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The Golden Ratio and Fibonacci Numbers

Richard A. Dunlap
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Underwood Dudley
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This book, first published in 1997 and reprinted four times since, treats some topics related to the golden ratio, τ = (1 + √5)/2, and to Fibonacci and Lucas numbers. It is almost entirely descriptive, pointing out various facts and results, and contains very little mathematics. It is aimed at a general reader with no previous knowledge of the subject.

The author shows how τ appears in the pentagon, dodecahedron, and icosahedron (whose volume is 5τ5/6 times its edge length, something that I didn’t know before) and in Penrose tilings, gives properties of Fibonacci and Lucas numbers and mentions how they occur in optimal spacing and search algorithms and elsewhere.

He does not endorse any of the silliness associated with τ, e.g., that it is built into the Great Pyramid or that a rectangle with dimensions 1 and τ is especially pleasing. However, his clear-sightedness deserts him when he calls his last chapter “Biological Applications.” He should have written “Biological Appearances.”

MAA members should keep this book in mind to recommend to those who would benefit from it.

Underwood Dudley has retired from DePauw University and is now living in Florida.

  • Basic Properties of the Golden Ratio
  • Geometric Problems in Two Dimensions
  • Geometric Problems in Three Dimensions
  • Fibonacci Numbers
  • Lucas Numbers and Generalized Fibonacci Numbers
  • Continued Fractions and Rational Approximants
  • Generalized Fibonacci Representation Theorems
  • Optimal Spacing and Search Algorithms
  • Commensurate and Incommensurate Projections
  • Penrose Tilings
  • Quasicrystallography
  • Biological Applications
  • Construction of the Regular Pentagon
  • The First 100 Fibonacci and Lucas Numbers
  • Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers