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피타고라스의 정리 III : 등각사각형의 관점에서

Pythagorean Theorem III : From the perspective of equiangular quadrilaterals

  • Jo, Kyeonghee (Division of Liberal Arts and Sciences, Mokpo National Maritime Univ.)
  • 투고 : 2020.03.26
  • 심사 : 2020.06.23
  • 발행 : 2020.06.30

초록

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.

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참고문헌

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