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'Metageometries' have been invented by Riemann and Lobatschewski as rivals to the assumptions of Euclid, and the brilliant writings of Poincaré have explained the human devices on which mathematical concepts rest. Euclidean geometry is reduced to a useful interpretation of the data of experience; it is not theoretically the only one.
Nevertheless, geometry forms the handiest system for applying to experience and calculating shapes and motions. But, ideally, other systems might be used. The 'metageometries' have constructed other ideal 'spaces' out of postulates differing from Euclid's, though when applied to real space their greater complexity destroys their value.
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