infinite Beauty - Faculteit der Wiskunde en Natuurwetenschappen

Figure 1: The Louvre museum houses a lot of artwork in which the golden ratio is used. The Louvre pyramid doesn’t
house this ratio, unlike the pyramid of Gizeh, which does. (Photo: K. Kap).
number is φ, phi, and the proportion it describes is
known as ‘the golden ratio’ (box 1).
iron Cakes
This mysterious number caught attention of painters,
biological researchers and architects and was often
used in their work, both intentionally and unintentionally.
Throughout history, people from different
disciplines were grasped by the divine ratio, used it
in their art works and looked for it everywhere in nature.
Iron cakes might accompany this sequence.
Iron cakes are not made from iron, but are baked on
a specific iron plate. This plate has a pattern of rhombuses
on it. When the ratio of the diagonals of the
rhombus on an iron cake baking plate is equal to ϕ,
that rhombus is called a golden rhombus. These golden
rhombuses can also be found in arrangements of
molecules 2 .
When a golden ratio is found somewhere, one could
assume that an object is self-similar. Self-similarity
occurs when a subject at a smaller scale looks like
itself, as it is the case for the line described in box
1, an arrangement of golden rhombuses on a baking
plate or a crystalline arrangement in a molecular
structure.
self-similarity
If there is one thing that supports the interesting theory
opposed by R. L. Oldershaw, convinced of the
significance of his finding, it is the golden ratio. He
proposes a Self-Similar Cosmological Paradigm that
proposes that nature is ordered in a transfinite, which
is not infinite, but more than finite, hierarchy of discrete
cosmological scales. 3-4
Box 1: The ratio of the length of fragments
α:β = (α+β): α, is called the golden ratio
α β
This golden ratio is an irrational number,
indicated by φ.
This ratio is thought to be important in
defining some properties of beauty.
This self-similarity can be found everywhere: in fractals,
molecules, and also in pyramids. Interestingly
enough, the golden ratio is also found all sorts of
organisms in nature. Especially people who work on
phyllotaxis, the study of leaf arrangements, come into
contact with this ratio very often. The number of petals
for example, is often a Fibonacci number. And the
Fibonacci numbers are related to the golden ratio, as
explained in box 2.
It is thought that both people and bees are attracted
by flowers because of the Fibonacci numbers that occur
in the arrangement of flower leaves and petals.
Architects and painters use because they believe it is
a number of “divine proportions” and believe that it
describes some kind of ideal ratio.
Change your face
Gunes and Piccardi 5 found that the golden ratio is a
good descriptor of the way in which facial features
should relate to each other to nominate a face as attractive.
They programmed a computer in such a way
that the program could assess facial beauty with the
use of rules of proportion based on the golden ratio.
math in nature
origin - universiteit leiden 19