infinite Beauty - Faculteit der Wiskunde en Natuurwetenschappen

20
math in nature
origin - universiteit leiden
Box 2: Johannes Kepler found that the
Fibonacci numbers are related to the golden
ratio:
Which means that the more n reaches
infinity, the more the ratio between the subsequent
Fibonacci numbers reaches φ.
Figure 2: The spirals in the middle of a sunflower are arranged
according to the Fibonacci numbers (photo: Uwe H. Friese,
Bremerhaven Germany 2005).
They tested the consistency of the computed results
by comparing them with the opinion of human referees.
The predictions were especially valuable when
applied to forecast the perceived beauty of vertical
proportions of facial features. With this knowledge in
mind the possibility is created to ask your plastic surgeon
to move your facial features to the right places.
But what’s really so golden about this ratio? It might
not explain all beauty. And we might have to take
the all-explaining feature of it with a pinch of salt
(Also see the article “Schoonheid is…” by Carlos de
Lannoy). Finding the golden ratio in nature might
be like gold; there is enough of it to trade or say something
about it, but not that much that the gold
becomes invaluable or that the ratio becomes unimportant.
Scientific theories might explain some of it
but cannot grasp the complete picture. Like beauty; a
concept is taken and made unspeakable, like the unspeakable
length of the infinite or transfinite number
of decimals of φ.
References:
• Livio, M. (2002) The golden ratio and aesthetics.
University of Cambridge Plus Magazine 22. Online
publication, plus.maths.org; accessed May 2011.
• Luo, Z. P. and Hashimoto, H. (2000) High-resolution
Electron Microscopy observation of a new crystalline
approximant W’ of Mg-Zn-Y icosahedral quasicrystal.
Micron 31: 487-492.
• Oldershaw, R. L. (1986) Cosmological self-similarity
and the principle of scale covariance. Astrophysics
and Space Science 128: 449-453.
• Oldershaw, R. L. (2008) Discrete Cosmological Self-
Similarity and Delta Scuti Variable Stars. Electronic
Journal of Theoretical Physics 5 (19): 123-132.
• Gunes, H. and Piccardi, M. Assessing facial beauty
through proportion analysis by image processing.
International Journal of Human-Computer Studies
64:1184-1199.