trenches and living quarters, and drives

title: Wake Island

text: a C-17 transport plane. At the same time, the THAAD system and the destroyer both launched missiles to intercept a medium-range ballistic missile, launched by a second C-17. Wake Island has no permanent inhabitants and access is restricted. However, as of 2017, there are about 100 Air Force personnel and American and Thai contractors resident any given time. On June 24, 1972, the United States Air Force assumed responsibility for the civil administration of Wake Island pursuant to an agreement between the Department of the Interior and the Department of the Air Force. The civil administration authority at Wake Island

title: Wake Island

text: but the group agreed that they were only interested in resettlement on Wake Island due to the presence of the U.S. military and the island's proximity to Bikini Atoll. Unfortunately for the Bikini Islanders, the U.S. Department of Defense responded that "any such resettlement is out of the question." In June 1979, the original Wake Island fighter aircraft unit now nicknamed the "Wake Island Avengers", the United States Marine Corps attack squadron VMA-211, landed their A-4 fighter jets at Wake. The squadron was en route from Japan to the U.S. mainland. From April 20 to 23, 1981, a party of

title: Wake Island

text: the starving soldiers. Ultimately about three-quarters of the Japanese garrison perished, and the rest survived only by eating tern eggs, the Pacific rats introduced by prehistoric voyagers, and what scant amount of vegetables they could grow in makeshift gardens among the coral rubble. With the end of hostilities with Japan and the increase in international air travel driven in part by wartime advances in aeronautics, Wake Island became a critical mid-Pacific base for the servicing and refueling of military and commercial aircraft. The United States Navy resumed control of the island, and in October 1945 400 Seabees from the 85th

title: Wake Island

text: On January 17, 1899, under orders from President William McKinley, Commander Edward D. Taussig of USS Bennington landed on Wake and formally took possession of the island for the United States.  After a 21-gun salute, the flag was raised and a brass plate was affixed to the flagstaff with the following inscription:

title: Wake Island

text: Federal Solutions, Inc. About 94 people live on the island, and access to it is restricted. Population fluctuates depending on operations being conducted by Missile Defense Agency activities. On December 11, 1941, Wake Island was the site of the Empire of Japan's first unsuccessful attack on American forces in the Battle of Wake Island when U.S. Marines, with some US Navy personnel and civilians on the island repelled an attempted Japanese invasion, sinking two enemy destroyers and a transport. The island fell to overwhelming Japanese forces 12 days later in a second attack, this one with extensive support from Japanese

title: Wake Island

text: demolished. There were no serious injuries, and the majority of the civilian population was evacuated after the storm. On August 28, 2006, the United States Air Force evacuated all 188 residents and suspended all operations as category 5 Super Typhoon Ioke headed toward Wake. By August 31 the southwestern eyewall of the storm passed over the island, with winds well over , driving a storm surge and waves directly into the lagoon inflicting major damage. A U.S. Air Force assessment and repair team returned to the island in September 2006 and restored limited function to the airfield and facilities leading

title: Wake Island

text: carrier-based aircraft returning from the attack on Pearl Harbor's naval and air bases in Hawaii further east, four days previously. Wake Island remained occupied by Japanese forces until the end of the war in September 1945. The submerged and emergent lands at the atoll are a unit of the Pacific Remote Islands Marine National Monument. Wake island, together with eight other insular areas, comprises the United States Minor Outlying Islands, a statistical designation defined by the International Organization for Standardization's ISO 3166-1 code. They are collectively represented by the ISO 3166-1 alpha-2 code ; Wake Island itself is represented by

title: Wake Island

text: increase in the number of commercial flights, on July 1, 1947, the Navy transferred administration, operations and maintenance of the facilities at Wake to the Civil Aeronautics Administration (CAA). In 1949, the CAA upgraded the runway by paving over the coral surface and extending its length to 7,000 feet. In June 1950, the Korean War began with the United States leading United Nations forces against North Korea. In July, the Korean Airlift was started and the Military Air Transport Service (MATS) used the airfield and facilities at Wake as a key mid-Pacific refueling stop for its mission of transporting men

title: Wake Island

text: Government had "no claim whatever to make on the sovereignty of the island, but that if any subjects are found on the island the Imperial Government expects that they should be properly protected as long as they are engaged in peaceful occupations." Wake Island was now clearly a territory of the United States, but during this period the island was only occasionally visited by passing American ships. One notable visit occurred in December 1906 when U.S. Army General John J. Pershing, later famous as the commander of the American Expeditionary Forces in western Europe during World War I, stopped at

title: Wake Island

text: on the pole in front of the airfield terminal building hung at half mast for 16 days to commemorate the number of days that the Americans held the island prior to surrendering to the Japanese 2nd Maizuru Special Naval Landing Force. Subsequently, the island has been used for strategic defense and operations during and after the Cold War, with Wake Island serving as a launch platform for military rockets involved in testing anti-missile defense systems and atmospheric re-entry trials. Wake's location allows for a safe launch and trajectory over the unpopulated ocean with open space for intercepts. In 1987, Wake

title: Wake Island (film)

text: a U.S. Navy patrol plane that is coming in, since he could provide intelligence to the U.S. Navy Department in Honolulu. Lewis refuses, but Caton orders him to go and file his official report. Later, Caton is informed that the largest-caliber ammunition is running out, so he has smaller guns spread around, and repositions his available men. Japanese planes approach in large numbers, causing major damage and inflicting numerous casualties. Only one pilot is left, Captain Patrick. When his plane is damaged, he bails out, but is killed while parachuting down. The Japanese again signal for surrender. Caton replies, "Come

title: Wake Island

text: weather. The isolated U.S. garrison was overwhelmed by a reinforced and greatly superior Japanese invasion force on December 23. American casualties numbered 52 military personnel (Navy and Marine) and approximately 70 civilians killed. Japanese losses exceeded 700 dead, with some estimates ranging as high as 1,000. Wake's defenders sank two Japanese fast transports ("P32" and "P33") and one submarine and shot down 24 Japanese aircraft. The relief fleet, en route, on hearing of the island's loss, turned back. In the aftermath of the battle, most of the captured civilians and military personnel were sent to POW camps in Asia, though

title: Battle of Wake Island

text: missing, and 49 wounded during the 15-day siege, while three US Navy personnel and at least 70 US civilians were killed, including 10 Chamorros, and 12 civilians wounded. 433 US personnel were captured. Japanese losses were 144 casualties, 140 SNLF and Army casualties with another 4 aboard ships. At least 28 land-based and carrier aircraft were also either shot down or damaged. The Japanese captured all men remaining on the island, the majority of whom were civilian contractors employed by the Morrison-Knudsen Company. Captain Henry T. Elrod, one of the pilots from VMF-211, was awarded the Medal of Honor posthumously

title: Battle of Wake Island

text: working anti-aircraft director among them); eighteen Browning heavy machine guns; and thirty heavy, medium and light water- and air-cooled machine guns. On 28 November, naval aviator Commander Winfield S. Cunningham, USN reported to Wake to assume overall command of U.S. forces on the island. He had 10 days to examine the defenses and assess his men before war broke out. On 8 December, just hours after the attack on Pearl Harbor (Wake being on the opposite side of the International Date Line), 36 Japanese Mitsubishi G3M3 medium bombers flown from bases on the Marshall Islands attacked Wake Island, destroying eight

title: Edward D. Taussig

text: salute when the flag reached the truck. At the time President William McKinley ordering that Wake Island be claimed as a U.S. possession was seen as questionable; however, no other nation had claimed the island and there was no native population. Wake Island was primarily taken for its strategic value as a cable station, midway between Hawaii and the Philippines. Departing from Wake Island at 5:35 p.m. on 17 January 1899, arrived at Guam on 23 January 1899. The island previously had been captured on 21 June 1898 by Captain Henry Glass of the who had left Francisco Portusach Martínez,

title: Wake Island

text: 113 Chinese illegal immigrants who had been interdicted in the Atlantic Ocean near Bermuda aboard the human smuggling vessel, the "Xing Da". On October 1, 2002, administrative control and support of Wake Island was transferred from the U.S. Army to the U.S. Air Force's 15th Wing, an aviation unit of Pacific Air Forces based at Hickam Air Force Base in Hawaii. The 15th Wing had previously been in control of Wake from July 1, 1973 to September 30, 1994. Although the Air Force was once again in control, the Missile Defense Agency would continue to operate the Wake Island Launch

title: Wake Island Airfield

text: Wake Island Airfield Wake Island Airfield is a military air base located on Wake Island, which is known for the Battle of Wake Island during World War II. It is owned by the U.S. Air Force and operated by the 611th Air Support Group. The airfield primarily serves military flight activity within the Wake Island region; however, military presence is minimal at the current time. The runway can be used for emergency landings by commercial jetliners flying transpacific routes. The first intention to build an air base surfaced in 1935, when Pan American World Airways (PAA) selected Wake Island as

title: Battle of Wake Island

text: Battle of Wake Island The Battle of Wake Island began simultaneously with the attack on Pearl Harbor naval/air bases in Hawaii and ended on 23 December 1941, with the surrender of the American forces to the Empire of Japan. It was fought on and around the atoll formed by Wake Island and its minor islets of Peale and Wilkes Islands by the air, land, and naval forces of the Japanese Empire against those of the United States, with Marines playing a prominent role on both sides. The island was held by the Japanese for the duration of the Pacific War

title: Battle of Wake Island

text: the guns on Wilkes. Early on the morning of 11 December, the garrison, with the support of the four remaining Wildcats, repelled the first Japanese landing attempt by the South Seas Force, which included the light cruisers , , and ; the destroyers , , , , , and ; two "Momi"-class destroyers converted to patrol boats ("Patrol Boat No. 32" and "Patrol Boat No. 33"), and two troop transport ships containing 450 Special Naval Landing Force troops. The US Marines fired at the invasion fleet with their six coast-defense guns. Major Devereux, the Marine commander under Cunningham, ordered the

