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Transcript
Fibonacci fraction∗
PrimeFan†
2013-03-22 1:00:40
n
where Fi is the
A Fibonacci fraction is a rational number of the form FFm
ith number of the Fibonacci sequence and n and m are integers in the relation
n < m. In the Fibonacci fractional series, each m = n + 2:
1 1 2 3 5 8 13 21 34
, , , , , , , , ,...
2 3 5 8 13 21 34 55 89
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.
References
[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
∗ hFibonacciFractioni
created: h2013-03-2i by: hPrimeFani version: h40584i Privacy
setting: h1i hDefinitioni h11B39i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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