德古阿定理
德古阿定理是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
参考资料
编辑- 埃里克·韦斯坦因. de Gua's theorem. MathWorld.
- Sergio A. Alvarez: Note on an n-dimensional Pythagorean theorem (页面存档备份,存于互联网档案馆), Carnegie Mellon University
- De Gua's Theorem, Pythagorean theorem in 3-D (页面存档备份,存于互联网档案馆) - graphical illustration and related properties of the tetrahedron
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.