Delving Deeper: Converging on the Eye of God

Abstract

The eye of God—the point at which the golden spiral appears to vanish—has long captivated the imagination of mathematicians. While preparing a paper on the Fibonacci numbers and the golden ratio, Francisco Rangel, a student of David Seppala-Holtzman's, decided to engage in some numeric experimentation. He came up with some surprising results that ultimately led to a conjecture about the eye of God. Our purpose here is to describe what he found, prove that his suspicions were indeed correct, and give a geometric interpretation of these results.