Curvature as Predictor of Beauty

Shape is everywhere. In a visual world, shape defines objects and our attitude towards them. What do we like? Where do we turn to? What products do we chose? Or even: who do we find attractive? All this (at least partly) is based on aesthetic appeal, which in turn is essentially linked to shape. Yet, the principles that determine what kind of shapes we perceive as beautiful and which ones we dislike are still not fully comprehended within experimental aesthetics. While prevailing theories take into account geometrical properties of shape, such as breadth proportions, we introduce curvature of contour as a promising predictor for aesthetic appreciation of shape.

The link between curvature and beauty has already been proposed by British artist William Hogarth (1697-1764). In his book “The Analysis of Beauty” (1753), he emphasized the relevance of curvature of contour for the aesthetic appeal of objects. In one of the Plates in this book, showing various objects, he included a Figure, number 49, in which he presented seven S-shaped lines varying in curvature (see Figure 1). Such lines are often commonly referred to as beauty lines (LoB). However, Hogarth was quite specific and declared line Number 4, which he considered as the most beautiful one, as LoB. Hogarth's assertion has established as a dogma of beauty and continues to influence various fields in aesthetics and design. Remarkably, this influence has mainly been based on Hogarth’s assumption. Prior to 2022, no researchers had empirically tested whether people actually perceive Hogarth’s LoB to be the most aesthetically pleasing. Therefore, we set out to test this assumption, and found that line 4 (i.e., the LoB) was perceived to be very attractive but was not seen as more beautiful than line 5 in a rating task or a forced-choice task (Hübner & Ufken, 2022). Thus, by and large, Hogarth’s claim has been confirmed empirically.

In our paper we were also able to quantify the nonlinear relation between curvature and preference across Hogarth’s seven lines. We hope that this lays the foundation for investigating the general role of curvature and its distribution for the beauty of S-shaped lines.

Literature

Hogarth, W. (1753). The Analysis of Beauty: Written with a View of Fixing the Fluctuating Ideas of Taste. Printed by J. Reeves for the Author.

Hübner, R., & Ufken, E. (2023). On the beauty of vases: Birkhoff’s aesthetic measure versus Hogarth’s line of beauty. Frontiers in Psychology, 14.<Open Access>

Hübner, R., & Ufken, E. (2022). Is Hogarth’s (1753) ‘line of beauty’ really the most beautiful? An empirical answer after more than 250 years. i-Perception, 13(2).<Open Access>