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Lune Of Hippocrates
In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune (mathematics), lune bounded by Circular arc, arcs of two circles, the smaller of which has as its diameter a Chord (geometry), chord spanning a right angle on the larger circle. Equivalently, it is a non-Convex set, convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It was the first curved figure to have its exact area calculated mathematically.. Translated from Postnikov's 1963 Russian book on Galois theory. History Hippocrates wanted to solve the classic problem of squaring the circle, i.e. constructing a square by means of straightedge and compass, having the same area as a given circle. He proved that the lune bounded by the arcs labeled ''E'' and ''F'' in the figure has the same area as triangle ''ABO''. This afforded some hope of solving the circle-squaring problem, since the lune is bounded only by arcs of circles. Thomas Little Heath, Heath concl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lune
Lune may refer to: Rivers *River Lune, in Lancashire and Cumbria, England *River Lune, Durham, in County Durham, England *Lune (Weser), a 43 km-long tributary of the Weser in Germany *Lune River (Tasmania), in south-eastern Tasmania, Australia Place names *Lune Aqueduct, east of the city of Lancaster in Lancashire, England *Lune Forest, Site of Special Scientific Interest in Cumbria, England *Lune River, Tasmania, Australia, a town near the mouth of the river of the same name *Lüne, a former village near Lüneburg in Saxony where Charlemagne mustered his troops against the Avars Mathematics * Lune (geometry), a 2-dimensional arc-defined convex-concave area ** Lune of Hippocrates, in geometry, a plane region bounded by arcs of circles and amenable to quadrature * Spherical lune, a 3-dimensional lune People *Ted Lune (born 1920), British actor, played Private Len Bone in the TV series ''The Army Game'' *Dragutin Jovanović-Lune (1892–1932), nicknamed Lune (Луне), Serbian gue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopædia Britannica
The (Latin for "British Encyclopædia") is a general knowledge English-language encyclopaedia. It is published by Encyclopædia Britannica, Inc.; the company has existed since the 18th century, although it has changed ownership various times through the centuries. The encyclopaedia is maintained by about 100 full-time editors and more than 4,000 contributors. The 2010 version of the 15th edition, which spans 32 volumes and 32,640 pages, was the last printed edition. Since 2016, it has been published exclusively as an online encyclopaedia. Printed for 244 years, the ''Britannica'' was the longest running in-print encyclopaedia in the English language. It was first published between 1768 and 1771 in the Scottish capital of Edinburgh, as three volumes. The encyclopaedia grew in size: the second edition was 10 volumes, and by its fourth edition (1801–1810) it had expanded to 20 volumes. Its rising stature as a scholarly work helped recruit eminent con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikolai Chebotaryov
Nikolai Grigorievich Chebotaryov (often spelled Chebotarov or Chebotarev, uk, Мико́ла Григо́рович Чеботарьо́в, russian: Никола́й Григо́рьевич Чеботарёв) ( – 2 July 1947) was a Ukrainian and Soviet mathematician. He is best known for the Chebotaryov density theorem. He was a student of Dmitry Grave, a Russian mathematician. Chebotaryov worked on the algebra of polynomials, in particular examining the distribution of the zeros. He also studied Galois theory and wrote a textbook on the subject titled ''Basic Galois Theory''. His ideas were used by Emil Artin to prove the Artin reciprocity law. He worked with his student Anatoly Dorodnov on a generalization of the quadrature of the lune, and proved the conjecture now known as the Chebotaryov theorem on roots of unity. Early life Nikolai Chebotaryov was born on 15 June 1894 in Kamianets-Podilskyi, Russian Empire (now in Ukraine). He entered the department of physics and ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isosceles Right Triangle
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of Natural number, whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometry, geometric problems without resorting to more advanced methods. Angle-based "Angle-based" special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degree (angle), degrees or radians, is e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut-the-knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and Mathematics, senior instructor at Hebrew University and software consultant at Ben Gurion University. He wrote extensively about arithmetic, probability, algebra, geometry, trigonometry and mathematical games. He was known for his contribution to heuristics and mathematics education, creating and maintaining the mathematically themed educational website ''Cut-the-Knot'' for the Mathematical Association of America (MAA) Online. He was a pioneer in mathematical education on the internet, having started ''Cut-the-Knot'' in October 1996.Interview with Alexander ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumcircle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm. Even if a polygon has a circumscribed circle, it may be different from its minimum bounding circle. For example, for an obtuse triangle, the minimum bounding circle has the longest sid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
