Solved cryptogram
Euclid's rule about parallel lines cannot be proved from the others, and dropping it works.
Mathematics Facts, sourced to Wolfram MathWorld.
Solve it yourself
This fact is a cryptogram here: 74 letters over 21 different ones, graded medium.
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What it means
For two thousand years geometers tried to derive the fifth postulate from the first four and failed. In the nineteenth century Bolyai, Lobachevsky and Gauss saw why: replace it and you get a geometry that is perfectly consistent, just not the one on a flat sheet. On a saddle, many lines through a point miss a given line; on a sphere, none do. Einstein later needed exactly that machinery to describe gravity.
The claim comes from Wolfram MathWorld.
- SourceWolfram MathWorld
- CollectionMathematics Facts
- Difficultymedium
- Length74 letters, 21 of them different
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