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A New Proof of the Pythagorean Theorem and Its Application to Element Decompositions in Topological Algebras

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  • Fred Greensite

Abstract

We present a new proof of the Pythagorean theorem which suggests a particular decomposition of the elements of a topological algebra in terms of an “inverse norm” (addressing unital algebraic structure rather than simply vector space structure). One consequence is the unification of Euclidean norm, Minkowski norm, geometric mean, and determinant, as expressions of this entity in the context of different algebras.

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  • Fred Greensite, 2012. "A New Proof of the Pythagorean Theorem and Its Application to Element Decompositions in Topological Algebras," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-15, August.
    • Handle: RePEc:hin:jijmms:353917
    DOI: 10.1155/2012/353917
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