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

参考资料
*

• Sergio A. Alvarez: [http://www.cs.bc.edu/~alvarez/NDPyt.pdf Note on an n-dimensional Pythagorean theorem] , Carnegie Mellon University

[http://www.gogeometry.com/solid/gua_theorem.htm De Gua's Theorem, Pythagorean theorem in 3-D*] - graphical illustration and related properties of the tetrahedron

扩展阅读

• Proof of de Gua's theorem and of generalizations to arbitrary tetrahedra and to pyramids.