# Columbia Encyclopedia

## Search results

116 results found

## geometry

(Encyclopedia)geometry [Gr.,=earth measuring], branch of mathematics concerned with the properties of and relationships between points, lines, planes, and figures and with generalizations of these concepts. Eucli...

## analytic geometry

(Encyclopedia)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 to geometric problems is primarily a...

## fractal geometry

(Encyclopedia)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, a property called self-similarity or s...

## differential geometry

(Encyclopedia)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 differential geometry involves ...

## algebraic geometry

(Encyclopedia)algebraic geometry, branch of geometry, based on analytic geometry, that is concerned with geometric objects (loci) defined by algebraic relations among their coordinates (see Cartesian coordinates). ...

## descriptive geometry

(Encyclopedia)descriptive geometry, branch of geometry concerned with the two-dimensional representation of three-dimensional objects; it was introduced in 1795 by Gaspard Monge. By means of such representations, g...

## projective geometry

(Encyclopedia)projective geometry, branch of geometry concerned with those properties of geometric figures that remain invariant under projection. The basic elements are points, lines, and planes, and the following...

## affine geometry

(Encyclopedia)affine geometry: see geometry.

## arc, in geometry

(Encyclopedia)arc, 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 r and subtending a central angle of θ radian...

## chord, in geometry

(Encyclopedia)chord kôrd [key], in geometry, straight line segment both end points of which lie on the circumference of a circle or other curve; it is a segment of a secant. A chord passing through the center of a...