MAA Writing Awards
Disentangling a Triangle
Award: Lester R. Ford
Year of Award: 2010
Publication Information: The American Mathematical Monthly, vol. 116, no. 3, March 2009, pp. 228-237.
Summary: The authors give a presentation of trigonometry's central theorems: in a few brief pages, decorated with repeated versions of the same simple figure consisting of an acute triangle set within its inscribed circle - each of the figures only slightly modified to highlight some particular relation among its pieces. Ptolemy's theorem, the law of sines, the nine-point circle, the standard sum and difference formulas for the trigonometric functions, these and a host of other well-known (and less well-known) results spring forth geometrically in these diagrams and in a few simple equations.
About the Authors: (From the Prizes and Awards booklet, MathFest 2010)