2) non-Euclidean geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...non-Euclidean geometry, branch of geometry in which the fifth postulate of Euclidean geometry, which allows one and only one line parallel to a given line through...

3) differential geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...differential geometry, branch of geometry in which the concepts of the calculus are applied to curves, surfaces, and other geometric entities. The approach in classical...

4) analytic geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...analytic geometry, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach...

5) fractal geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...fractal geometry, branch of mathematics concerned with irregular patterns made of parts that are in some way similar to the whole, e.g., twigs and tree branches,...

6) projective geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...projective geometry, branch of geometry concerned with those properties of geometric figures that remain invariant under projection. The basic elements are points,...

7) algebraic geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...algebraic geometry, branch of geometry, based on analytic geometry, that is concerned with geometric objects (loci) defined by algebraic relations among their coordinates...

8) affine geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...affine geometry, see geometry....

9) descriptive geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...descriptive geometry, branch of geometry concerned with the two-dimensional representation of three-dimensional objects; it was introduced in 1795 by Gaspard Monge....

10) arc, in geometry. The Columbia Encyclopedia, Sixth Edition. 2001
...arc, in geometry, in geometry, a curved line or any part of it; in particular, a portion of the circumference of a circle. The length s of an arc of a circle of radius...