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

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

Author(s) -

Fred Greensite

Publication year - 2012

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2012/353917

Subject(s) - mathematics , pythagorean theorem , norm (philosophy) , vector space , algebraic number , minkowski space , geometric algebra , algebra over a field , topological algebra , pure mathematics , topological space , algebra representation , mathematical analysis , geometry , political science , law

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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