Jordan's Inequality


Jordan's inequality states that for


Consider a unit circle, OA = 1 with a point P on the circle. Construct a perpendicular from P to the horizontal line with M being the foot of the perpendicular and Q its reflection. Let x be the measure of the angle POM. The line PM has length sin x.

Construct a circle of radius MP and center at M.

Prove Jordan's Inequality.


Details.

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Reference: Yuefeng, Feng. (1996) Proof without words. Mathematics Magazine. 69, p. 126.