title: Wake Island

text: all islands not administered by the Department of Agriculture. On July 27, 1923, , a World War I minesweeper, brought the Tanager Expedition to Wake Island under the leadership of ornithologist Alexander Wetmore, and a tent camp was established on the eastern end of Wilkes. From July 27 to August 5, the expedition charted the atoll, made extensive zoological and botanical observations and gathered specimens for the Bishop Museum, while the naval vessel under the command of Lt. Cmdr. Samuel Wilder King conducted a sounding survey offshore. Other achievements at Wake included examinations of three abandoned Japanese feather poaching camps,

title: Wake Island

text: 7 in Hawaii, which is on the other side of the International Date Line), at least 27 Japanese Mitsubishi G3M "Nell" medium bombers flown from bases on Kwajalein in the Marshall Islands attacked Wake Island, destroying eight of the 12 Grumman F4F Wildcat fighter aircraft belonging to United States Marine Corps Fighter Squadron 211 (VMF-211) on the ground. The Marine garrison's defensive emplacements were left intact by the raid, which primarily targeted the aircraft. The garrison – supplemented by civilian construction workers employed by Morrison-Knudsen Corp. – repelled several Japanese landing attempts. An American journalist reported that after the initial

title: Battle of Wake Island

text: the island, blindfolded and executed with a machine gun. One of the prisoners (whose name has never been discovered) escaped, apparently returning to the site to carve the message "98 US PW 5-10-43" on a large coral rock near where the victims had been hastily buried in a mass grave. The unknown American was recaptured, and Sakaibara personally beheaded him with a "katana". The inscription on the rock can still be seen and is a Wake Island landmark. On 4 September 1945, the remaining Japanese garrison surrendered to a detachment of US Marines. The handover of Wake was officially conducted

title: Shigematsu Sakaibara

text: to rear admiral a year later, on October 15, 1944. The Japanese garrison on Wake Island formally surrendered to the United States on September 4, 1945. After the war, Sakaibara was taken into custody by the American occupation authorities, extradited to Guam, and sentenced to death by a military tribunal for war crimes in connection with his actions in the "Wake Island Massacre". He was hanged on June 18, 1947. Until the end, he maintained, "I think my trial was entirely unfair and the proceeding unfair, and the sentence too harsh, but I obey with pleasure." Shigematsu Sakaibara A native

title: Battle of Wake Island

text: consisting of 12 F4F-3 Wildcat fighters, commanded by marine aviator Major Paul A. Putnam, USMC. Also, present on the island were 68 U.S. Navy personnel and about 1,221 civilian workers for the Morrison-Knudsen Civil Engineering Company. Forty-five Chamorro men (native Micronesians from the Mariana Islands and Guam) were employed by Pan American Airways at the company's facilities on Wake Island, one of the stops on the Pan Am Clipper trans-Pacific amphibious air service initiated in 1935. The Marines were armed with six /51 cal pieces, originating from the old battleship ; twelve /50 cal anti-aircraft guns (with only a single

title: Wake Island

text: Pan Am passenger flight landed at Wake, and in July Pan Am's last cargo flight departed the island, marking the end of the heyday of Wake Island's commercial aviation history. During this same time period the U.S. military had transitioned to longer-range C-5A and C-141 aircraft, leaving the C-130 as the only aircraft that would continue to regularly use the island's airfield. The steady decrease in air traffic control activities at Wake Island was apparent and was expected to continue into the future. On June 24, 1972, responsibility for the civil administration of Wake Island was transferred from the FAA

title: Wake Island

text: to the day of the first Japanese air raid in December 1941, forcing the U.S. into World War II (see below). On February 14, 1941, President Franklin D. Roosevelt issued Executive Order 8682 to create naval defense areas in the central Pacific territories. The proclamation established "Wake Island Naval Defensive Sea Area", which encompassed the territorial waters between the extreme high-water marks and the three-mile marine boundaries surrounding Wake. "Wake Island Naval Airspace Reservation" was also established to restrict access to the airspace over the naval defense sea area. Only U.S. government ships and aircraft were permitted to enter the

title: Wake Island

text: of wine per day until a heavy rain shower came on the sixth day. After 31 days of hardship, drifting westward in the longboat, they reached Kosrae (Strong's Island) in the Caroline Islands. Capt. Vandervord attributed the loss of "Dashing Wave" to the erroneous manner in which Wake Island "is laid down in the charts. It is very low, and not easily seen even on a clear night." With the annexation of Hawaii in 1898 and the seizure of Guam and the Philippines during the Spanish–American War that same year, the United States began to consider unclaimed and uninhabited Wake

title: Wake Island

text: to the United States Air Force under an agreement between the Secretary of the Interior and the Secretary of the Air Force. In July, the FAA turned over administration of the island to the Military Airlift Command (MAC), although legal ownership stayed with the Department of the Interior, and the FAA continued to maintain the air navigation facilities and provide air traffic control services. On December 27, the Chief of Staff of the Air Force (CSAF) Gen. John D. Ryan directed MAC to phase out en-route support activity at Wake Island effective June 30, 1973. On July 1, 1973, all

title: Wake Island

text: June 18, 1947, on Guam. The remains of the murdered civilians were exhumed and reburied at the National Memorial Cemetery of the Pacific in section G. On September 4, 1945, the Japanese garrison surrendered to a detachment of United States Marines under the command of Brig. Gen. Lawson H. M. Sanderson. At that point the garrison had been almost cut off from supplies since the 1943 air raids, and was reduced to the point of starvation. While the islands' sooty tern colony had received some protection as a source of eggs, the Wake Island rail was hunted to extinction by

title: Wake Island


question: who is the number one ranked golfer in the world right now

answers: Dustin Johnson

title: Martin Kaymer

text: golfer in the world, making him only the second German (after Bernhard Langer) to be the top-ranked golfer in the world. At the time he was the second youngest to reach world number one behind Tiger Woods, soon surpassed by Rory McIlroy in March 2012, who gained the top ranking at age 22. In April, he relinquished his number one ranking after eight weeks to Westwood, who won the Indonesian Masters. After reaching the number one ranking, Kaymer decided to undergo a swing change to be able to move the ball both ways. Frustrated with his disappointing results at the

title: Adam Scott (golfer)

text: a 10-under-par 62 during the first round of the Arnold Palmer Invitational. He went on to finish third in the tournament behind the winner Matt Every and Keegan Bradley after a poor four-over-par 76 in the final round. On May 19, 2014, Scott took over as the World's #1 ranked golfer. Scott is the 17th golfer to be ranked number one since official rankings began. He is also the second Australian and the first since Greg Norman in 1998. A week after becoming world #1, Scott strengthened his ranking with a win at the Crowne Plaza Invitational at Colonial, being

title: Joaquín Niemann

text: Joaquín Niemann Joaquín Niemann (born 7 November 1998) is a Chilean professional golfer. He was the number one ranked amateur golfer from May 2017 to April 2018. Niemann was the number one ranked golfer in the World Amateur Golf Ranking for 44 weeks, from May 2017 to April 2018, when he turned professional. Niemann planned to play at the University of South Florida, but he was unable to gain entry due to his TOEFL scores. Niemann won the 2017 Mark H. McCormack Medal for being the top-ranked player in the World Amateur Golf Ranking at the conclusion of the summer's

title: Ariya Jutanugarn

text: background for top-10. <nowiki>*</nowiki> as of the 2018 season Position in Women's World Golf Rankings at the end of each calendar year. Professional Ariya Jutanugarn Ariya Jutanugarn (, , ; born 23 November 1995) is a Thai professional golfer who plays on the American-based LPGA Tour. She was born in Bangkok. She is the first golfer, male or female, from Thailand to win a major championship. She became the number one ranked golfer in the Women's World Golf Rankings in June 2017. Jutanugarn has an older sister, Moriya, who is also a professional golfer. Their parents are father Somboon and

title: List of World Number One male golfers

text: The following is a list of the 20 golfers who have risen to the top of the Official World Golf Ranking. As of April 22, 2018, Dustin Johnson is the number one ranked golfer.  Tiger Woods has spent the most consecutive weeks (281) and most total weeks (683) in that position. Three golfers have spent an entire calendar year atop the rankings: Nick Faldo (1993), Greg Norman (1996), and Woods (2000, 2001, 2002, 2003, 2006, 2007, 2008, 2009).

