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A Generalization of de Gua's Theorem with a Vector Proof.
A Generalization of de Gua's Theorem with a Vector Proof.
- Source :
-
Mathematical Intelligencer . Sep2024, Vol. 46 Issue 3, p236-238. 3p. - Publication Year :
- 2024
-
Abstract
- This article discusses a generalization of de Gua's theorem, which is a three-dimensional analogue of the Pythagorean theorem. The theorem states that if a tetrahedron has a right-angled corner, then the square of the area of the face opposite that corner equals the sum of the squares of the areas of the other three faces. The article presents an extension of this theorem to an arbitrary tetrahedron and provides a vector proof. The article also introduces the concept of the areal vector of a triangle and presents a lemma related to the theorem. The given text provides a proof of Theorem 1, which is a generalization of the Pythagorean theorem in space. The proof involves applying Lemma 1 and using vector calculations. The text also includes a diagram (Figure 2) to illustrate the theorem. [Extracted from the article]
Details
- Language :
- English
- ISSN :
- 03436993
- Volume :
- 46
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematical Intelligencer
- Publication Type :
- Academic Journal
- Accession number :
- 180036484
- Full Text :
- https://doi.org/10.1007/s00283-023-10288-0