Problem of the Week 796:

Gold in ratios

Can you find positive real numbers a <= b such that a/b is closer to the golden ratio than b/(a+b)?

Recall that the golden ratio phi is (Sqrt[5] - 1)/2 (approx. 0.618) and it has the property that if x/y = phi then also y/(x+y) = phi.

Source: Putz (and Mozart?), very pretty article in October issue of Mathematics Magazine.

(The title of course refers to the $1.00 my students get for a correct solution.)

See Jeff Erickson's solution.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

1 October 1998