From the Golden Rectangle and Fibonacci to Pedagogy and Problem Posing

Abstract

There is a wealth of valuable material on the golden section, and “fallout” from it as well, Indeed, the problem of constructing the golden rectangle with straightedge and a pair of compasses, and its relationship to constructing the regular pentagon with similar tools, is documented in Euclid's Elements (Euclid 1956; vol. 1, bk. 2, prop. 11; vol. 2, bk. 4. prop. 11). In the thirteenth century, the Italian mathematician Leonardo Fibonacci found connections between that aspect of geometry and number theory, and today there is a mathematical journal that is devoted exclusively to such issues. The golden section has appeared not only in mathematics but in architecture and art as well. The Parthenon in Greece, for example, has the proportions of the golden rectangle, and various portions of Michelangelo's David, from the joints of the fingers to the relative placement of the navel with respect to the total height, exemplify the golden ratio.