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Good Math by Mark C. Chu-Carroll

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What Is the Golden Ratio?

What is this golden ratio thing, anyway? It’s the number that is a solution for the equation (a + b)/a = (a/b). In other words, given a rectangle where the ratio of the length of its sides is 1:φ, when you remove the largest possible square from it, you’ll get another rectangle whose sides have the ratio φ:1. If you take the largest square from that, you’ll get a rectangle whose sides have the ratio 1:φ. And so on. You can see an image of the basic idea in Figure 3, The golden ratio.

images/pdf/phi.png
Figure 3. The golden ratio: The golden ratio is the ratio of the sides of an ideal rectangle. When you remove the largest possible square ...

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