Why the Golden Spiral is Golden

Abstract

SummaryIt is shown that there is a logarithmic spiral that segments a straight line through its pole in the golden ratio ϕ. This is the same spiral that is often referred to in the literature as the “Golden Spiral” Using the tools of analytic geometry and parametric vector equations, it is shown that the golden spiral is actually a member of a family of spirals defined by a generalized equation. The spirals exist as a continuum defined by a real number q > 1. When q=ϕ, the spiral segments a line through its pole in the golden ratio. That is the characteristic feature that sets it apart from all the other spirals in the continuum. Additional informationNotes on contributorsOtis F. GrafOtis F. Graf Jr. (otis.graf@hccs.edu) received a BS in physics and math and a Ph.D. in aerospace engineering from the University of Texas at Austin. He began his career doing trajectory planning, mission analysis and software development for NASA at the Johnson Space Center in Houston, TX. Later he joined IBM and designed large data storage systems for US and international research organizations. After retirement from IBM he joined the adjunct faculty at Houston Community College where he tutors math and physics students who are on an academic path to university engineering degrees.