Thread: Spherical and Hyperbolic Geometry

Spherical (elliptic) and Hyperbolic geometry is a consequence of replacing Euclid’s parallel axiom with an axiom that contradicts it. What are some of the revolutionary paradigm shifts that accompanied this research in the eighteenth century?

Originally Posted by Mel

Spherical (elliptic) and Hyperbolic geometry is a consequence of replacing Euclid’s parallel axiom with an axiom that contradicts it. What are some of the revolutionary paradigm shifts that accompanied this research in the eighteenth century?

19th century

One consequence is general relativity, another is the discrediting of Kant's claim that the "truths" of Geometry are a-priori truths.

CB