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The Pythagorean Trigonometric Identity is a special case of Lagrange’s Identity in three and seven dimensions. As such Pythagoras’s Theorem cannot hold outside of 3D or 7D. It is argued here that it in fact only holds in 3D.
https://www.researchgate.net/publication/322559041_Pythagoras's_Theorem_and_Special_Relativity

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