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In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).
The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Greek (ankylοs), meaning "crooked, curved," and the English word "ankle". Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".
Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
==Measuring angles== Termination of X-axis in anticlockwise direction is called angle. Two angles are sometimes called congruent if there exists an isometry that transforms one of the angles into the other angle. The size of an angle is normally characterized by the smallest positive rotation that maps one of the rays into the other. Two angles are congruent if and only if they correspond to the same (smallest positive) rotation. Thus an angle as two rays is characterized by an angle of rotation. To avoid confusion when no isometry exists between particular representations of angles, angles that Euclid called "equal" are described as "equal in measure".
In many geometrical situations, angles that differ by an exact multiple of a full circle are effectively equivalent (it makes no difference how many times a line is rotated through a full circle because it always ends up in the same place). However, this is not always the case. For example, when tracing a curve such as a spiral using polar coordinates, an extra full turn gives rise to a quite different point on the curve.
In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the circle r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen):
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The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered.
With the notable exception of the radian, most units of angular measurement are defined such that one full circle (i.e. one revolution) is equal to n units, for some whole number n. For example, in the case of degrees, A full circle of n units is obtained by setting in the formula above. (Proof. The formula above can be rewritten as One full circle, for which units, corresponds to an arc equal in length to the circle's circumference, which is 2πr, so . Substituting n for θ and 2πr for s in the formula, results in )
The angle of the equilateral triangle is 1/6 of a full circle. It was the unit used by the Babylonians, and is especially easy to construct with ruler and compasses. The degree, minute of arc and second of arc are sexagesimal subunits of the Babylonian unit. 1 Babylonian unit = 60° = π/3 rad ≈ 1.047197551 rad.
In rational geometry the spread between two lines is defined at the square of sine of the angle between the lines. Since the sine of an angle and the sine of its supplementary angle are the same any angle of rotation that maps one of the lines into the other leads to the same value of the spread between the lines.
These measurements clearly depend on the individual subject, and the above should be treated as rough approximations only.
In geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC (i.e. the lines from point A to point B and point A to point C) is denoted ∠BAC or BÂC. Sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex ("angle A").
Potentially, an angle denoted, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C, the anticlockwise angle from B to C, the clockwise angle from C to B, or the anticlockwise angle from C to B, where the direction in which the angle is measured determines its sign (see Positive and negative angles). However, in many geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant, and no ambiguity arises. Otherwise, a convention may be adopted so that ∠BAC always refers to the anticlockwise (positive) angle from B to C, and ∠CAB to the anticlockwise (positive) angle from C to B.
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and
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for two numbers x and y. So an angle in the Euclidean plane can be legitimately given by two numbers x and y.
To the ratio y/x there correspond two angles in the geometric range 0 < θ < 2π, since
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This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.
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In a complex inner product space, the expression for the cosine above may give non-real values, so it is replaced with
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or, more commonly, using the absolute value, with
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The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.
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in a Hilbert space can be extended to subspaces of any finite dimensions. Given two subspaces with , this leads to a definition of angles called canonical or principal angles between subspaces.
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In astronomy, a given point on the celestial sphere (that is, the apparent position of an astronomical object) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system. Astronomers measure the angular separation of two stars by imagining two lines through the centre of the Earth, each intersecting one of the stars. The angle between those lines can be measured, and is the angular separation between the two stars.
Astronomers also measure the apparent size of objects as an angular diameter. For example, the full moon has an angular diameter of approximately 0.5°, when viewed from Earth. One could say, "The Moon subtends an angle of half a degree." The small-angle formula can be used to convert such an angular measurement into a distance/size ratio.
Category:Elementary geometry Category:Trigonometry
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Name | Kurt Angle |
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Names | Kurt Angle |
Birth date | December 09, 1968 |
Birth place | Mt. Lebanon, Pennsylvania |
Resides | Pittsburgh, Pennsylvania |
Billed | Pittsburgh, Pennsylvania |
Trainer | Dave SchultzDory Funk, Jr.Tom Prichard |
Debut | October 15, 1998 |
Kurt Steven Angle (born December 9, 1968) is an American professional wrestler, actor and 1996 Olympic gold medalist. He is currently under contract with Total Nonstop Action Wrestling, where he is a former four-time TNA World Heavyweight Champion, and recognized by the promotion as a 13-time World Champion. He is best known for his time in World Wrestling Federation / Entertainment (WWF/E).
