德古阿定理

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De gua theorem 1.svg

德古阿定理勾股定理的三维形式,以法国数学家让·保罗·德古阿·德马尔弗(Jean Paul de Gua de Malves)命名。

若從一個正六面體截下一角O形成一截角錐(記为ABCO),則

 S_{ABC}^2 = S_{\color {blue} ABO}^2 + S_{\color {green} ACO}^2 + S_{\color {red} BCO}^2

参考资料[编辑]

扩展阅读[编辑]

  • Kheyfits, Alexander. The Theorem of Cosines for Pyramids. The College Mathematics Journal (Mathematical Association of America). 2004, 35 (5): 385–388. JSTOR 4146849.  Proof of de Gua's theorem and of generalizations to arbitrary tetrahedra and to pyramids.