This article was originally published with the title “ Non-Euclidean Geometry before Euclid ” in Scientific American Magazine Vol. 221 No. 5 (November 1969), p. 87 doi:10.1038 ...

tessellations of the plane, symmetry groups, Platonic and Archimedean solids, spirals, Fibonacci numbers, the golden mean, phyllotaxis, spaces of dimension greater than three, and non-Euclidean ...

This profound development is explained by analogy with non-Euclidean geometry In 1963 it was proved that a celebrated mathematical hypothesis put forward by Georg Cantor could not be proved.

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships ... we reared a group of rats inside non-Euclidean spherical environments from birth, thus depriving ...