title: Rickie Fowler

text: Rickie Fowler Rick Yutaka Fowler (born December 13, 1988) is an American professional golfer who plays on the PGA Tour. He was the number one ranked amateur golfer in the world for 37 weeks in 2007 and 2008. On January 24, 2016 he reached a career high fourth in the Official World Golf Ranking following his victory in the Abu Dhabi HSBC Golf Championship. Born and raised in Murrieta, California, Fowler attended Murrieta Valley High School. For years, he played only on a driving range and is almost entirely self-taught. In his senior year in high school, Fowler won the

title: Ryu So-yeon

text: the number one golfer in the Women's World Golf Rankings. Ryu took classes at Yonsei University while also competing full-time on the LPGA Tour. She graduated in February 2013 with a degree in sports business. LPGA Tour playoff record (2–3) Defeated Hee Kyung Seo in a three-hole playoff: Ryu (3-4-3=10) and Seo (3-6-4=13)<br> "Results not in chronological order before 2018." ^ The Evian Championship was added as a major in 2013. DNP = did not play DQ = disqualified CUT = missed the half-way cut T = tied Green background for a win. Yellow background for a top-10 finish. <nowiki>*</nowiki>

title: Luke Donald

text: Golfer of the Year. He also became the first Englishman to win the PGA Tour Player of the Year award, the PGA Tour's Vardon Trophy and the Mark H. McCormack Award for the most weeks at number one during a calendar year. He was later awarded honorary life membership of the European Tour for his achievements in 2011. In May 2011, Donald became the number one golfer in the Official World Golf Ranking after winning the BMW PGA Championship at Wentworth Club. He held the number one position for 40 weeks between May 2011 and March 2012 before Rory McIlroy

title: Rory McIlroy

text: Rory McIlroy Rory McIlroy, (born 4 May 1989) is a professional golfer from Northern Ireland who is a member of both the European and PGA Tours. He was world number one in the Official World Golf Ranking for 95 weeks. He is a four-time major champion, winning the 2011 U.S Open, (setting a tournament record score of −16), 2012 PGA Championship (with a tournament record margin of victory (8 strokes)), 2014 Open Championship, and 2014 PGA Championship. Along with Jack Nicklaus, Tiger Woods and Jordan Spieth he is one of four players to win three majors by the age of

title: Jordan Spieth

text: Jordan Spieth Jordan Alexander Spieth (born July 27, 1993) is an American professional golfer on the PGA Tour and former world number one in the Official World Golf Ranking. He is a three-time major winner and the 2015 FedEx Cup champion. In April 2016, "Time" magazine named Spieth to its list of the "100 Most Influential People", noting that he "exemplifies everything that's great about sports." Spieth's first major win came in the 2015 Masters Tournament, when he shot a 270 (−18) and pocketed $1.8 million. He tied the 72-hole record set by Tiger Woods in 1997 and became the

title: Jon Rahm

text: Jon Rahm Jon Rahm Rodríguez (born 10 November 1994) is a Spanish professional golfer. He was the number one golfer in the World Amateur Golf Ranking for a record 60 weeks and was the low amateur at the 2016 U.S. Open. Prior to this event, Rahm was ranked 766 in the Official World Golf Ranking. On 21 January 2018, Rahm reached a career-high ranking of No. 2 in the world after winning the CareerBuilder Challenge. Born in Barrika, Basque Country, Spain, Rahm played collegiate golf for the Arizona State Sun Devils where he won 11 college tournaments, which is second

title: Albane Valenzuela

text: the number one ranked golfer in Switzerland. Valenzuela plays college golf at Stanford University and is set to graduate in 2020. Valenzuela reached the final of the U.S. Women's Amateur, losing to Sophia Schubert. Sources: Albane Valenzuela Albane Valenzuela (born 1997) is a Swiss amateur golfer. She was born in New York City to a Mexican father and French mother. She became a Swiss citizen at age 14. Valenzuela took low amateur honors at the 2016 ANA Inspiration with a tie for 65th. She also made the cut at the 2016 U.S. Women's Open. She had 2 top 5 finishes

title: Phil Mickelson

text: of worldwide wins. Mickelson, one of the favorites for the U.S. Open at Pebble Beach, shot 74 and 66 on Thursday and Friday to sit a shot off the lead. However, two weekend scores of 73 gave him a T4 finish. During the remainder of the 2010 season, Mickelson had multiple opportunities to become the number one player in the world rankings following the travails of Tiger Woods. However, a string of disappointing finishes by Mickelson saw the number one spot eventually go to Englishman Lee Westwood. In the days leading up to the PGA Championship at Whistling Straits (near

title: Vijay Singh

text: Vijay Singh Vijay Singh, CF (Hindi: विजय सिंह), ; born 22 February 1963), nicknamed "The Big Fijian", is an Indo-Fijian professional golfer who was Number 1 in the Official World Golf Ranking for 32 weeks in 2004 and 2005. Vijay was the 12th man to reach the world No. 1-ranking and was the only new world No. 1 in the 2000s decade. He has won three major championships (The Masters in 2000 and the PGA Championship in 1998 and 2004) and was the leading PGA Tour money winner in 2003, 2004 and 2008. He was elected to the World Golf

title: Justin Thomas (golfer)

text: Justin Thomas (golfer) Justin Louis Thomas (born April 29, 1993) is an American professional golfer who plays on the PGA Tour and a former World Number One. In 2017, Thomas experienced a breakout year, winning four PGA Tour events, including the PGA Championship, his maiden major championship, and also winning the FedEx Cup championship. In May 2018, Thomas became the 21st player to top the Official World Golf Ranking. Thomas was born and raised in Louisville, Kentucky. Prior to his junior year in high school, he played in the Wyndham Championship on the PGA Tour in August 2009 and became

title: Rickie Fowler

text: = Round in which player lost in match play "T" = tied <nowiki>*</nowiki>As of the 2018 season. Amateur Professional Rickie Fowler Rick Yutaka Fowler (born December 13, 1988) is an American professional golfer who plays on the PGA Tour. He was the number one ranked amateur golfer in the world for 37 weeks in 2007 and 2008. On January 24, 2016 he reached a career high fourth in the Official World Golf Ranking following his victory in the Abu Dhabi HSBC Golf Championship. Born and raised in Murrieta, California, Fowler attended Murrieta Valley High School. For years, he played only

title: Patrick Cantlay

text: Patrick Cantlay Patrick Cantlay (born March 17, 1992) is an American professional golfer who was the number one golfer in the World Amateur Golf Ranking for 55 weeks. He finished in the top-25 of his first four PGA Tour events as an amateur in 2011, including being the low amateur at the U.S. Open. The following week, Cantlay shot the lowest round in PGA Tour history by an amateur when he shot a course record 60 at the Travelers Championship. On November 5, 2017, Cantlay won the Shriners Hospitals for Children Open in a playoff for his first PGA Tour

title: Official World Golf Ranking

text: 2011, the possession of the No. 1 ranking would be the subject of much discussion among European golf commentators as it passed from Westwood to Kaymer, back to Westwood and then in May to Luke Donald, who took No. 1 spot by defeating Westwood in a playoff for the BMW PGA Championship. Donald, in becoming the fifteenth world No. 1, also became the first ever to reach No. 1 before having won or finished runner-up in a major championship in his career. Donald's position at the top of the rankings was justified by his consistency through the rest of the

title: Lee Westwood

text: near misses including three runner-up finishes. He has represented Europe in ten Ryder Cups. In October 2010, Westwood became the World number one golfer, ending the reign of Tiger Woods, and becoming the first British golfer since Nick Faldo in 1994 to hold that position. He held the number one position for a total of 22 weeks. Born in Worksop, Nottinghamshire, Westwood began to play golf aged 13 with a half set bought by grandparents. His father John, a mathematics teacher, took up the game at the same time to encourage his son. A talented sportsman at school, Lee played

title: Justin Rose

text: 2007 and July 2008. In March 2012, Rose won his first World Golf Championship event at the WGC-Cadillac Championship and as a result, he re-entered the world top 10. After finishing second to Tiger Woods in the 2013 Arnold Palmer Invitational, he rose to a then career-high world ranking of 3rd. After the Open Championship in 2018 he rose to world number 2. Following a loss to Keegan Bradley in a sudden-death playoff in the 2018 BMW Championship, Rose climbed to World Number 1 in the Official World Golf Ranking. He won the 2018 FedEx Cup Playoffs and its US

title: Luke Donald

text: Donald played a pitch for his third shot to leave himself a putt of no more than six feet for birdie. Westwood's approach shot to the green spun back into the water hazard. Westwood chipped out from the drop zone and made double bogey, leaving Donald to hole out for a birdie to win the title and become the new world number one. Donald was the third Englishman to hold the number one position in the Official World Golf Ranking since its inception in 1986. In July 2011, Donald won his first tournament as the world number one at the

title: Brooks Koepka

text: Brooks Koepka Brooks Koepka (born May 3, 1990) is an American professional golfer who plays on the PGA Tour. He became World Number 1 in the Official World Golf Ranking in October 2018, after winning the 2018 CJ Cup. He had won the U.S. Open and PGA Championship earlier in the year. He started his career on the European Challenge Tour and eventually the European Tour. He played collegiate golf at Florida State University. Koepka claimed his first major championship at the U.S. Open in 2017 at Erin Hills, Wisconsin. He successfully defended his title in 2018 at Shinnecock Hills

title: Lydia Ko

text: Lydia Ko Lydia Ko (born 24 April 1997) is a Korean-born New Zealand professional golfer who became the No. 1-ranked woman professional golfer on 2 February 2015 at of age, making her the youngest player of either gender to be ranked No. 1 in professional golf. Upon winning The Evian Championship in France on 13 September 2015, she became the youngest woman, at age , to win a major championship. Her closing round of 63 was a record lowest final round in the history of women's golf majors. On 3 April 2016, she won the ANA Inspiration, for her second

title: World Amateur Golf Ranking

text: The first to do so was Rory McIlroy, who was when he became the No. 1 amateur and when he first became the world No. 1 professional. Lydia Ko was the second to accomplish this feat, she was only and held the ranking for a record 130 consecutive weeks, and she was a mere when she first reached the pinnacle of the Rolex Rankings. Jordan Spieth was the most recent person to accomplish this feat, he was when he topped the amateur rankings and when he reached No. 1 in the Official World Golf Ranking. Events are ranked in eight

title: Henrik Stenson

text: in the OWGR ranking on 3 November 2013. He finished the 2013 season ranked first on the PGA Tour in greens in regulation, first in ball striking, second among money leaders, third in total driving, fourth in scoring average, and seventh in driving accuracy percentage. On 17 November 2013, he won the DP World Tour Championship, Dubai with a record-breaking performance (an aggregate 263 score at 25-under par), thereby also winning the Race to Dubai which he was already leading. Having already won the FedEx Cup Series in September, he thus became the first player to win the FedEx Cup

title: Cristie Kerr

text: Cristie Kerr Cristie Kerr (born October 12, 1977) is an American professional golfer who plays on the LPGA Tour. She has 20 wins on the LPGA Tour, including two major championships, and over $19 million in career earnings. Kerr was the number one-ranked golfer in the Women's World Golf Rankings for three time periods in 2010. She is naturally left handed but plays golf right handed. Kerr was born in Miami, Florida, and started playing golf at the age of eight. She had a successful amateur career, winning the 1994 Junior Orange Bowl International Golf Championship and the 1995 Women's

