Jordan's Inequality
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In mathematics, Jordan's inequality, named after
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 ...
, states that : \fracx\leq \sin(x) \leq x\textx \in \left ,\frac\right It can be proven through the
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 w ...
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. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting t ...
(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. 167-168
online 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 links


Jordan's inequality
at the Proof Wiki
Jordan's and Kober's inequalities
at cut-the-knot.org *{{MathWorld, title=Jordan's inequality, urlname=JordansInequality Inequalities (mathematics)