title: Aesthetic judgment of triangular shape: compactness and not the golden ratio determines perceived attractiveness.
abstract: Many studies over a period of more than a century have investigated the influence of the golden ratio on perceived geometric beauty. Surprisingly, very few of these studies used triangular shapes. In Experiment 1, we presented right triangles that differed in regard to their elongation determined by increasing the length of one side relative to another. Attractiveness ratings did not peak at the golden ratio, but there was a very strong influence of axis ratio overall. Participant ratings were a negative decreasing function of ratio. Triangles that pointed upward were judged as significantly more attractive than those that pointed down. We interpret these results according to a compactness hypothesis: triangles that are more compact are less likely to move or break and are thus considered more pleasing. Orientation also affects aesthetics. Upward-pointing triangles with a base parallel to the ground, regardless of their compactness, are also considered more perceptually stable and attractive. These findings were replicated across stimulus type in a second experiment with isosceles triangles and across testing procedure in a third experiment using a paired comparison technique.
authors.affiliation: Department of Psychology, Manhattan College, 4513 Manhattan College Parkway, Riverdale, NY 10471, USA; e-mail:  jay.friedenberg@manhattan.edu.
authors.forename: Jay
authors.initials: J
authors.lastname: Friedenberg
keywords: aesthetics; axis ratio; elongation; golden ratio; perceived attractiveness; triangles