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 ...

asking what four-dimensional shapes can be obtained by deforming four-dimensional Euclidean geometry. The article by Heikkilä and Pekka Pankka has been published in the Annals of Mathematics journal.