Angle was involved in amateur wrestling during both high school and college. In college at Clarion University of Pennsylvania, he won numerous accolades, including being a two-time National Collegiate Athletic Association Division I champion. After graduating, he won the 1995 World Championship tournament. Angle then competed in the 1996 Summer Olympics in Atlanta, Georgia, where he won a gold medal in heavyweight freestyle wrestling.
Initially turning down an offer to join the World Wrestling Federation (WWF), Angle signed a multi-year contract with the company in 1998. His first big push in the company was in February 2000, when he held both the European Championship and the Intercontinental Championship at the same time. Not long after, Angle began pursuing the WWF Championship. He continued to be a part of main event matches until August 2006, when Angle was granted a release from his contract. Throughout his tenure in the company, he was a six-time world champion (four-time WWF/E Champion, World Heavyweight Champion and WCW Champion), he also held the United States Championship, Intercontinental Championship, European Championship, Hardcore Championship and WWE Tag Team Champion once each. In addition, he was the winner of the King of the Ring tournament in 2000, the tenth Triple Crown Champion, and the fifth Grand Slam Champion.
After leaving WWE, Angle joined Total Nonstop Action Wrestling (TNA), where he became the second wrestler in TNA to win TNA's Triple Crown and the first man to hold all three TNA championships simultaneously. While in TNA, his real-life wife Karen began accompanying him to the ring and playing a part in his on-screen storylines. Angle has also made appearances for New Japan Pro Wrestling as well as Inoki Genome Federation, where he held their version of the IWGP Heavyweight Championship. In addition, he is a three-time TNA World Heavyweight Champion, the second Triple Crown winner in TNA history—being the only one to hold all the required titles at once (while also holding the IWGP Title, making him a quadruple champion for a brief time). Angle is the only wrestler in history to be a Triple Crown winner in both WWE and TNA, and is also a two time King of the Mountain winner, winning at the 2007 and 2009 Slammiversary PPV event. In 2010 the Wrestling Observer Newsletter named Angle the Wrestler of the Decade of the 2000s.
Angle started amateur wrestling at the age of six. where he won varsity letters in football and wrestling and was an All-State linebacker. Angle also placed third in the state wrestling tournament as a junior and was the 1987 Pennsylvania State Wrestling Champion as a senior.
Upon graduating from high school, Angle attended the Clarion University of Pennsylvania, where he continued to wrestle at an amateur level.
After graduating from college, Angle continued to wrestle. In 1995, he won a gold medal at the World Championships in Atlanta, Georgia. Following this victory, Angle began preparing for the 1996 Summer Olympics under Dave Schultz at the Pennsylvanian Foxcatcher Club, In the fall of 2006, Angle stated that he temporarily became addicted to the analgesic Vicodin after injuring his neck. defeating the Iranian Abbas Jadidi by officials' decision after the competitors wrestled to an eight minute, one-one draw. The bout saw Jadidi earn a point after two minutes and 46 seconds by turning Angle, and Angle earning a point of his own with a takedown after three minutes and eleven seconds. The officials' decision was protested by Jadidi.
In 1997, following the incident, Angle worked for a year as a sportscaster on Pittsburgh's local Fox affiliate WPGH-TV. billing himself as the "Eurocontinental Champion". He dropped both of his titles without ever conceding a fall in a two falls Triple Threat match with Chris Benoit and Chris Jericho at Wrestlemania 2000. The match had been agreed on to Angle's behalf by his mentor, Bob Backlund.
After dropping the WWE United States Championship to Edge, the duo were booked into a lengthy feud. During this feud, Edge started the "you suck" chants every time Angle entered a WWE ring, usually in tune with Angle's entrance music. He continued to feud with Michaels upon being drafted from SmackDown! to Raw in the 2005 WWE Draft Lottery, After Hiroshi Tanahashi retained the IWGP Heavyweight Championship against Nakamura in the main event, Angle challenged him for the title, which Tanahashi accepted. Angle was then the special enforcer for the Title vs. Career match between Jarrett and Sting at Bound for Glory, but, as part of the worked finish, he took out referee Rudy Charles and assumed the referee's role for the rest of the match-up.
