However it was in the new geometries of Bolyai and Lobachevsky, Riemann, Clifford and Klein, and Sophus Lie that Klein's idea to 'define a geometry via its symmetry group' proved most influential.
Porén foi nas novas xeometrías de Bolyai e Lobachevsky, Riemann, Clifford e Klein, e Sophus Lie, que a idea de Klein de "definir unha xeometría por medio dun grupo de simetría" demostrou ter maior influencia.