Adults and 5-year-old children draw rectangles and triangles around a prototype but not in the golden ratio


Dr. Edouard Gentaz, CNRS, «Laboratoire de Psychologie et NeuroCognition», Domaine Universitaire, Université Pierre Mendès France (Grenoble 2), 1251 avenue centrale, BP 47, 38040 Grenoble Cedex 9, France (e-mail:


This study uses a production task to probe the representations of two geometrical shape categories (rectangles and triangles) in adults and children before the onset of geometry instruction. We specifically assessed whether drawings of these shapes would average around a prototype and whether the prototypical side-length ratio of the shapes would be situated in the range of the ‘golden ratio’, as it has been reported in the perception domain. We asked 78 adults and 68 five-year-old children to draw one rectangle and one triangle. In both populations, the prototypical rectangle was horizontally oriented with a ratio between sides superior to the ‘golden’ value of 1.62. For the triangle, both children and adults tended to produce horizontal acute isosceles triangles with a ratio inferior to the golden value. These findings suggest that adults’ and children's shape categories of triangles and rectangles are organized around a prototypical shape, but the characteristics of this prototype may differ to a certain extent with the ones observed in previous perceptual tasks. Implications of this perception/production dissociation for length concept development, as well as the potential origins of these prototypes are discussed.