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 - 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.