Geometry is the field of mathematics dealing with figures in a given space.
- Main article: Euclidean geometry
The most common type of geometry used in pre-collegiate mathematics competitions is Euclidean geometry. This type of geometry was first formally outlined by the Greek mathematician Euclid in his book The Elements.
- Main article: The Eleventh Postulate
The eleventh postulate stated in the book,
- “Through any line and a point not on the line, there is exactly one line passing through that point parallel to the line”
was the subject of a controversy for many centuries. This postulate is the basis of Euclidean geometry.
Non-Euclidean geometry are geometries in which the eleventh postulate is altered. Types of non-Euclidean geometry include: