On the beauty of vases: Birkhoff's aesthetic measure versus Hogarth's line of beauty

Vases continue to be important aesthetic objects in almost all developed cultures. Nevertheless, there is little to no systematic research on the shape characteristics that determine their beauty. A famous exception is Birkhoff, who in his 1933 book used the geometric ratios of vases to calculate their beauty. One form factor that he discussed theoretically but did not include in his aesthetic measure is the outline curvature of vases. This is despite the fact that William Hogarth recognized curvature as relevant to the aesthetic evaluation of forms as early as 1753, demonstrating this with his Line of Beauty. Given the great influence of these two ideas, the aim of the present study was to examine their contribution to the aesthetics of vases. For this objective, we designed a set of symbolic vases by systematically varying width and curvature, and asked participants to rate their beauty in an online experiment. The results show that both geometric ratios and curvature contribute to the beauty of the vases.