2017•International Journal of Mathematical Education in Science and TechnologyRequires access

A deduction of the Golden Spiral equation via powers of the Golden Ratio ϕ

Maurício Zahn

Abstract

This paper presents an interesting deduction of the Golden Spiral equation in a suitable polar coordinate system. For this purpose, the concepts of Golden Ratio and Golden Rectangle, and a significant result for the calculation of powers of the Golden Ratio ϕ using terms of the Fibonacci sequence are mentioned. Finally, various geometrical considerations that help us deduce the sought equation are presented.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Golden ratio, Fibonacci number, Golden Rule, Mathematics, Rectangle, Spiral (railway), Calculus (dental), Arithmetic