asking what four-dimensional shapes can be obtained by deforming four-dimensional Euclidean geometry. In 1981, the Russian-French mathematician Misha Gromov, winner of the Abel Prize, asked whether ...

Two-dimensional (2D) shapes are completely flat. 2D shapes can be found printed in a book or on a website. 2D shapes have sides and corners. A rectangle has 4 straight sides and 4 corners.

using carefully conceived geometric shapes to create an optical illusion of depth, and patterns she describes as “moving in a four-dimensional way.” “I realized that in designing ...