What is the difference between Euclidean and non-Euclidean geometry?
The first non-Euclidean geometries were worked on probably in the 19th century. In Euclidean geometry, given a straight line and a point, there is only one other straight line that passes through the point and is parallel to the first line. But even in ancient times, mathematicians wondered if this was indeed true. In the 19th century the mathematicians Bolyai, Lobachevsky, and Gauss thought there might be many parallel lines that pass through that point, even in two dimensions. In Euclidean space they might look curved, but in non-Euclidean space they would look straight. Euclidean and non-Euclidean geometry are two different theories. They have differing axioms. Physicists have concluded that space is probably non-Euclidean.
