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The golden ratio

It has also been known for a long time that the Golden Ratio (Golden Section, Golden Mean or Divine Proportion) enables to build a logarithmic spiral easily.
Let's consider the golden rectangle ABDC (AB/AC = 1.618). If we remove the square EBDF, we obtain a new golden rectangle AEFC (indeed, we see that the ratio EF/AE equals 1.618). The operation is repeated as many times as we wish and, in the squares which are obtained in that way, arcs of circumference (represented in blue) are traced.

This spiral governs the disposition of the leaves around the stem as it does for the shape of the snail's shell and the horns of the bovines. So, the golden ratio is present in the horns of the Ram though, in this case, the changes of the rolling up scheme give the spiral a twisted look. Everything happens as if the criosphinxes had the task of reminding the observer that the golden ratio is present everywhere on the site of Thebes.

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