Visual foundations of Euclidean geometry

ElsevierVolume 136, August 2022, 101494Cognitive PsychologyHighlights•

In Euclidean geometry, forms are defined by their shape and size.

Participants from the US and the Amazon searched for deviants amongst planar forms.

All groups identified deviants defined in terms of shape or size.

Only US adults drew distinctions between mirror images.

Visual representations may play a foundational role for Euclidean knowledge.

Abstract

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded.

Keywords

Mathematical cognition

Visual perception

Euclidean geometry

Cognitive development

Spatial Cognition

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© 2022 Published by Elsevier Inc.

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