At Final Resolution, Angle was booked to defeat Samoa Joe in a thirty minute Iron Man match 3–2 to earn a shot at the NWA World Heavyweight Championship at Against All Odds, At the PPV event, Cage, still holding the physical NWA Championship belt, defended what was billed as the "World Heavyweight Championship" against Angle and Sting. Angle was the victor of said contest by making Sting submit, who had technically just pinned Cage, and was announced as the new "World Heavyweight Champion". At the event, Angle became the TNA World Heavyweight Champion by defeating Cage, Samoa Joe, A.J. Styles, and Chris Harris. On the following episode of Impact!, Joe (now holding the X Division and Tag Team Championships, with Angle holding the TNA and (IGF recognized) IWGP Heavyweight Championships) challenged Angle to a match at Hard Justice where it was winner take all. Angle, however, dropped both the X Division and Tag Team Titles to Jay Lethal and Team Pacman, respectively, at No Surrender. At Bound for Glory, Angle lost the TNA World Title to Sting, but won it back on the October 25 edition of Impact!.
Angle then joined forces with A.J. Styles and Tomko as The Angle Alliance at Turning Point against Samoa Joe, Kevin Nash, and Scott Hall. Styles had planned for Christian's Coalition and The Angle Alliance to team up together, but Christian Cage demanded to be the leader of The Angle Alliance after Cage denied Angle's request of being his "lackey". At Final Resolution, Angle successfully defended the TNA World Heavyweight Championship against Cage due to interference from Styles and again at Against All Odds with help from Tomko. At Lockdown, Angle lost the TNA World Heavyweight Championship to Samoa Joe after being pinned.
He married Karen Angle In the spring of 2008, Angle made his film debut in the short film Chains. He played a racist prison deputy, credited as The Deputy. – innovated
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Category:1968 births Category:American professional wrestlers Category:American sport wrestlers Category:Living people Category:Olympic athletes who wrestled professionally Category:Olympic gold medalists for the United States Category:Olympic wrestlers of the United States Category:People from Mt. Lebanon, Pennsylvania Category:Professional wrestling executives Category:Sportspeople from Pennsylvania Category:Wrestlers at the 1996 Summer Olympics Category:Clarion University of Pennsylvania alumni Category:Pennsylvania Republicans Category:Fictional kings
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Name | Sharron Angle |
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Office | Member of the Nevada Assembly from the 26th District |
Term start | January 3, 2003 |
Term end | January 3, 2007Politician |
Party | Republican |
Alma mater | University of Nevada, Reno |
Spouse | Ted Angle |
Religion | Southern Baptist |
Website | sharronangle.com |
In 2005, she was the sole voter against a bill that split the property tax abatement by applying a 3% rate to residential and 8% rate to commercial property.
On October 3 Nevada's largest newspaper Las Vegas Review-Journal endorsed her bid for U.S. Senate against Reid.
Angle has repeatedly "refuted the rumor that she's a Scientologist",
After President Obama secured agreement by BP to commit $20 billion to compensate victims of the Deepwater Horizon oil spill, Angle denounced the arrangement, calling it a "slush fund." When she was criticized for her comment, however, she retracted the term "slush fund" and said that BP should pay for the consequences of the spill.
Congressman Jim Clyburn said in January 2011 that "Sharron Angle's endorsement of 'Second Amendment remedies' in her losing Nevada campaign against Senate Majority Leader Harry Reid contributed to the shooting of Rep. Gabrielle Giffords." Columnist E.J. Dionne did not "blame" Angle, but he did point out the connection between her call for "Second Amendment remedies" and the 2011 Tucson shooting. CBS News, in a "nationwide telephone poll" of 673 adults, with a margin of error of 4 %, found that "'57 percent of respondents said the harsh political tone had nothing to do with the shooting, compared to 32 percent who felt it did.'"
