Perceptual Foundations of Euclidean Geometry
Résumé
Euclidean geometry defines objects that can be realized in space, and may therefore be founded in spatial perception. We investigated whether the perception of small, 2-dimen- sional visual forms could provide cognitive foundations for Euclidean knowledge, by asking two questions. First, are humans sensitive to form variations that are relevant to Eu- clidean geometry (e.g. changes in angle)? Second, can ob- servers easily disregard variations that are irrelevant to Eu- clidean geometry (e.g., changes in scale)? Participants from the U.S. (age 3-34 years) and from the Amazon (age 5-67) were asked to locate deviants in panels of 6 forms of vari- able orientation. Results indicate that perception of forms aligns with a restricted version of Euclidean geometry, where forms are defined in terms of metric proportions and global size, but mirror images are assimilated. Moreo- ver, children below 6 did not clearly analyze forms in terms of the shape property of angle.
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