what is Euclidean’s fifth postulate, and how was it refuted?

Question

*Euclid dammit

In: 6

Answer 1

It is essentially a statement defining the properties of parallel lines, namely that, given a line and a point off that line, there is only one possible line through that point parallel to the first line.

It wasn’t “refuted” rather people were unable to demonstrate that this postulate could be derived from the other axioms and postulates of Euclid’s geometry. Because of these, you can simply decide not to use it and, if you choose to note use it, you open yourself to other kinds of geometries such as spherical geometry (in which there are no parallel lines through a given point) or hyperbolic geometry (in which there are infinite parallel lines through a given point).