The Shape of Things: But Not the Golden Section

Abstract

For two-dimensional rectangular objects, a fundamental characteristic is the ratio of height and width. Ratios were calculated for paintings that are both high art and popular art. They show excellent agreement in both the shapes of the distributions and the medians of approximately 1.3. Ratios were calculated for two-dimensional art supplies and other objects. With some exceptions, the representative ratios for many of these objects are also close to 1.3. Two mathematical ratios are suggested. One is 4:3, found in the first Pythagorean triple, the three sides of a right triangle. The other is the plastic number studied by Richard Padovan. Although neither has the status of the golden section, either ratio would be a better candidate for describing the regularity in the proportions of rectangular objects.