Eli5: Why Euclid’s fifth postulate cannot be proven?
In: 4
There are places where all four of the other postulates are true, but the fifth is false. [Hyperbolic Geometry](https://en.wikipedia.org/wiki/Hyperbolic_geometry) is an example, it’s the geometry of a “saddle-shaped” plane. Because there are legitimate geometries where all the other postulates are true, but the fifth is not, it follows that the fifth cannot depend on the other four.
If you accept only the four postulates and make no commitment to the fifth postulate either way, then you get [Absolute Geometry](https://en.wikipedia.org/wiki/Absolute_geometry) whose results are weaker (as they have no Pythagorean Theorem or alternatives), but the results apply to both Euclidean and Non-Euclidean geometry.
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