APPENDIx 3 GOldEN mEAN (GOldEN SECTION) the Golden Section refers to a rectangle of any size that has a length that is 1.62 (1.618) times that of its width. A practical application to the golden section is in making a decision on how to crop a photograph. the closer the cropped print is to the golden mean, the more pleasing the print size should be. in photography, for example, with a 3 3 5 inch print, the 5-inch side is 1.66 times longer than the 3-inch side. As a ratio, it is written 5:3. rectangles with such a ratio are considered to be pleasing to the eye. Prints that are 4 3 5 inches, 8 3 10, and 16 3 20 have a ratio that is less than the golden mean, being only 1.25. once-popular 35 mm film was 24 3 35 mm and had a ratio of 1.46. the golden section has a long history going back to early greek and egyptian times and has been used in art and architecture for centuries. the Parthenon and the egyptian pyramids serve as examples. it is also found in growth patterns of nature, curves of sunflowers, seashells, and galaxies. the golden section is also known as the golden mean and the golden rectangle, and in egypt it was know as the sacred ratio. on the previous page is the cross-section of a nautilus shell, showing the expanded spiral growth pattern. fibonacci (1180­1250), an italian mathematician, had a passion for numbers and discovered a series of num- bers that describe not only the expanding growth pattern of things in nature but also the golden section.