Jordan's inequality explained

In mathematics, Jordan's inequality, named after Camille Jordan, states that

(2)/(\pi) x\leq \sin(x) \leq x for x \in \left[ 0 , (\pi)/(2) \right].

It can be proven through the geometry of circles (see drawing).^[1]

Notes

1. Feng Yuefeng, Proof without words: Jordan`s inequality, Mathematics Magazine, volume 69, no. 2, 1996, p. 126

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