In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows; the hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. If the plane intersects both halves of the double cone but does not pass through the apex of the cones the conic is a hyperbola. Hyperbolas arise in many ways: as the curve representing the function f = 1 / x in the Cartesian plane, as the path followed by the shadow of the tip of a sundial, as the shape of an open orbit, such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or, more any spacecraft exceeding the escape velocity of the nearest planet, as the path of a single-apparition comet, as the scattering trajectory of a subatomic particle, in radio navigation, when the difference between distances to two points, but not the distances themselves, can be determined,and so on.
Each branch of the hyperbola has two arms which become straighter further out from the center of the hyperbola. Diagonally opposite arms, one from each branch, tend in the limit to a common line, called the asymptote of those two arms. So there are two asymptotes, whose intersection is at the center of symmetry of the hyperbola, which can be thought of as the mirror point about which each branch reflects to form the other branch. In the case of the curve f = 1 / x the asymptotes are the two coordinate axes. Hyperbolas share many of the ellipses' analytical properties such as eccentricity and directrix; the correspondence can be made with nothing more than a change of sign in some term. Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids, hyperbolic geometry, hyperbolic functions, gyrovector spaces; the word "hyperbola" derives from the Greek ὑπερβολή, meaning "over-thrown" or "excessive", from which the English term hyperbole derives. Hyperbolae were discovered by Menaechmus in his investigations of the problem of doubling the cube, but were called sections of obtuse cones.
The term hyperbola is believed to have been coined by Apollonius of Perga in his definitive work on the conic sections, the Conics. The names of the other two general conic sections, the ellipse and the parabola, derive from the corresponding Greek words for "deficient" and "applied"; the rectangle could be shorter than the segment or exceed the segment. A hyperbola can be defined geometrically as a set of points in the Euclidean plane: A hyperbola is a set of points, such that for any point P of the set, the absolute difference of the distances | P F 1 |, | P F 2 | to two fixed points F 1, F 2, is constant denoted by 2 a, a > 0: H =. The midpoint M of the line segment joining the foci is called the center of the hyperbola; the line through the foci is called the major axis. It contains the vertices V V 2, which have distance a to the center; the distance c of the foci to the center is called linear eccentricity. The quotient c a is the eccentricity e; the equation | | P F 2 | − | P F 1 | | = 2 a can be viewed in a different way: If c 2 is the circle with midpoint F 2 and radius 2 a the distance of a point P of the right branch to the circle c 2 equals the distan
Mike Compton is an American bluegrass mandolin player and former protégé of the Father of Bluegrass, Bill Monroe. He is considered a modern master of bluegrass mandolin. Befriended and mentored by Bill Monroe, the acknowledged Father of Bluegrass Music, Mike Compton is one of today's foremost interpreters of Monroe's genre-creating mandolin style. Mandolin students from around the world make the pilgrimage to his annual Monroe Mandolin Camp in Nashville, where Compton and a select handful of other experts teach everything from the basics of bluegrass mandolin to the most intimate details of Monroe's endlessly inspiring mandolin style. Mike Compton's decades of touring and recording — with musical luminaries ranging from rockstars Sting, Gregg Allman, Elvis Costello, to straight-from-the-still acoustic legends such as John Hartford, Doc Watson, Peter Rowan, Ralph Stanley, David Grisman — have established Compton as a true master of the modern American mandolin and a premier interpreter of roots and Americana musical styles.
Compton's master of mandolin is at once exceptional. A compelling entertainer either alone or with a group, his skills as a singer, instrumentalist and accompanist make him in-demand as a band member and ensemble player at festivals and concert halls, recording sessions, music workshops, as a private instructor. With more than 120 recordings in his discography, including work with Willie Nelson, Dolly Parton, Patty Loveless, Compton has helped keep mandolin a cool, relevant sound as the modern musical styles ebb and evolve to reach an broadening audience. A native of (Mississippi, Compton picked up the mandolin in his teens and absorbed the area's native blues, old-time country, bluegrass sounds. Compton learned music from an early age. Compton began playing the trombone but switched to guitar instead and to mandolin playing old-time music with his cousin, he became interested in bluegrass music and learned to play like Bill Monroe. At the Bean Blossom Bluegrass Festival in 1975, he met Monroe.
