The development of geometrical intuitions

triangle completion in imaginary worlds
The development of geometrical intuitions

Euclidean plane geometry builds on intuitions so compelling that they were believed for centuries to have the force of logical necessity.  Where do these intuitions begin, and how are they elaborated over development?  Behavioral studies of human infants, preschool children, and older children up to adolescence are shedding light both on abstract but limited geometric representations that emerge in the first year of life, on the more explicit representations that emerge from 2 to 6 years as children master spatial symbols such as maps, and on the intuitions relating distances to angles that children begin to articulate between 6 and 12 years.  Computational models of this process explore the role of mental simulation in the emergence of these intuitions.

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