Taiki Sato

Every Convex Polyhedron with Directly Congruent Scalene Triangular Faces Is a Tetrahedron

Let T be an oriented scalene Euclidean triangle. We prove that every convex polyhedron whose outward-oriented facets are directly congruent to T is a disphenoid tetrahedron. Consequently, such a polyhedron exists if and only if T is acute; in particular, right and obtuse scalene...

A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle

This record contains the English and Japanese versions of “A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle,” together with the TeX source files and bibliography. The paper presents a proof of the Pythagorean theorem based on signed orthogona...

A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle

This record contains the English and Japanese versions of “A Proof of the Pythagorean Theorem via Signed Projections of a Rotating Right Triangle,” together with the TeX source files and bibliography. The paper presents a proof of the Pythagorean theorem based on signed orthogona...