title: Justin Thomas (golfer)

text:
in which player lost in match play
 "T" = tied
 <nowiki>*</nowiki>As of the 2018 season. Professional Justin Thomas (golfer) Justin Louis Thomas (born April 29, 1993) is an American professional golfer who plays on the PGA Tour and a former World Number One. In 2017, Thomas experienced a breakout year, winning four PGA Tour events, including the PGA Championship, his maiden major championship, and also winning the FedEx Cup championship. In May 2018, Thomas became the 21st player to top the Official World Golf Ranking. Thomas was born and raised in Louisville, Kentucky. Prior to his junior year in high

title: Vijay Singh

text: picking up a win early in 2005, Singh lost his world number 1 ranking when Tiger Woods won the Ford Championship at Doral on 6 March, but just two weeks later he took it back again after notching up top three finishes in three consecutive weeks. Followings Woods' win at the 2005 Masters, Singh once again lost his place as World No. 1 in the Official World Golf Ranking and finished tied for fifth place. In April, he became the youngest living person elected to the World Golf Hall of Fame, garnering 56% of the ballot. Thirty-year-old Karrie Webb was

title: Nick Faldo

text: Nick Faldo Sir Nicholas Alexander Faldo, (born 18 July 1957) is an English professional golfer who is now mainly an on-air golf analyst. A top player of his era, renowned for his single-minded dedication to the game, he was ranked No. 1 on the Official World Golf Ranking for a total of 97 weeks. His 41 professional wins include 30 victories on the European Tour and six major championships: three Open Championships (1987, 1990, 1992) and three Masters (1989, 1990, 1996). Faldo has since become a television pundit for major golf championships. In 2006, he became the lead golf analyst

title: Martin Kaymer

text: Martin Kaymer Martin Kaymer ( ; born 28 December 1984) is a German professional golfer. A winner of two major championships, he was also the No. 1 ranked golfer in the Official World Golf Ranking for eight weeks in 2011. Kaymer sank a putt on the 18th hole on the final day of the Ryder Cup in 2012, which retained the cup for Europe and successfully overturned a four-point deficit against the United States at the start of the final day's play. In May 2014, Kaymer won The Players Championship, the flagship event of the PGA Tour. A month later,

title: List of World Number One male golfers


question: who has the oldest team in the nba

answers: Sacramento Kings

answers: New York Knickerbockers

title: San Antonio Spurs

text: Celtics (17), Los Angeles Lakers (16), Chicago Bulls (6), and Golden State Warriors (6). The Spurs currently rank first among active franchises for the highest winning percentage in NBA history, and have a winning head-to-head regular season record against every active NBA franchise. In their 40 NBA seasons since 1976–77, the Spurs have won 22 division titles. They have made the playoffs in 27 of the last 28 seasons (since 1989–90) and have only missed the playoffs four times since entering the NBA; they have not missed the playoffs in the 20 seasons since Tim Duncan was drafted by the

title: Women's National Basketball Association

text: Cappie Pondexter, Katie Smith, Lisa Leslie, Sue Bird, Candice Dupree, and Lauren Jackson. The league's all-time leader in points per game is Cynthia Cooper, who averaged 21.0 points per game in five seasons with the Houston Comets (1997–2000, 2003). In 2007, Paul Westhead of the Phoenix Mercury became the first person to earn both NBA and WNBA championship rings as a coach. In 2008, 50-year-old Nancy Lieberman became the oldest player to play in a WNBA game. She signed a seven-day contract with the Detroit Shock and played one game, tallying two assists and two turnovers in nine minutes of

title: Jason Terry

text: with the Milwaukee Bucks. On February 24, 2017, in Milwaukee's 109–95 loss to the Utah Jazz, Terry became the oldest player to play for the Bucks, at 39 years, 162 days, passing Dale Ellis (39 years, 155 days). On April 10, 2017, he had season highs of 15 points and five 3-pointers in an 89–79 win over the Charlotte Hornets. That was the only time in 74 games in 2016–17 that he finished with 10 points or more. On September 18, 2017, Terry re-signed with the Bucks. On December 5, 2017, he was ruled out for two or more weeks

title: Jason Kidd

text: Heat in six games, despite being down after the first three. Kidd averaged 9.3 points, 7.3 assists, 4.5 rebounds, and 1.9 steals per game during the Mavericks' 21-game championship run. At 38 years of age, he became the oldest starting point guard ever to lead his team to the championship. Shortened by a lockout the 2011–12 season turned out to be the last for Kidd in the Mavericks uniform. With 39-year-old Kidd averaging career lows in minutes, points and assists for the regular season, the defending champions were swept by the Oklahoma City Thunder in the first round of the

title: National Basketball Association

title: John Long (basketball)

text: was named the starter, Long later played for the Indiana Pacers, where he was backed up by Reggie Miller before playing for the Atlanta Hawks. After playing overseas and in the minor leagues for several years, Long signed with the Toronto Raptors for one season, and he retired in 1997 with 12,131 career points. At the time, the 41-year-old Long was the second oldest player in the NBA behind Robert Parish, who was 43. Two of John Long's nephews, Terry Mills and Grant Long, also played in the NBA. The nephews were teammates in Detroit during the 1996-1997 season. All

title: Juwan Howard

text: season. Howard's April 17 start in the season finale against the Orlando Magic marked Howard's 900th career start. On May 30, during halftime of game 5 of the Eastern Conference championship against the Indiana Pacers, Howard delivered a passionate speech that fired up the team in its clinching game. With the retirement of Grant Hill on June 1, 2013, Howard became the oldest active player in the NBA at age 40. During the playoffs, Howard did not play, but he served as a quasi-assistant coach. In college, Howard was regarded as one of the best defensive big men in the

title: 2015 NBA Playoffs

text: first round of the playoffs, of the teams who had previously won an NBA championship, the Chicago Bulls had the shortest drought at 17 years, having most recently won an NBA championship in 1998, while the Atlanta Hawks had the longest overall drought at 57 years, having won their only previous championship in 1958 when the franchise was based in St. Louis. For the first time since 1970, the Hawks made the Conference Finals (then called the Division Finals). Since 1970, they had lost all 15 Division or Conference Semifinal series they participated in. The Warriors made their first conference

title: Vince Carter

text: start of the season and made all eight of his shots, including six from beyond the arc, to score a season-high 24 points and lead the Grizzlies past the Milwaukee Bucks 113–93. He became the first 40-year-old in NBA history to hit six triples in one game. At 40 years, 46 days old, Carter also became the oldest player to start an NBA game since Juwan Howard in April 2013. On March 29 against the Indiana Pacers, Carter passed Ray Allen for 22nd on the NBA all-time scoring list. In the Grizzlies' regular-season finale on April 12 against the Dallas

title: Kyle Korver

text: his first NBA All-Star selection as a reserve for the Eastern Conference in the 2015 NBA All-Star Game, replacing the injured Dwyane Wade. At 33 years and 11 months old, he became the fourth-oldest first-time All-Star. On March 11, in a loss to the Denver Nuggets, Korver passed Kobe Bryant for 12th on the all-time three-pointers made list. Four days later, in a win over the Los Angeles Lakers, Korver left the game with a broken nose after taking an offensive foul from Ed Davis with 8:59 left in the first half. The injury ended a streak of 51 consecutive

title: Andre Ingram

text: out the 2016–17 season. He returned to the team, now called the South Bay Lakers, for the 2017–18 season. Ingram averaged 9.1 points, 2.5 rebounds and 1.1 assists in 47 games (seven starts) for the South Bay Lakers in 2017–18, shooting a league-best 47.5 percent from three-point range. On April 9, 2018, Ingram signed with the Los Angeles Lakers for the final two games of the 2017–18 NBA season. He made his NBA debut the following day, scoring 19 points with four 3-pointers in a 105–99 loss to the Houston Rockets. At 32 years old, Ingram became the oldest American

title: Pau Gasol

text: game with 19 points and 17 rebounds, as the Bulls were defeated by the Miami Heat 89–84. On February 9, Gasol was named as Jimmy Butler's replacement on the 2016 Eastern Conference All-Star squad. On February 27, he recorded his eighth career triple-double and first as a Bull with 22 points, 16 rebounds and a career-high 14 assists in a 103–95 loss to the Portland Trail Blazers. At 35 years old, he became the oldest player to record a triple-double since Kobe Bryant did so at 36 years old in 2014. On March 7, he recorded his second triple-double of

title: David Stern

text: and Danny Green for a nationally televised game against the Miami Heat. Popovich has frequently sat out his starters on road trips over the years in order to ensure they have enough rest for the playoffs, the Spurs are one of the oldest teams in the league. Stern was outraged when he learned of this, and said on the night of the game that the Spurs' actions were "unacceptable", and that "substantial sanctions [would] be forthcoming." On November 30, Stern fined the Spurs $250,000 for what he called "a disservice to the league and the fans." According to Stern, Popovich

title: Kevin Willis

text: NBA seasons. He shares the record for most seasons played in the NBA with Robert Parish, Kevin Garnett, Vince Carter and Dirk Nowitzki. During the 2004–05 season, Willis was the oldest player in the league at age 42, and he would continue to be until his retirement at the conclusion of the 2006–07 season at the age of 44. Born in Los Angeles, Willis graduated from Pershing High School in Detroit and joined the basketball team in his junior year. Willis played competitively at Jackson College for his freshman season and transferred to Michigan State University, where he would play

