Non-Euclidean geometry refers to certain types of geometry which differ from plane and solid geometry which dominated the realm of mathematics for several centuries. There are other types of geometry which do not assume all of Euclid's postulates such as hyperbolic geometry, elliptic geometry, spherical geometry, descriptive geometry, differential geometry, geometric algebra, and multidimensional geometry. These geometries deal with more complex components of curves in space rather than the simple plane or solids used as the foundation for Euclid's geometry. The first five postulates of Euclidean geometry will be listed in order to better understand the changes that are made to make it non-Euclidean.

1.) A straight line can be drawn from any point to any point.

2.) A finite straight line can be produced continuously in a straight line.

3.) A circle may be described with any point as center and any distance as a radius.

4.) All right...