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, 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 c ...

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

*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

Notes

Further reading

External links