Fibonacci fraction

A Fibonacci fraction is a rational numberPlanetmathPlanetmathPlanetmath of the form FnFm where Fi is the ith number of the Fibonacci sequenceMathworldPlanetmath and n and m are integers in the relationMathworldPlanetmath n<m. In the Fibonacci fractional series, each m=n+2:


The most important application of Fibonacci fractions is in botany: plants arrange the leaves on their stems (phyllotaxy) in many different ways, but “only those conforming to a Fibonacci fraction allow for efficient packing of leaf primordia on the meristem surface.” There is also an application in optics.


  • 1 P. A. David “Leaf Position in Ailanthus Altissima in Relation to the Fibonacci Series” American Journal of Botany 26 2 (1939): 67
  • 2 R. W Pearcy & W Yang “The functionalPlanetmathPlanetmathPlanetmath morphology of light capture and carbon gain in the Redwood forest understorey plant Adenocaulon bicolor Hook” Functional Ecology 12 4 (1998): 551
  • 3 H. C. Rosu, J. P. Trevino, H. Cabrera & J. S. Murguia, “Self-image effects for diffraction and dispersion” Electromagnetic Phenomena 6 2 (2006): 204 - 211
Title Fibonacci fraction
Canonical name FibonacciFraction
Date of creation 2013-03-22 18:03:18
Last modified on 2013-03-22 18:03:18
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11B39