Euclid of Alexandria, in his “Elements” (300 BC), gave us the first clear definition what he called “The Extreme and Mean Ratio” but what was later raised to loftier levels and called “The Golden Ratio” and “The Divine Proportion”.
The ratio actually has two Greek letters used to symbolize it: phi (φ) is more commonly used and is named after “Phidias”– a Greek sculptor (more on that later). But professional mathematicians often use tau (τ) because “tau” is the first letter in “tomi” which means “the section” in Greek.
Phi is a fascinating irrational number. I am enjoying Mario Livio’s book “The Golden Ratio” which I will use as fodder for a few posts. But first, I thought I’d get readers a little invested with an exercise!
Help Euclid find the spot, “C”, on the line segment AB that fulfills the equation to its right. In other words: What point do you think creates “The Divine Proportion”?