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http://dx.doi.org/10.14477/jhm.2020.33.3.155

Pythagorean Theorem III : From the perspective of equiangular quadrilaterals  

Jo, Kyeonghee (Division of Liberal Arts and Sciences, Mokpo National Maritime Univ.)
Publication Information
Journal for History of Mathematics / v.33, no.3, 2020 , pp. 155-165 More about this Journal
Abstract
Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.
Keywords
Rectangle; Equiangular Quadrilateral; Right triangle; Proper triangle; Pythagorean theorem;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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