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

$S_{ABC}^2=S_{ABO}^2+S_{ACO}^2+S_{BCO}^2$

参考资料

• Template:MathWorld
• Sergio A. Alvarez: Note on an n-dimensional Pythagorean theorem Template:Wayback, Carnegie Mellon University
• De Gua's Theorem, Pythagorean theorem in 3-D Template:Wayback - graphical illustration and related properties of the tetrahedron

扩展阅读

• Template:Cite journal Proof of de Gua's theorem and of generalizations to arbitrary tetrahedra and to pyramids.