Euclid · Mathematics

The Fifth Postulate and the Shape of Space

Euclid’s troublesome fifth postulate about parallel lines - why mathematicians tried for two thousand years to prove it, and how their failure led to the discovery of non-Euclidean geometries and a revolution in our understanding of space.

What you'll be able to recall

You learned about Euclid’s fifth (parallel) postulate, the long effort to prove it, and the discovery of non-Euclidean geometry. Explain what the postulate says and why its independence was so revolutionary.

Leads to Lobachevsky.

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