Euclid's Random Walk: Developmental Changes in the Use of Simulation for Geometric Reasoning

Yuval Hart, L. Mahadevan, Moira R. Dillon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to 12-year-old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children's visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to reason using mental simulations of visual extrapolations.

Original languageAmerican English
Article numbere13070
JournalCognitive Science
Issue number1
StatePublished - Jan 2022

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