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Kinds of mathematical concept :
- frame of reference (6 kinds, 21 facts) - A set of axes to which positions and motions in a system can be referred.
- geometrical object (73 kinds, 251 facts)
- number (513 kinds, 2047 facts)
- statistical concept (16 kinds, 39 facts)
- symmetry (14 kinds, 46 facts) - A property of a physical system that does not change when the system is transformed in some manner. For instance, a sphere is rotationally symmetrical since its appearance does not change if it is rotated., State of a system such that it has a significant quantity that remains invariant after a transformation. More generally, an apt or pleasing proportion based upon such a state., The property of being unchanged after some transformation. A square, for example, has a 4-sided rotational symmetry. It appears the same after it is rotated by 90 degrees.
- symmetry breaking (2 kinds, 15 facts) (asymmetry) - A violation of symmetry., A reduction in the amount of symmetry a system appears to have, usually associated with a phase transition., A set of mathematical transformations that represent a symmetry., The process by which an intrinsic symmetry of a system is disrupted. For example, a compass, in the absence of any outside magnetic field, has rotational symmetry and is equally likely to point in any direction. The magnetic field of the earth breaks the symmetry and causes the compass to point in a particular direction, toward the earth's north magnetic pole. In some cosmological models, the infant universe was much more symmetric than it is today. As the universe aged and cooled, some of these symmetries were permanently broken., In cosmology and particle physics, a state in which traces of an earlier symmetry may be discerned. A broken symmetry condition differs from chaos in that its parts can in theory be united in a symmetrical whole, like the pieces of a jigsaw puzzle.
- transformation (12 kinds, 30 facts)
- unit (140 kinds, 605 facts)
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