德古阿定理

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。

De gua theorem 1.svg

若从一个正六面体截下一角O形成一截角锥(记为ABCO),则

参考资料

扩展阅读

  • 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.