<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Motivated by a result of [Lucio R. Berrone: The associativity of the Pythagorean law, Amer. Math. Monthly <bold>116 </bold>(2009), 936-939] we deal with the functional equation</p><p>and its variants to distinguish the classical Pythagorean theorem from among its numerous abstract generalizations.</p></abstract>

Motivated by a result of [Lucio R. Berrone: The associativity of the Pythagorean law, Amer. Math. Monthly 116 (2009), 936-939] we deal with the functional equationand its variants to distinguish the classical Pythagorean theorem from among its numerous abstract generalizations.

Abstract Pythagorean Theorem and Corresponding Functional Equations

Institute of of Mathematics Silesian University Bankowa 14 PL–40-007 Katowice POLAND

Tatra Mountains Mathematical Publications

{"article-title":"Abstract Pythagorean Theorem and Corresponding Functional Equations"}

Motivated by a result of [Lucio R. Berrone: The associativity of the Pythagorean law, Amer. Math. Monthly 116 (2009), 936-939] we deal with the functional...

Abstract Pythagorean Theorem and Corresponding Functional Equations

Published Online: Aug 13, 2013

Page range: 67 - 75

DOI: https://doi.org/10.2478/tmmp-2013-0020

Keywords
Pythagorean Law, height function, associativity, quasi-arithmetic mean

This content is open access.

Abstract Pythagorean Theorem and Corresponding Functional Equations

Published Online: Aug 13, 2013

Page range: 67 - 75

DOI: https://doi.org/10.2478/tmmp-2013-0020

KeywordsPythagorean Law, height function, associativity, quasi-arithmetic mean

This content is open access.

Keywords
Pythagorean Law, height function, associativity, quasi-arithmetic mean