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佩多不等式 - Wikipedia

佩多不等式

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幾何學佩多不等式,是關連兩個三角形不等式,以唐·佩多(Don Pedoe)命名。這不等式是說,如果第一個三角形的邊長為a,b,c,面積為f,第二個三角形的邊長為A,B,C,面積為F,那麼:

A^2(b^2+c^2-a^2)+B^2(a^2+c^2-b^2)+C^2(a^2+b^2-c^2)\geq 16Ff

等式成立當且僅當兩個三角形對應邊成比例,也就是a / A = b / B = c / C

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