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The affine Pythagorean theorem of Pappus

open access: yes, 1993
One version of Pappus's theorem is as follows. Let \(A\) and \(B\) be parallelograms constructed outside a triangle \(ABC\), such that \(A\) has a side \(AB\) and \(B\) has a side \(BC\). Let \(P\) be the point of intersection of the sides of \(A\) and \(B\) opposite to \(AB\) and \(BC\).
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PYTHAGOREAN THEOREM IN VARIOUS GEOMETRIES

open access: yesSUSh Scientific Proceedings
The work is devoted to the Pythagorean Theorem, known in school geometry, which expresses the relationship between the legs and the hypotenuse in a right triangle. This theorem is valid both in the elliptic plane (Riemann plane) and in the hyperbolic plane (Lobachevsky plane), in which triangles are considered as geodesics.
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