# Did geometric patterns in nature suggest the early notions of proportion and ratios?

I'm very interested to learn about historical phenomenology of proportion and ratios, i.e. I want to know how and why people in the past introduced these concepts. As far as I understand symmetric objects or patterns in geometric figures found in nature suggest the idea of proportion and ratios to human mind. But can someone explain how exactly they came to be studied with examples and details?

• The word "proportion" has at least two meanings. The technical meaning used in Mathematics, and a different meaning in art etc. If you are asking about mathematical meaning, the answer is readily available: read Euclid. If it is about the other meaning, this is perhaps out of scope of this list. – Alexandre Eremenko Feb 13 '15 at 21:15
• Non-trivial Greek mathematics seems to have been entirely founded on the concept of proportion (Euclid, starting in book... 4? Maybe 5?). The Egyptians had fractions (Rhind papyrus) but seemed to think of them more as units chopped into smaller pieces, rather than as as a kind of relation between magnitudes. – Jack M Feb 13 '15 at 21:54
• The origin of the concept in mathematics and art is the same, relating different magnitudes, and it certainly long predates Euclid. And the notion of proportion in painting, sculpture, and architecture is pretty much the same as in elementary geometry, which is explicitly used there. – Conifold Feb 15 '15 at 3:46

According to Xenocrates (4th century BC), Pythagoras noticed that different sounds appear in consonance to us when the lengths of strings producing them are $$2:1$$, and in dissonance when they are $$9:8$$, etc. Attribution to Pythagoras in this case is very likely fabricated, but Pythagoreans did develop a system of musical tuning based on such observations. This one is the closest to coming from nature, but still involves instruments.