title: Kobe Bryant

text: season, his 19th season with the Lakers, who had replaced D'Antoni with Bryant's former Lakers teammate, Byron Scott. On November 30, 2014, in a 129–122 overtime victory against the Toronto Raptors, Bryant recorded his 20th career triple-double with 31 points, 12 assists and 11 rebounds. At age 36, he became the oldest NBA player to ever achieve 30 points, 10 rebounds, and 10 assists in a game. On December 14, Bryant became the NBA's third all-time leading scorer, passing Jordan (32,292) in a 100–94 win against Minnesota. He played in the first 27 games of the season, averaging team-highs with

title: Vince Carter

text: history. Carter also passed Charles Oakley for 24th on the NBA's career games played list with 1,283. On November 14, in a win over the Utah Jazz, Carter had his second 20-point game of the season, joining Michael Jordan and Patrick Ewing as the only players in NBA history to put up 20 points and 5+ rebounds off the bench at the age of 39, with Carter being the oldest at 39 years and 287 days. Carter missed seven games in early December with a right hip flexor strain. On January 11, Carter hit his 1,989th career three-pointer to move

title: Bernard James

text: Bernard James Bernard Ronald James (born February 7, 1985) is an American professional basketball player who last played for Limoges CSP of the LNB Pro A. He played college basketball for Florida State University. He is also the oldest player ever to be drafted in the National Basketball Association (NBA) at 27 years and 148 days old. In a 2012 piece for "The Tipoff", the magazine of the United States Basketball Writers Association, "ESPN.com" writer Dana O'Neil called James...the most unconventional of high school dropouts, a kid who grew disenchanted with the social hierarchy of school yet would head to

title: Cliff Robinson (basketball, born 1966)

text: on February 22, 1995, Robinson would be forced to end his 461 iron man streak of consecutive games played for which he started his career. This streak stands as a franchise record for the Trail Blazers. Robinson signed with the Phoenix Suns as a free agent on August 25, 1997, where he remained for four more seasons. The highlight of his tenure with the Suns was registering a career-best 50 points against the Denver Nuggets on January 16, 2000. He became the oldest player at 33 years of age and two months to register his first 50-point game. Robinson was

title: Providence Steamrollers

text: in a season with six, in the 1947–48 season. However, the 2011-2012 Charlotte Bobcats hold the record for the lowest winning percentage in NBA history, with .106. Also during the 1947–48 season, the Steamrollers' coach Nat Hickey activated himself as a player for one game two days before his 46th birthday, setting a still-standing record as the oldest player in NBA history. Providence Steamrollers The Providence Steamrollers were a Basketball Association of America team based in Providence, Rhode Island. As of 2018, the Steamrollers remain the last professional sports franchise from one of the Big Four leagues to be based

title: Karl-Anthony Towns

text: the Atlanta Hawks 126–114. The 56 points surpassed Mo Williams' franchise record of 52 points set on January 13, 2015, against the Indiana Pacers. He also became the youngest player (22 years, 133 days) with 50 points and 15 rebounds in a game since Shaquille O'Neal (22 years, 45 days) on April 20, 1994 against the Timberwolves. In the Timberwolves' regular season finale on April 11, 2018, Towns had 26 points and 14 rebounds in a 112–106 overtime win over the Denver Nuggets. The win clinched Minnesota a spot in the playoffs for the first time since 2004—no team in

title: The Carolinas

text: by both states, the three teams are all based in NC, two in Charlotte and the third in Raleigh. All of the sports teams are fairly recent additions; the oldest team, the NFL's Panthers, was established in 1995, while the youngest, the Hornets, was added to the NBA in 2004 as the Charlotte Bobcats, although a prior NBA team also named the Hornets played in Charlotte from 1988 before leaving for New Orleans in 2002. The Bobcats were renamed the Hornets in May 2014, one season after the former New Orleans Hornets decided to rebrand themselves as the Pelicans. At

title: Pablo Prigioni

text: one-year contract with the New York Knicks for the rookie minimum. At age 35, Prigioni became the oldest rookie in NBA history, when he made his debut on November 2, 2012. He became the team's starting point guard for the last two months of the 2012–13 season, as well as for the playoffs. In game 6 of the Knicks' first-round playoff series against the Boston Celtics, Prigioni made 3 three-pointers in the first quarter. The Knicks won 88–80, to advance to the second round of the playoffs for the first time in 13 years. On July 10, 2013, Prigioni re-signed

title: Kevin Willis

text: play in 2005–06, was reported to take the team's vacant 15th roster spot. The deal became official when he signed a 10-day contract with the Mavericks on April 2, 2007. He appeared in five late regular season games and was on the Mavericks playoff roster as the 12th man but did not play in the Mavericks shock early first round exit. By playing five games during 2006–07, Willis became the oldest person to play more than one game in an NBA season (Providence Steamrollers coach Nat Hickey activated himself for one game in 1948, at 45 years and 363 days

title: History of the Golden State Warriors

text: of Blake and Crawford and the play of 35-year-old Jermaine O'Neal (who returned sooner than expected from wrist surgery), the Warriors were one of the winningest teams in the NBA after the all-star break. Nonetheless, and despite several victories over top contenders, the team displayed a pattern of losing games to inferior teams even at their home arena. On April 11, in a 112–95 stomping of the Los Angeles Lakers at the Staples Center, the Warriors clinched a playoff berth in consecutive seasons for the first time since 1991 and 1992. However, just one day earlier in a loss against

title: Nathaniel Clifton

text: first season helped lead the team to its first-ever appearance in the NBA finals, losing in game seven. During his eight seasons in the NBA, Clifton averaged 10 points and 9 rebounds per game. He was named to the 1957 NBA All-Star team, scoring 8 points in 23 minutes in the game. At age 34, he became the oldest player in NBA history to be named an All-Star. In 1957, Clifton was part of a multi-player trade between the Knicks and the Fort Wayne Pistons, but after one season in Detroit he retired from basketball. In the summer of 1958,

title: Nancy Lieberman

text: age of 39, she was the WNBA's oldest player. In 1998, she was hired as General Manager and Head Coach of the WNBA's Detroit Shock. She coached for three seasons. After leaving the Shock, Lieberman worked as a women's basketball analyst on ESPN. On July 24, 2008, at 50 years old, Lieberman signed a seven-day contract with the Detroit Shock, breaking her own previous record as the oldest player in league history. She played one game and had two assists and two turnovers against the Houston Comets. The Comets defeated the Shock 79–61. On August 13, 2008, she was part

title: Karl Malone

text: times. Malone led the NBA in free throws made a league-record seven times. He was a physical defender and rebounder, and one of the most durable players ever in the NBA. He maintained a high level of play even at age 40, becoming the oldest player to both log a triple-double and to be a starter on an NBA Finals-bound team. Malone's work ethic showed prominently in his formative years in the NBA, when he raised his free throw shooting percentage from below 50% to 75%. Malone wore number 32 for the Utah Jazz. He wore number 11 for the

title: Jerry Colangelo

text: Christian based school of business after Jerry Colangelo, replacing Ken Blanchard's name sake. He became the youngest general manager in professional sports in 1968 after being hired as general manager for the Phoenix Suns. He has the second longest tenure running the same NBA franchise, exceeded only by Red Auerbach of the Boston Celtics. In the summer of 2005, Colangelo was named director of USA Basketball whose team represented the United States in the 2008 Beijing Olympics and 2010 FIBA World Championship. Since 2009, he has served as Chairman of the Naismith Memorial Basketball Hall of Fame. Colangelo also serves

title: Golden State Warriors

text: was the longest for the franchise since the 1975 championship year, and fell just one win short of the team record of 11 consecutive wins. To strengthen their underperforming bench, the Warriors made a three-team trade on January 15, sending Douglas to the Miami Heat and picking up guards Jordan Crawford and MarShon Brooks from the Boston Celtics. A day before the trade deadline, the Warriors traded Kent Bazemore and Brooks to the Los Angeles Lakers in exchange for veteran point guard Steve Blake. Boosted by the additions of Blake and Crawford and the play of 35-year-old Jermaine O'Neal (who

title: Nat Hickey

text: Nat Hickey Matthew J. "Nat" Hickey (January 30, 1902 – September 16, 1979) was an American professional basketball coach/player and baseball player. He turned to coaching basketball after his retirement from playing in 1942, but returned to play two games with the Providence Steamrollers of the Basketball Association of America while serving as the team's coach in 1948. Aged 45 years old at the time of his two appearances, Hickey holds the record for the oldest player in NBA history. As a 5'11" guard/forward, Hickey played from the 1920s through 1940s with multiple early professional teams, including the Hoboken St.

title: National Basketball Association

long_answer: The Basketball Association of America was founded in 1946 by owners of the major ice hockey arenas in the Northeastern and Midwestern United States and Canada. On November 1, 1946, in Toronto, Ontario, Canada, the Toronto Huskies hosted the New York Knickerbockers at Maple Leaf Gardens, in a game the NBA now refers to as the first played game in NBA history. The first basket was made by Ossie Schectman of the Knickerbockers. Although there had been earlier attempts at professional basketball leagues, including the American Basketball League and the NBL, the BAA was the first league to attempt to play primarily in large arenas in major cities. During its early years, the quality of play in the BAA was not significantly better than in competing leagues or among leading independent clubs such as the Harlem Globetrotters. For instance, the 1948 ABL finalist Baltimore Bullets moved to the BAA and won that league's 1948 title, and the 1948 NBL champion Minneapolis Lakers won the 1949 BAA title. Prior to the 1948–49 season, however, NBL teams from Fort Wayne, Indianapolis, Minneapolis, and Rochester jumped to the BAA, which established the BAA as the league of choice for collegians looking to turn professional.


