Is the Geometry of Space Euclidean or Non-Euclidean?

From 1870 to 1914, public interest grew in the idea that space might not be Euclidean. This interest was inextricably linked with the idea that space might be four-dimensional, which was also mixed up with the idea that time could be considered as a dimension. All these ideas are separate, as matters of mathematical fact, but they attracted a tremendous amount of interest, not least because of the prospect that one could travel in the fourth dimension, or in time, in ways denied to us hitherto. [ABSTRACT FROM AUTHOR]