The divine proportion is (a + b)/a = a/b (see Fig. 5.13 ), which can be written

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The divine proportion is (a + b)/a = a/b (see Fig. 5.13 ), which can be written 1 + (b/a) = a/b. Now let x = a/b,which gives 1 + (1/x) = x. Multiply both sides of this equation by x to get a quadratic equation and then use the quadratic formula to show that one answer is x = (1 + ˆš5)/2 (the golden ratio).


Figure 5.13

b

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A Survey of Mathematics with Applications

ISBN: 978-0134112107

10th edition

Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde

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