查看“︁德古阿定理”︁的源代码

[[File:De_gua_theorem_1.svg|thumb|upright=1.4|]]
'''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
:<math> S_{ABC}^2 = S_{\color {blue} ABO}^2 + S_{\color {green} ACO}^2 + S_{\color {red} BCO}^2 </math>

==参考资料==
* {{MathWorld|title=de Gua's theorem|urlname=deGuasTheorem}}
* Sergio A. Alvarez: [http://www.cs.bc.edu/~alvarez/NDPyt.pdf ''Note on an n-dimensional Pythagorean theorem''] {{Wayback|url=http://www.cs.bc.edu/~alvarez/NDPyt.pdf |date=20121002171401 }}, Carnegie Mellon University
*[http://www.gogeometry.com/solid/gua_theorem.htm  ''De Gua's Theorem, Pythagorean theorem in 3-D''] {{Wayback|url=http://www.gogeometry.com/solid/gua_theorem.htm |date=20130403115131 }} - graphical illustration and related properties of the tetrahedron

==扩展阅读==
* {{cite journal |last1=Kheyfits |first1=Alexander |year=2004 |title=The Theorem of Cosines for Pyramids |url=https://archive.org/details/sim_college-mathematics-journal_2004-11_35_5/page/385 |journal=The College Mathematics Journal |publisher=Mathematical Association of America |volume=35 |issue=5 |pages=385–388 |jstor=4146849}} Proof of de Gua's theorem and of generalizations to arbitrary tetrahedra and to pyramids.

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[[Category:几何定理]]