Hyperbolic geometry is a type of non-Euclidean geometry that differs from Euclidean geometry in its axioms. It is used to describe curved surfaces such as the hyperbolic PLANE. Euclidean geometry is the traditional form of geometry, which is based on the axioms of Euclid and is used to describe flat surfaces such as a PLANE. PLANE geometry is a branch of Euclidean geometry that deals with the properties of flat surfaces. SOLID geometry is a branch of Euclidean geometry that deals with the properties of three-dimensional shapes.