There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which includes the principal group as a sub-group, then the invariant theory of this group gives a definite kind of geometry, and every possible geometry can be obtained in this way.


Translated by E.R. Hedrick and C.A. Noble, Elementary Mathematics from an Advanced Standpoint, Part Second, Chapter II, Section 6 (p. 133), Dover Publications. 1939

Felix Klein Quotes

There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which...

There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which...

There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which...

There appears a fundamental principle which can serve to characterize all possible geometries... Given any group of transformations in space which...