A Fibonacci fraction is a rational number of the form where is the th number of the Fibonacci sequence and and are integers in the relation . In the Fibonacci fractional series, each :

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.

Bibliography

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 functional 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