After Compton had finished his education at the Meridian Junior College he gravitated to Nashville and joined Hubert Davis and the Season Travelers in 1977. Four years in 1981, he left Davis' band, he spent the early 1980s working as a cook, a printer, as a part-time musician. In the mid 1980s, Compton helped found one of the 20th Century's most admired and influential bluegrass groups, the iconic Nashville Bluegrass Band. After a bus accident, which left Mark Hembree injured, Compton reassessed his life temporarily quitting the business and moved to the Catskills, working as a cottage caretaker. Compton continued to dabble with music recording albums with various artists, in 1995, he recorded with Bill Monroe's Bluegrass Boys. Compton couldn't stay away from his craft and In the mid 1990s, he joined John Hartford in touring, recording several albums together with him. In 2000, Compton returned once again to the Nashville Bluegrass Band and continues to tour and play with this group, now 30+ years in the business.
Compton tours internationally with the brother duet partnership duo of Compton & Newberry, with the super-group Helen Highwater Stringband, as a soloist. When A-list Americana producer T Bone Burnett needed experts in authentic rural musical styles to anchor the landmark O Brother, Where Art Thou? movie project and subsequent tour, he called upon Compton's unique knowledge and signature mandolin style to authenticate the Soggy Bottom Boys' roots sound. That Grammy-Award Album of the Year winning album went on to sell seven million copies, sparked a global revival in old-time and bluegrass musical styles. Connoisseur of hand-painted vintage silk ties, popularizer of the denim overall urban fashion statement, lover of iconic men's hats and curator of oddball official days, Mike Compton thrives at the intersection of traditional funk and modern authenticity. Skilled in bluegrass, old-time string band music, country blues, roots Americana styles, much more, Compton soars beyond easy categorization as an acoustic mandolin player and singer.
Gifted at tastefully incorporating rural, roots-based lead and rhythm mandolin styles into modern Americana music, Compton's unique musical skill set allows him to entertain audiences ranging from rockers and urban hipsters to die-hard country and bluegrass fans. In 2001 and 2002, Compton was nominated as IBMA Mandolinist of the Year. In 2002, O Brother, Where Art Thou?, an album containing one of his songs, was awarded the Grammy Award for best album. In recognition of his achievements, he received a commendation from the Mississippi State Senate. Bluegrass music Country music Mandolin Grammy Awards International Bluegrass Music Association Americana Music Association Grand Ole Opry Carlin, Country Music: A Biographical Dictionary, Taylor & Francis Rosenberg, Neil V. - Wolfe, Charles K. The Music of Bill Monroe, University of Illinois Press Official site Mandolin Magazine Article Mike Compton biography at nashvillebluegrassband.net Mike Compton at AllMusic Mike Compton discography at Discogs
Captain Sir Elias Wynne Cemlyn-Jones, known as Wynne Cemlyn-Jones, was a Welsh Liberal Party politician. He was the son of Anglesey farmer John Cemlyn-Jones of Penmaenmawr, he was educated at Shrewsbury School. In 1914, he married Muriel Gwendolin Owen, they had two daughters. His wife died in 1930. In 1912, he became Private Secretary to Anglesey's Liberal MP Sir Ellis Griffith, when he was appointed Under-Secretary of State for the Home Department, he supported Griffith in his task of steering the Welsh Disestablishment Bill through the House of Commons. He was admitted to the Middle Temple on 16 July 1913. In 1914, after the bill was passed and war broke out, he signed up to serve in the Royal Welch Fusiliers, he was Called to the Bar at Middle Temple on 17 November 1919 and was appointed a Member of the Order of the British Empire in the 1919 New Year Honours. His first introduction to politics had come from working for his local Liberal MP, Sir Ellis Griffith, he got involved in civic affairs on Anglesey.
In 1919 he was elected to Anglesey County Council. He served on this body as a Councillor, until he was appointed to it as an Alderman in 1928, he was Liberal candidate for the Unionist seat of South Croydon at the 1923 General Election. It was not a promising seat for the Liberals, whose candidate had polled 25.2% in 1922, finishing third. He was unable to advance the Liberal position, he became Chairman of Anglesey County Council. He was Liberal candidate for the Radnor division at the 1929 General Election; this was a far better prospect as the Liberals had held the seat up until the 1924 General Election when they narrowly lost the seat to the Unionists in a close three-way battle, with Labour third. He managed to increase the Liberal share of the vote, but Labour came through to take the seat from third place, he was Chairman of the Selection Committee of Anglesey County Council. He was Vice-President of County Councils Association, he was knighted for public services in Anglesey. He died at Llandudno Hospital in Wales, age 79