Category:Candidates in United States elections, 2006 Category:Candidates in United States elections, 2010 Category:Southern Baptists Category:Members of the Nevada Assembly Category:Nevada Republicans Category:People from Klamath Falls, Oregon Category:People from Reno, Nevada Category:Tea Party movement Category:Women state legislators in Nevada Category:1949 births Category:Living people
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Name | John Cena |
---|---|
Names | John CenaMr. PThe Prototype |
Height | |
Birth date | April 23, 1977 |
Birth place | West Newbury, Massachusetts |
Resides | Tampa, FloridaWest Newbury, Massachusetts (WWE) |
Trainer | Ultimate Pro WrestlingOhio Valley Wrestling |
Debut | 2001 |
Cena started his professional wrestling career in 2000, wrestling for Ultimate Pro Wrestling, where he held the UPW Heavyweight Championship. In 2001, Cena signed a contract with the World Wrestling Federation (WWF) and was sent to Ohio Valley Wrestling (OVW) where he held the OVW Heavyweight Championship and the OVW Southern Tag Team Championship (with Rico Constantino).
Outside of wrestling, Cena has released the rap album You Can't See Me, which debuted at #15 on the US Billboard 200 chart, and starred in the feature films The Marine (2006), 12 Rounds (2009), and Legendary (2010). the son of Carol and John Cena, Sr. which is still used on some of his WWE merchandise. While in UPW, Cena held the UPW Heavyweight Championship for just shy of a month in April 2000. In 2001, he signed a developmental contract with the World Wrestling Federation (WWF) and was assigned to its developmental territory Ohio Valley Wrestling (OVW).
Cena made his television debut answering an open challenge by Kurt Angle on June 27, 2002. Cena ultimately lost to a hard amateur wrestling-style pin. In October, Cena and Billy Kidman took part in a tag team tournament to crown the first WWE Tag Team Champions of the SmackDown! brand, losing in the first round.
Shortly after the Kidman attack, on a Halloween themed episode of SmackDown, Cena dressed as Vanilla Ice performing a freestyle rap. The next week, Cena received a new character: a rapper who cut promos while rhyming. As the gimmick grew, Cena began adopting a variant of the 1980s WWF logo — dropping the "F" — as his "signature symbol", along with the slogan " Life". Buchanan was later replaced by Red Dogg, until he was sent to the Raw brand in February.
For the first half of 2003, Cena sought the WWE Championship and chased the reigning champion, Brock Lesnar, performing weekly "freestyles" challenging him to matches. until Cena reclaimed the original belt in an "I Quit" match at Judgment Day. After winning the championship, Cena began feuding with Triple H, which the crowd began booing Cena and cheering the intended Triple H.
show.]] In July, after Edge won the championship from Van Dam in a Triple Threat match that also involved Cena, — he introduced his own version of Cena's "custom" belt, this one with his logo placed on the spinner. Federline appeared at Cyber Sunday to hit Cena with the World Heavyweight Chamionship during the match, helping King Booker retain his championship. Two weeks later, in a video update on WWE.com, Dr. Andrews and Cena's physical trainer both said that he was several weeks ahead of where he was expected to be in his rehabilitation at that time. renewing their feud from 2005. Cena defeated JBL at Judgment Day and then at One Night Stand in a First Blood match. The following day, Cena and Otunga lost the Tag Team Championship to fellow Nexus members Heath Slater and Justin Gabriel, when Barrett ordered Otunga to lay down and lose the title. Once the film was released on DVD, it fared better, making $30 million in rentals in the first twelve weeks.
His second film, also produced by WWE Studios, was 12 Rounds.
Cena hosted the Australian Nickelodeon Kids Choice Awards with Natalie Bassingthwaighte on October 11, 2008 in Melbourne, Australia. Tampa Bay Rays, Cena collects muscle cars and has over 20, some of which are one-of-a-kind. / STF–U – 2005–Present; WWE
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Name | Brock Lesnar |
---|---|
Birth name | Brock Edward Lesnar |
Birth date | July 12, 1977 |
Birth place | Webster, South Dakota, United States |
Other names | The Next Big Thing |
Residence | Alexandria, Minnesota |
Nationality | American |
Height | Striking Coach: Erik Paulson Boxing: Peter WelchJiu-Jitsu: Rodrigo Medeiros He played during the preseason for the Minnesota Vikings, but ended up being a late cut. Lesnar returned to professional wrestling at the end of 2005, and joined New Japan Pro Wrestling, where he won the IWGP Heavyweight Championship in his first match. He was stripped of the title in July 2006, although he held the physical belt until June 2007. |
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