# Convex and concave surface

A: Body with a convex curved surface
B: Body with a concave curved surface
Both body shapes z. B. with cylinder lenses

Convex and concave surfaces are terms used to describe a surface of a body in three-dimensional space or a part of it. The prerequisite is that part of the room can be defined as inside and the rest as outside .

The (partial) surface of a body is convex if the straight line between arbitrarily selectable points of this surface runs completely within the body. Other areas of the surface are not to be considered. This means that the outwardly curved surface of a concave-convex lens is also to be regarded as convex if the straight line between opposite points of the edge runs partially outside the (concave) side of the lens.
Example: The (partial) surface of a convex body is a convex surface
The (partial) surface of a body is concave if the straight line between arbitrarily selectable points on this surface runs completely outside the body. Other areas of the surface are not to be considered.

The resulting in a planar section of a convex or concave surface figure is in the analysis as a convex or concave function , respectively.

A convex surface comes e.g. B. in the case of optical lenses as a light-collecting surface and in the case of mirrors as a diffusing surface, whereby it is mostly spherical , often also cylindrical , but rarely ( rotationally symmetrical ) is aspherical in shape. In the applications of a concave surface in optics, the effects are reversed.

The domed roof of a building is a convex and its underside (both spherical) a concave surface.

The lower chord of a fish-belly girder has a convex outer surface (cylindrical; the girder, which is usually designed as a framework, is intended as a solid body).

A hollow fillet is characterized by its concave surface (cylindrical with a straight fillet).

## swell

1. Alexandrov, A, D .: The inner geometry of the convex surfaces. Akademie-Verlag Berlin, 1955.