question: where are the mitochondria located in the sperm

answers: midpiece

title: Mitochondrion

text: mitochondria are inherited from one parent only. In humans, when an egg cell is fertilized by a sperm, the egg nucleus and sperm nucleus each contribute equally to the genetic makeup of the zygote nucleus. In contrast, the mitochondria, and therefore the mitochondrial DNA, usually come from the egg only. The sperm's mitochondria enter the egg, but do not contribute genetic information to the embryo. Instead, paternal mitochondria are marked with ubiquitin to select them for later destruction inside the embryo. The egg cell contains relatively few mitochondria, but it is these mitochondria that survive and divide to populate the

title: Mitochondrial DNA

text: inherited exclusively from the mother; the mitochondria in mammalian sperm are usually destroyed by the egg cell after fertilization. Also, most mitochondria are present at the base of the sperm's tail, which is used for propelling the sperm cells; sometimes the tail is lost during fertilization. In 1999 it was reported that paternal sperm mitochondria (containing mtDNA) are marked with ubiquitin to select them for later destruction inside the embryo. Some "in vitro" fertilization techniques, particularly injecting a sperm into an oocyte, may interfere with this. The fact that mitochondrial DNA is maternally inherited enables genealogical researchers to trace maternal

title: Spermatozoon

text: lies in the middle piece. Middle piece: It has 10–14 spirals of mitochondria surrounding the axial filament in the cytoplasm. It provides motility, and hence is called the powerhouse of the sperm. It also has a ring centriole (annulus) with unknown function. Tail: It is the longest part (50×10 m), having an axial filament surrounded by cytoplasm and plasma membrane, but at the posterior end the axial filament is naked. Semen has an alkaline nature and the spermatozoa do not reach full motility (hypermotility) until they reach the vagina, where the alkaline pH is neutralized by acidic vaginal fluids. This

title: Mitochondrion

text: per cell, making up 1/5 of the cell volume. The mitochondrial content of otherwise similar cells can vary substantially in size and membrane potential, with differences arising from sources including uneven partitioning at cell divisions, leading to extrinsic differences in ATP levels and downstream cellular processes. The mitochondria can be found nestled between myofibrils of muscle or wrapped around the sperm flagellum. Often, they form a complex 3D branching network inside the cell with the cytoskeleton. The association with the cytoskeleton determines mitochondrial shape, which can affect the function as well: different structures of the mitochondrial network may afford the

title: Sperm

text: The mammalian sperm cell consists of a head, neck, a midpiece and a tail. The head contains the nucleus with densely coiled chromatin fibres, surrounded anteriorly by an acrosome, which contains enzymes used for penetrating the female egg. The neck contains the sperm centriole. The midpiece has a central filamentous core with many mitochondria spiralled around it, used for ATP production for the journey through the female cervix, uterus and uterine tubes.  The tail or "flagellum" executes the lashing movements that propel the spermatocyte.

title: Human mitochondrial genetics

text: cases, some mitochondria or a mitochondrion from the sperm cell enters the oocyte but paternal mitochondria are actively decomposed. Genes in the "human mitochondrial genome" are as follows. It was originally incorrectly believed that the mitochondrial genome contained only 13 protein-coding genes, all of them encoding proteins of the electron transport chain. However, in 2001, a 14th biologically active protein called humanin was discovered, and was found to be encoded by the mitochondrial gene MT-RNR2 which also encodes part of the mitochondrial ribosome (made out of RNA): Unlike the other proteins, humanin does not remain in the mitochondria, and interacts

title: Neuropathy, ataxia, and retinitis pigmentosa

text: This condition is inherited in a pattern reflecting its location in mitochondrial DNA, which is also known as maternal inheritance. This pattern of inheritance applies to genes contained in mitochondrial DNA. Because egg cells, but not sperm cells, contribute mitochondria to the developing embryo, only females pass mitochondrial conditions to their children. Mitochondrial disorders can appear in every generation of a family and can affect both males and females, but fathers do not pass mitochondrial traits to their children. Most of the body's cells contain thousands of mitochondria, each with one or more copies of mitochondrial DNA. The severity of

title: Spermatocyte

text: or hermaphrodite. In hermaphrodite "C. elegans", sperm production occurs first and is then stored in the spermatheca. Once the eggs are formed, they are able to self-fertilize and produce up to 350 progeny. At puberty, spermatogonia located along the walls of the seminiferous tubules within the testis will be initiated and start to divide mitotically, forming two types of A cells that contain an oval shaped nucleus with a nucleolus attached to the nuclear envelope; one is dark (Ad) and the other is pale (Ap), which can be seen in Figure 3. The Ad cells are spermatogonia that will stay

title: Oocyte activation

text: This combination of the two genomes is called syngamy. The sperm contributes a pronucleus and a centriole to the egg. Most other components and organelles are rapidly degraded. Mitochondria are rapidly ubiquinated and destroyed. Oxidative stress theory is a hypothesis that it is evolutionarily favourable for mitochondria from the father to be destroyed, as it there is a greater possibility that the mitochondrial DNA has become mutated or damaged. This is because mtDNA is not protected by histones and has poor repair mechanisms. Due to the increased metabolic activity of the sperm compared to the egg, due to its motility,

title: Sperm

text: is formed in a unique way, which is named Cytosolic ciliogenesis, since all or part of axoneme of the sperm tail is formed in the cytoplasm or get exposed to the cytoplasm. Fawcett, D. W. (1981) Sperm Flagellum. In: The Cell. D. W. Fawcett. Philadelphia, W. B. Saunders Company. 14: pp. 604-640. Lehti, M. S. and A. Sironen (2017). "Formation and function of sperm tail structures in association with sperm motility defects." Biol Reprod 97(4): 522-536. Sperm Sperm is the male reproductive cell and is derived from the Greek word (σπέρμα) "sperma" (meaning "seed"). In the types of sexual reproduction

title: Haplogroup

text: to provide energy to the cell. Mitochondria are thought to be reduced descendants of symbiotic bacteria that were once free living. One indication that mitochondria were once free living is that each contains a circular DNA, called mitochondrial DNA (mtDNA), whose structure is more similar to bacteria than eukaryotic organisms (see endosymbiotic theory). The overwhelming majority of a human's DNA is contained in the chromosomes in the nucleus of the cell, but mtDNA is an exception. An individual inherits his or her cytoplasm and the organelles contained by that cytoplasm exclusively from the maternal ovum (egg cell); sperm only pass

title: Spermatid

text: although present in round spermatids, appears to be lost as they develop into elongated spermatids. Spermatid The spermatid is the haploid male gametid that results from division of secondary spermatocytes. As a result of meiosis, each spermatid contains only half of the genetic material present in the original primary spermatocyte. Spermatids are connected by cytoplasmic material and have superfluous cytoplasmic material around their nuclei. When formed, "early round spermatids" must undergo further maturational events to develop into spermatozoa, a process termed spermiogenesis (also termed "spermeteliosis"). The spermatids begin to grow a living thread, develop a thickened mid-piece where the mitochondria

title: Ascidiacea

text: on the vitelline coat. The sperm's mitochondria are left behind as the sperm enters and drives through the coat; this translocation of the mitochondria might provide the necessary force for penetration. The sperm swims through the perivitelline space, finally reaching the egg plasma membrane and entering the egg. This prompts rapid modification of the vitelline coat, through processes such as the egg's release of glycosidase into the seawater, so no more sperm can bind and polyspermy is avoided. After fertilization, free calcium ions are released in the egg cytoplasm in waves, mostly from internal stores. The temporary large increase in

title: Uniparental inheritance

text: transcription, they are commonly known to inherit genes from only one parental type. In the case of mitochondria, maternal inheritance is almost the exclusive form of inheritance. Although, during egg cell fertilization, mitochondria are brought into the fertilized cell both by the egg cell and the sperm, the paternal mitochondria are usually marked with ubiquitin and are later destroyed. Even if they are not destroyed, the DNA's of different mitochondria rarely genetically recombine with one another. Thus, mitochondria in most animals are inherited from the maternal type only. Like all other genetic concepts, the discovery of uniparental inheritance stems from

title: Oocyte

text: mRNAs and proteins found in the oocytes of the African clawed frog. The oocyte receives mitochondria from maternal cells, which will go on to control embryonic metabolism and apoptotic events. The partitioning of mitochondria is carried out by a system of microtubules that will localize mitochondria throughout the oocyte. In certain organisms, such as mammals, paternal mitochondria brought to the oocyte by the spermatozoon are degraded through the attachment of ubiquitinated proteins. The destruction of paternal mitochondria ensures the strictly maternal inheritance of mitochondria and mitochondrial DNA or mtDNA. In mammals, the nucleolus of the oocyte is derived solely from

title: Paternal mtDNA transmission

text: lineage far back in time. Y chromosomal DNA, paternally inherited, is used in an analogous way to trace the agnate lineage. In sexual reproduction, paternal mitochondria found in the sperm are actively decomposed, thus preventing "paternal leakage". Mitochondria in mammalian sperm are usually destroyed by the egg cell after fertilization. In 1999 it was reported that paternal sperm mitochondria (containing mtDNA) are marked with ubiquitin to select them for later destruction inside the embryo. Some in vitro fertilization (IVF) techniques, particularly intracytoplasmic sperm injection (ICSI) of a sperm into an oocyte, may interfere with this. It is now understood that

title: Seminiferous tubule

text: repair processes. Deficiencies in the enzymes employed in these repair processes may lead to infertility. Seminiferous tubule Seminiferous tubules are located within the testes, and are the specific location of meiosis, and the subsequent creation of male gametes, namely spermatozoa. The epithelium of the tubule consists of a type of sustentacular cells known as Sertoli cells, which are tall, columnar type cells that line the tubule. In between the Sertoli cells are spermatogenic cells, which differentiate through meiosis to sperm cells. Sertoli cells function to nourish the developing sperm cells. They secrete testis-determining factor, a binding protein which increases the

title: Mitochondrion

text: emphasizes the integration of the mitochondria, the product of an endosymbiotic event, into diverse cellular processes. Mitochondria (and related structures) are found in all eukaryotes (except one—the Oxymonad "Monocercomonoides" sp.). Although commonly depicted as bean-like structures they form a highly dynamic network in the majority of cells where they constantly undergo fission and fusion. The population of all the mitochondria of a given cell constitutes the chondriome. Mitochondria vary in number and location according to cell type. A single mitochondrion is often found in unicellular organisms. Conversely, the chondriome size of human liver cells is large, with about 1000–2000 mitochondria

