Jordan's Inequality
In mathematics, Jordan's inequality, named after Camille Jordan, states that : \fracx\leq \sin(x) \leq x\textx \in \left[0,\frac\right]. It can be proven through the geometry of circles (see drawing).Feng Yuefeng, Proof without words: Jordan`s inequality, Mathematics Magazine, volume 69, no. 2, 1996, p. 126 Notes Further reading *Serge Colombo: ''Holomorphic Functions of One Variable''. Taylor & Francis 1983, , p. 167-168online copy *Da-Wei Niu, Jian Cao, Feng Qi''Generealizations of Jordan's Inequality and Concerned Relations'' U.P.B. Sci. Bull., Series A, Volume 72, Issue 3, 2010, *Feng Qi''Jordan's Inequality: Refinements, Generealizations, Applications and related Problems''. RGMIA Res Rep Coll (2006), Volume: 9, Issue: 3, Pages: 243–259 *Meng-Kuang Kuo''Refinements of Jordan's inequality'' Journal of Inequalities and Applications 2011, 2011:130, doi:10.1186/1029-242X-2011-130 External linksJordan's inequalityat the Proof WikiJordan's and Kober's inequalities
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Jordan Inequality
Jordan, officially the Hashemite Kingdom of Jordan, is a country in the Southern Levant region of West Asia. Jordan is bordered by Syria to the north, Iraq to the east, Saudi Arabia to the south, and Israel and the occupied Palestinian territories to the west. The Jordan River, flowing into the Dead Sea, is located along the country's western border within the Jordan Rift Valley. Jordan has a small coastline along the Red Sea in its southwest, separated by the Gulf of Aqaba from Egypt. Amman is the country's capital and List of cities in Jordan, largest city, as well as the List of largest cities in the Levant region by population, most populous city in the Levant. Inhabited by humans since the Paleolithic period, three kingdoms developed in Transjordan (region), Transjordan during the Iron Age: Ammon, Moab and Edom. In the third century BC, the Arab Nabataeans established Nabataean Kingdom, their kingdom centered in Petra. The Greco-Roman world, Greco-Roman period saw the ...
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Jordans Inequality
Jordans may refer to: Communities * Jordans, Buckinghamshire, a village in England * Friendship, Wake County, North Carolina, an unincorporated community formerly known as Jordans * Pipestem, West Virginia, an unincorporated community in Summers County also known as Jordans Chapel Other uses * Air Jordan, a brand of Nike shoes sponsored by American basketball player Michael Jordan * Jordans' anomaly, a familial abnormality of white blood cell morphology * Jordans Mine, on the Isle of Portland in Dorset, England * Jordanshöhe, a mountain in central Germany See also * * Jordan (other) Jordan is a country in the Middle East. Jordan or Jordán may also refer to: People * Jordan (name), a list of people with this given name or surname ** Camille Jordan (1838-1922), French mathematician ** Michael Jordan, American basketball playe ...

Camille Jordan
Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in group theory and for his influential ''Cours d'analyse''. Biography Jordan was born in Lyon and educated at the École polytechnique. He was an engineer by profession; later in life he taught at the École polytechnique and the Collège de France, where he had a reputation for eccentric choices of notation. He is remembered now by name in a number of results: * The Jordan curve theorem, a topological result required in complex analysis * The Jordan normal form and the Jordan matrix in linear algebra * In mathematical analysis, Jordan measure (or ''Jordan content'') is an area measure that predates measure theory * In group theory, the Jordan–Hölder theorem on composition series is a basic result. * Jordan's theorem on finite linear groups Jordan's work did much to bring Galois theory into the mainstream. He also investigated the Mat ...
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Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ...
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Circles
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus: a ring-shaped object, the region bounded by two concentric circles. * Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up ...
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