Dictionary

symmetry

A situation has a symmetry if certain changes make no difference. For instance: a mirror-symmetric image that you view in a mirror looks the same. A perfect sphere looks the same, even if it is rotated around an arbitrary axis through its centre point (“spherical symmetry”).

In particle physics, there are more abstract symmetries, less readily pictured, such as supersymmetry.

Definitioner

symmetry

sphere

A spherical surface is a simple example for a curved surface. It is easily pictured as a surface embedded in three-dimensional space: a spherical surface is the set of all points at a certain fixed distance from a given point (the point being the centre of the sphere). Mathematically, a spherical surface can be described without recourse to three-dimensional space - when mathematicians talk of the geometry of such a surface, they (almost) always mean the "inner geometry": Those properties of the surface noticeable to two-dimensional beings, living and working in that surface, capable of measuring distances and angles in it. Sphere is regularly used as a synonym for spherical surface (instead of describing a solid, three-dimensional ball). And not only for the two-dimensional spherical surface described above, but also for its analogues in lower and higher dimensions. A one-sphere, for instance, is the same as a circle, a two-sphere is the spherical surface defined above, a three-sphere its three-dimensional analogue.

point

Elementary "building block" of geometrical entities such as surfaces or more general spaces. For instance, a surface is the set of all its points, of all possible locations on the surface, and all geometrical objects in that surface are defined by the points that belong to them - for instance, a line on the surface is the set of (infinitely many) points.

Dictionary

symmetry

Further Articles

Tag Cloud