title: Mitochondrial fusion

text: Fzo. In "Drosophila", Fzo is found in postmeiotic spermatids and the dysfunction of this protein results in male sterility. However, a deletion of Fzo1 in budding yeast results in smaller, spherical mitochondria due to the lack of mitochondrial DNA (mtDNA). The balance between mitochondrial fusion and fission in cells is dictated by the up-and-down regulation of mitofusins, OPA1/Mgm1, and Drp1/Dnm1. Apoptosis, or programmed cell death, begins with the breakdown of mitochondria into smaller pieces. This process results from up-regulation of Drp1/Dnm1 and down-regulation of mitofusins. Later in the apoptosis cycle, an alteration of OPA1/Mgm1 activity within the inner mitochondrial membrane

title: Spermatocyte

text: Spermatocyte Spermatocytes are a type of male gametocyte in animals. They derive from immature germ cells called spermatogonia. They are found in the testis, in a structure known as the seminiferous tubules. There are two types of spermatocytes, primary and secondary spermatocytes (Figure 1). Primary and secondary spermatocytes are formed through the process of spermatocytogenesis (Figure 3). Primary spermatocytes are diploid (2N) cells. After Meiosis I, two secondary spermatocytes are formed. Secondary spermatocytes are haploid (N) cells that contain half the number of chromosomes. All male animals produce spermatocytes, even hermaphrodites such as "C. elegans", which exist as a male

title: Mitochondrion

text: Mitochondrion The mitochondrion (plural mitochondria) is a double-membrane-bound organelle found in most eukaryotic organisms. Some cells in some multicellular organisms may, however, lack them (for example, mature mammalian red blood cells). A number of unicellular organisms, such as microsporidia, parabasalids, and diplomonads, have also reduced or transformed their mitochondria into other structures. To date, only one eukaryote, "Monocercomonoides", is known to have completely lost its mitochondria. The word mitochondrion comes from the Greek , , "thread", and , , "granule" or "grain-like". Mitochondria generate most of the cell's supply of adenosine triphosphate (ATP), used as a source of chemical energy.

title: Fertilisation

text: the oocyte. Fusion between the oocyte plasma membranes and sperm follows and allows the sperm nucleus, the typical centriole, and atypical centriole that is attached to the flagellum, but not the mitochondria, to enter the oocyte. The protein CD9 likely mediates this fusion in mice (the binding homolog). The egg "activates" itself upon fusing with a single sperm cell and thereby changes its cell membrane to prevent fusion with other sperm. Zinc atoms are released during this activation. This process ultimately leads to the formation of a diploid cell called a zygote. The zygote divides to form a blastocyst and,

title: Spermatid

text: Spermatid The spermatid is the haploid male gametid that results from division of secondary spermatocytes. As a result of meiosis, each spermatid contains only half of the genetic material present in the original primary spermatocyte. Spermatids are connected by cytoplasmic material and have superfluous cytoplasmic material around their nuclei. When formed, "early round spermatids" must undergo further maturational events to develop into spermatozoa, a process termed spermiogenesis (also termed "spermeteliosis"). The spermatids begin to grow a living thread, develop a thickened mid-piece where the mitochondria become localised, and form an acrosome. Spermatid DNA also undergoes packaging, becoming highly condensed. The

title: Seminiferous tubule

text: Seminiferous tubule Seminiferous tubules are located within the testes, and are the specific location of meiosis, and the subsequent creation of male gametes, namely spermatozoa. The epithelium of the tubule consists of a type of sustentacular cells known as Sertoli cells, which are tall, columnar type cells that line the tubule. In between the Sertoli cells are spermatogenic cells, which differentiate through meiosis to sperm cells. Sertoli cells function to nourish the developing sperm cells. They secrete testis-determining factor, a binding protein which increases the concentration of testosterone inside the seminiferous tubules. Embryologically, they also secrete the anti-Müllerian hormone (AMH)

title: Sperm motility

text: activated. The change in cell volume which alters intracellular ion concentration can also contribute to the activation of sperm motility. In some mammals, sperm motility is activated by increase in pH, calcium ion and cAMP, yet it is suppressed by low pH in the epididymis. The tail of the sperm - the flagellum - confers motility upon the sperm, and has three principal components: Back and forth movement of the tail results from a rhythmical longitudinal sliding motion between the anterior and posterior tubules that make up the axoneme. The energy for this process is supplied by ATP produced by

title: Sperm

text: Sperm Sperm is the male reproductive cell and is derived from the Greek word (σπέρμα) "sperma" (meaning "seed"). In the types of sexual reproduction known as anisogamy and its subtype oogamy, there is a marked difference in the size of the gametes with the smaller one being termed the "male" or sperm cell. A uniflagellar sperm cell that is motile is referred to as a spermatozoon, whereas a non-motile sperm cell is referred to as a spermatium. Sperm cells cannot divide and have a limited life span, but after fusion with egg cells during fertilization, a new organism begins developing,

title: Mitochondrion

text: up the inner chamber and that the size and shape of the mitochondria varied from cell to cell. The popular term "powerhouse of the cell" was coined by Philip Siekevitz in 1957. In 1967, it was discovered that mitochondria contained ribosomes. In 1968, methods were developed for mapping the mitochondrial genes, with the genetic and physical map of yeast mitochondrial DNA being completed in 1976. There are two hypotheses about the origin of mitochondria: endosymbiotic and autogenous. The endosymbiotic hypothesis suggests that mitochondria were originally prokaryotic cells, capable of implementing oxidative mechanisms that were not possible for eukaryotic cells; they

title: Mitochondrial disease

text: may also be the result of acquired mitochondrial dysfunction due to adverse effects of drugs, infections, or other environmental causes (see MeSH). Nuclear DNA has two copies per cell (except for sperm and egg cells), one copy being inherited from the father and the other from the mother. Mitochondrial DNA, however, is strictly inherited from the mother and each mitochondrial organelle typically contains between 2 and 10 mtDNA copies. During cell division the mitochondria segregate randomly between the two new cells. Those mitochondria make more copies, normally reaching 500 mitochondria per cell. As mtDNA is copied when mitochondria proliferate, they

title: Mitochondrion

text: compared to academic knowledge such as the role of the mitochondrion, which has been considered comparatively impractical. General Mitochondrion The mitochondrion (plural mitochondria) is a double-membrane-bound organelle found in most eukaryotic organisms. Some cells in some multicellular organisms may, however, lack them (for example, mature mammalian red blood cells). A number of unicellular organisms, such as microsporidia, parabasalids, and diplomonads, have also reduced or transformed their mitochondria into other structures. To date, only one eukaryote, "Monocercomonoides", is known to have completely lost its mitochondria. The word mitochondrion comes from the Greek , , "thread", and , , "granule" or "grain-like".

title: Spermatogenesis arrest

text: in either oligospermia or azoospermia as mentioned above. Oligospermia is when extremely low concentrations of fertile sperm are found in semen or ejaculate, while azoospermia is when no fertile sperm are found in the semen or ejaculate. Spermatogenesis is controlled by androgens, namely testosterone and follicle-stimulating hormone (FSH), these are the most important androgens that control the process. FSH uses very specific G-coupled receptors that can be found only on Sertoli cells, this hormone is secreted by the pituitary gland, located in the brain. While testosterone, is produced within the testicles by Leydig cells. This hormone is the main androgenic

title: Sperm


question: how many lines of symmetry are there in a equilateral triangle

answers: 3

title: Equilateral polygon

text: exists a principal diagonal "d" such that and a principal diagonal "d" such that Triambi are equilateral hexagons with trigonal symmetry: Equilateral polygon In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it

title: Equilateral polygon

text: Equilateral polygon In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting. All regular polygons and isotoxal polygons are equilateral. An equilateral triangle is a regular triangle

title: Equilateral triangle

text: Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Denoting the common length of the sides of the equilateral triangle as "a", we can determine using the Pythagorean theorem that: Denoting the radius of the circumscribed circle as "R", we can determine using trigonometry that: Many of these quantities

title: Equilateral triangle

text: a triangle with any two sides "a" and "b", and an angle "C" between them is Each angle of an equilateral triangle is 60°, so The sine of 60° is formula_50. Thus since all sides of an equilateral triangle are equal. Equilateral triangles have frequently appeared in man made constructions: Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon,

title: Equilateral triangle

text: An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. Its symmetry group is the dihedral group of order 6 D3.

title: Equilateral triangle

text: knowing that any one of them is true directly implies that we have an equilateral triangle. Three kinds of cevians concide, and are equal, for (and only for) equilateral triangles: Every triangle center of an equilateral triangle coincides with its centroid, which implies that the equilateral triangle is the only triangle with no Euler line connecting some of the centers. For some pairs of triangle centers, the fact that they coincide is enough to ensure that the triangle is equilateral. In particular: For any triangle, the three medians partition the triangle into six smaller triangles. Morley's trisector theorem states that,

title: Equilateral triangle

text: in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle. Napoleon's theorem states that, if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, the centers of those equilateral triangles themselves form an equilateral triangle. A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral. Viviani's theorem states that, for any interior point "P" in an equilateral triangle with distances "d", "e", and "f" from the sides and altitude "h", independent of

title: Triangle center

text: similarly constructed equilateral triangles based on the other two sides of triangle ABC. Then the lines AA', BB' and CC' are concurrent and the point of concurrence is the 1st isogonal center. Its trilinear coordinates are Expressing these coordinates in terms of "a", "b" and "c", one can verify that they indeed satisfy the defining properties of the coordinates of a triangle center. Hence the 1st isogonic center is also a triangle center. Then "f" is bisymmetric and homogeneous so it is a triangle center function. Moreover the corresponding triangle center coincides with the obtuse angled vertex whenever any vertex

title: Equilateral triangle

text: is the only triangle with integer sides and three rational angles as measured in degrees. The equilateral triangle is the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes) (the heptagonal triangle being the only obtuse one). Equilateral triangles are found in many other geometric constructs. The intersection of circles whose centers are a radius width apart is a pair of equilateral arches, each of which can be inscribed with an equilateral triangle. They form faces of regular and uniform polyhedra. Three of the five Platonic solids are composed of equilateral

title: Symmetry (geometry)

text: plane is called mirror symmetric (see mirror image). The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's mirror image. Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match.

