types of geometry

Euclidean Geometry

Euclidean geometry is based on established rules, or postulates, developed by Euclid (c.300 BC). Euclidean geometry can be divided into plane geometry and solid geometry. Plane geometry involves the study of two-dimensional figures such as lines, angles, triangles, and circles. Solid Geometry involves the study of three-dimensional figures such as spheres, cubes, and cylinders. Some of the topics studied in Euclidean geometry include the congruence and similarity of triangles, the properties of parallel and perpendicular lines, the properties of circles and spheres, and the measurement of area or volume of figures.
One of the most famous postulates is the Parallel Postulate. This postualte states "through a point not on a given line, only one line can be drawn parallel to the given line". For example,


l is the only line parallel to line AB. Line AB can be drawn through point P. For many centuries after Euclid, mathematicians tried to prove that the parallel ...