Jordan's Inequality

picture info	Jordan's Inequality In mathematics, Jordan's inequality, named after Camille Jordan, states that : \fracx\leq \sin(x) \leq x\textx \in \left ,\frac\right It can be proven through the geometry of 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. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ... (see drawing).Nach 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, Is ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	Jordan Inequality Jordan ( ar, الأردن; Romanization of Arabic, tr. ' ), officially the Hashemite Kingdom of Jordan,; Romanization of Arabic, tr. ' is a country in Western Asia. It is situated at the crossroads of Asia, Africa, and Europe, within the Levant region, on the Transjordan (region), East Bank of the Jordan River. Jordan is bordered by Saudi Arabia to the south and east, Iraq to the northeast, Syria to the north, and the State of Palestine, Palestinian West Bank, Israel, and the Dead Sea to the west. It has a coastline in its southwest on the Gulf of Aqaba's Red Sea, which separates Jordan from Egypt. Amman is Jordan's capital and largest city, as well as its economic, political, and cultural centre. Modern-day Jordan has been inhabited by humans since the Paleolithic period. Three stable kingdoms emerged there at the end of the Bronze Age: Ammon, Moab and Edom. In the third century BC, the Arab Nabataeans established their Nabataean Kingdom, Kingdom with Petra as the capital. La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	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 ** Michael Jordan, former NBA Player * Jordan (footballer, born 1932), Jordan da Costa, Brazili ... {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	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 Mathie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	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. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special ki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]