A Study on Extention of the Pythagorean Theorem from R\(_2\) to R\(_3\) Using the Pythagorean Triples
Mururu Ntabari *
Department of Mathematics, Meru University of Science and Technology, Kenya.
Loyford Njagi
Department of Mathematics, Meru University of Science and Technology, Kenya.
Josphine Mutembei
Department of Mathematics, Meru University of Science and Technology, Kenya.
*Author to whom correspondence should be addressed.
Abstract
The study investigates theoretically the transition of the Pythagorean theorem from \(\mathbb{R}^2\) to \(\mathbb{R}^3\) (three-dimensional space). The research shows that for any Pythagorean triples a, b and c then \(a^3+b^3+c^3=d^3\) holds. The investigation further highlights the interplay between volumes of three geometrical constructs. In other words, volume a\(^3\) plus volume b\(^3\) plus volume c\(^3\) equals volume d\(^3\).
Keywords: Pythagorean triples, Pythagorean theorem, three-dimensional space, geometrical constructs