title: Viviani's theorem

text: an equilateral triangle give coordinates for making ternary plots, such as flammability diagrams. More generally, they allow one to give coordinates on a regular simplex in the same way. The sum of the distances from any interior point of a parallelogram to the sides is independent of the location of the point. The converse also holds: If the sum of the distances from a point in the interior of a quadrilateral to the sides is independent of the location of the point, then the quadrilateral is a parallelogram. The result generalizes to any 2"n"-gon with opposite sides parallel. Since the

title: Equilateral pentagon

text: relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane. When the equilateral pentagon is dissected into triangles, two of them appear as isosceles (triangles in orange and blue) while the other one is more general (triangle in green). We assume that we are given the adjacent angles formula_1 and formula_2. According to the law of sines the length of the line dividing the green and blue triangles is: The square of the length of the line dividing the orange and green triangles is: According to the law of cosines, the cosine

title: Central line (geometry)

text: "a", "b", "c" ) : "v" ( "a", "b", "c" ) : "w" ( "a", "b", "c" ) ) be a triangle center. The line whose equation is is the trilinear polar of the triangle center "X". Also the point "Y" = ( 1 / "u" ( "a", "b", "c" ) : 1 / "v" ( "a", "b", "c" ) : 1 / "w" ( "a", "b", "c" ) ) is the isogonal conjugate of the triangle center "X". Thus the central line given by the equation is the trilinear polar of the isogonal conjugate of the triangle center (

title: Symmetry (geometry)

text: A circle has infinitely many axes of symmetry passing through its center, for the same reason. If the letter T is reflected along a vertical axis, it appears the same. This is sometimes called vertical symmetry. One can better use an unambiguous formulation; e.g., "T has a vertical symmetry axis" or "T has left-right symmetry". The triangles with reflection symmetry are isosceles, the quadrilaterals with this symmetry are the kites and the isosceles trapezoids. For each line or plane of reflection, the symmetry group is isomorphic with C (see point groups in three dimensions), one of the three types of

title: Triangle center

text: of an isosceles triangle must lie on its line of symmetry. For an equilateral triangle all three components are equal so all centers coincide with the centroid. So, like a circle, an equilateral triangle has a unique center. This is readily seen to be a triangle center function and (provided the triangle is scalene) the corresponding triangle center is the excenter opposite to the largest vertex angle. The other two excenters can be picked out by similar functions. However as indicated above only one of the excenters of an isosceles triangle and none of the excenters of an equilateral triangle

title: Triangle

text: their internal angles, measured here in degrees. A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral. Triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise (see Non-planar triangles, below). In rigorous treatments, a triangle is therefore called a "2-simplex" (see also Polytope). Elementary facts about triangles were presented by Euclid in books 1–4

title: Equilateral triangle

text: root formula_33 of 1 the triangle is equilateral if and only if Given a point "P" in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when "P" is the centroid. In no other triangle is there a point for which this ratio is as small as 2. This is the Erdős–Mordell inequality; a stronger variant of it is Barrow's inequality, which replaces the perpendicular distances to the sides with the distances from "P"

title: Triangle center

text: of all is the line ("t","t","t") which corresponds to the set of all equilateral triangles. The point of concurrence of the perpendicular bisectors of the sides of triangle ABC is the circumcenter. The trilinear coordinates of the circumcenter are Let "f"("a","b","c") = "a"("b" + "c" − "a"). Then so f is a triangle center function. Since the corresponding triangle center has the same trilinears as the circumcenter it follows that the circumcenter is a triangle center. Let A'BC be the equilateral triangle having base BC and vertex A' on the negative side of BC and let AB'C and ABC' be

title: Triangle

text: given by and both again holding if and only if the triangle is equilateral. There are infinitely many lines that bisect the area of a triangle. Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter. There can be one, two, or three of these for any given triangle. The formulas in this section are true for all Euclidean triangles. The medians

title: Reflection symmetry

text: think about the symmetric function is that if the shape were to be folded in half over the axis, the two halves would be identical: the two halves are each other's mirror images. Thus a square has four axes of symmetry, because there are four different ways to fold it and have the edges all match. A circle has infinitely many axes of symmetry. Triangles with reflection symmetry are isosceles. Quadrilaterals with reflection symmetry are kites, (concave) deltoids, rhombuses, and isosceles trapezoids. All even-sided polygons have two simple reflective forms, one with lines of reflections through vertices, and one through

title: Equilateral triangle

text: have simple relationships to the altitude ("h") of each vertex from the opposite side: In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors, and the medians to each side coincide. A triangle "ABC" that has the sides "a", "b", "c", semiperimeter "s", area "T", exradii "r", "r", "r" (tangent to "a", "b", "c" respectively), and where "R" and "r" are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true. Thus these are properties that are unique to equilateral triangles, and

title: Weyl group

text: are just lines, and the Weyl group is the symmetry group of an equilateral triangle, as indicated in the figure. As a group, formula_9 is isomorphic to the permutation group on three elements, which we may think of as the vertices of the triangle. Note that in this case, formula_9 is not the full symmetry group of the root system; a 60-degree rotation preserves formula_1 but is not an element of formula_9. We may consider also the formula_21 root system. In this case, formula_2 is the space of all vectors in formula_23 whose entries sum to zero. The roots consist

title: The Method of Mechanical Theorems

text: fulcrum. The reason is that if the triangle is divided into infinitesimal line segments parallel to "E", each segment has equal length on opposite sides of the median, so balance follows by symmetry. This argument can be easily made rigorous by exhaustion by using little rectangles instead of infinitesimal lines, and this is what Archimedes does in On the Equilibrium of Planes. So the center of mass of a triangle must be at the intersection point of the medians. For the triangle in question, one median is the line "y" = "x"/2, while a second median is the line "y"

title: Equilateral triangle

text: terms of side length "a" can be derived directly using the Pythagorean theorem or using trigonometry. The area of a triangle is half of one side "a" times the height "h" from that side: The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base "a", and the hypotenuse is the side "a" of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem so that Substituting "h" into the area formula (1/2)"ah" gives the area formula for the equilateral triangle: Using trigonometry, the area of

title: Morley's trisector theorem

text: triangle and "A, B," and "C" are the angles of the original triangle. Since the area of an equilateral triangle is formula_43 the area can be expressed as Morley's theorem entails 18 equilateral triangles. The triangle described in the trisector theorem above, called the first Morley triangle, has vertices given in trilinear coordinates relative to a triangle "ABC" as follows: Another of Morley's equilateral triangles that is also a central triangle is called the second Morley triangle and is given by these vertices: The third of Morley's 18 equilateral triangles that is also a central triangle is called the third

title: Equilateral triangle

text: to the points where the angle bisectors of ∠"APB", ∠"BPC", and ∠"CPA" cross the sides ("A", "B", and "C" being the vertices). For any point P in the plane, with distances "p", "q", and "t" from the vertices A, B, and C respectively, For any point P on the inscribed circle of an equilateral triangle, with distances "p", "q", and "t" from the vertices, and For any point P on the minor arc BC of the circumcircle, with distances "p", "q", and "t" from A, B, and C respectively, and moreover, if point D on side BC divides PA into

title: Isodynamic point

text: across line formula_9 (the intersection of circles centered at formula_49 and formula_50 through formula_40), and constructing an equilateral triangle inwards on side formula_9 of the triangle (the apex formula_53 of this triangle is the intersection of two circles having formula_9 as their radius). The line formula_55 crosses the similarly constructed lines formula_56 and formula_57 at the first isodynamic point. The second isodynamic point may be constructed similarly but with the equilateral triangles erected outwards rather than inwards. Alternatively, the position of the first isodynamic point may be calculated from its trilinear coordinates, which are The second isodynamic point uses trilinear

title: Equilateral triangle

text: area of all those circumscribed around a given circle is equilateral. The ratio of the area of the incircle to the area of an equilateral triangle, formula_30, is larger than that of any non-equilateral triangle. The ratio of the area to the square of the perimeter of an equilateral triangle, formula_31 is larger than that for any other triangle. If a segment splits an equilateral triangle into two regions with equal perimeters and with areas "A" and "A", then If a triangle is placed in the complex plane with complex vertices "z", "z", and "z", then for either non-real cube

title: Similarity system of triangles

text: Napoleon's theorem. He then built off Napoleon by proving that if an equilateral triangle was constructed with equilateral triangles incident on each vertex, the midpoints of the connecting lines between the non-incident vertices of the outer three equilateral triangles create an equilateral triangle. Other similar work was done by the French Geometer Thébault in his proof that given a parallelogram and squares that lie on each side of the parallelogram, the centers of the squares create a square. Mauldon then analyzed coplanar sets of triangles, determining if they were similarity systems based on the criterion, if all but one of

title: Equilateral polygon

text: with 60° internal angles. An equilateral quadrilateral is called a rhombus, an isotoxal polygon described by an angle α. It includes the square as a special case. A convex equilateral pentagon can be described by two angles α and β, which together determine the other angles. Concave equilateral pentagons exist, as do concave equilateral polygons with any larger number of sides. An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon (a polygon that is both equilateral and equiangular). A tangential polygon (one that has an incircle tangent to all its sides) is equilateral

title: Equilateral triangle