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I’ve recently been interested in tetrahedra.

What made me interested is the “fascinating” resemblence between tetrahedra and triangles.

For instance in a trerectangular tetrahedron the square of the area of the “hypotenuse” face equals the sum of the squares of the other three faces, which clearly is a 3D version of the Pythagorean theorem .

There are other fascinating parts about the circumscribed and inscribed spheres, the condition the “hypotenuse” face in a trerectangular tetrahedron must be acute.

I’ve also come across imaginary numbers ,throughout my research on Google!!

What I ask for is as follows : A textbook/article/part of a texbook (any referenc) which discusses tetrahedra and their “amazing” properties.

Alo
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  • This is not my goal of posting this question ,but I would also be glad if someone explains the “magic” between triangles and tetrahedra (For instance the Pythagorean theorem and its 3D counterpart) – Alo Jul 22 '20 at 21:43
  • At hedronometry.com (basically a link to some blog posts), I've compiled a few notes about tetrahedra (both Euclidean and non-) ... in particular, the dimensionally-enhanced trigonometry of tetrahedra (hence, "hedronometry") that includes not only the Pythagorean relation (aka, de Gua's Theorem) but also Laws of Cosines (which introduce the surprisingly-useful notion of tetrahedral "pseudofaces"). Please forgive the embarrassing roughness of older notes; I was using them primarily to practice TeX formatting. :) – Blue Jul 22 '20 at 21:56

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