De Gua's theorem
Theorem
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De Gua's theorem
Theorem
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-angle corner is the sum of the squares of the areas of the other three faces: A A B C 2 = A A B O 2 + A A C O 2 + A B C O 2 {\displaystyle A_{ABC}^{2}=A_{\color {blue}ABO}^{2}+A_{\color {green}ACO}^{2}+A_{\color {red}BCO}^{2}} De Gua's theorem can be applied for proving a sp...
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From Wikipedia
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-angle corner is the sum of the squares of the areas of the other three faces: A A B C 2 = A A B O 2 + A A C O 2 + A B C O 2 {\displaystyle A_{ABC}^{2}=A_{\color {blue}ABO}^{2}+A_{\color {green}ACO}^{2}+A_{\color {red}BCO}^{2}} De Gua's theorem can be applied for proving a special case of Heron's formula.
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