A New Theorem Relating the Tangent Secant Theorem to the Golden Ratio

TL;DR

This paper introduces a new geometric theorem linking the Tangent Secant theorem to the golden ratio, making the ratio's emergence more natural and accessible across disciplines.

Contribution

It presents a novel theorem that explicitly connects the Tangent Secant theorem to the golden ratio, clarifying its geometric and interdisciplinary significance.

Findings

Establishes a direct geometric link between the Tangent Secant theorem and the golden ratio.

Demonstrates how this connection simplifies understanding of the golden ratio in physics.

Enhances educational approaches to teaching classical geometry and the golden ratio.

Abstract

The golden ratio is usually shrouded in mystique and mystery, however, showing its emergence from a familiar geometric setting makes it a more natural phenomenon. In this work, we present a new theorem connecting the Tangent Secant theorem to the golden ratio. Such a connection enhances the learning process of the theorem, and it demystifies the golden ratio in physics and other disciplines.