Description of Euler bricks using Fibonacci's identity

TL;DR

This paper explores the use of Fibonacci's identity to describe Euler bricks, including those with noninteger diagonals, and establishes relations between different types of Euler bricks.

Contribution

It introduces a novel application of Fibonacci's identity to Euler bricks and links their properties with Fibonacci's identity and Euler's formula.

Findings

Fibonacci's identity can generate Euler bricks.

Relations between Euler bricks with integer and noninteger diagonals are established.

A new method to describe Euler bricks with noninteger diagonals is proposed.

Abstract

We show how the Fibonacci's identity is used to obtain Euler bricks. Also,we put forward the relation between Fibonacci's identity and Euler's formula, which provides the description of Euler's bricks with noninteger spatial diagonal. Finally,we establish a relation between the Euler bricks with integer and noninteger spatial diagonals.