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Glossary

6 The Beauty of Symmetry

 

Cayley's Theorem

This result says that the symmetries of geometric objects can be expressed as groups of permutations.

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Continuous Symmetry

An object possessing continuous symmetries can remain invariant while one symmetry is turned into another. A circle is an example of an object with continuous symmetries.

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Galois Theory

This area of mathematics relates symmetry to whether or not an equation has a "simple" solution.

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Group

A group is just a collection of objects (i.e., elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation, each element must have an inverse, the set must have an identity element, the set must be closed, and the set must be associative under the operation.

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Invarient

The state of appearing unchanged.

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Noether's Theorem

This result relates conserved physical quantities, like conservation of energy, to continuous symmetries of spacetime.

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Polynomial

A polynomial is an algebraic "sentence" containing an unknown quantity.

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Symmetry

Symmetry, in a mathematical sense, is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance, repetition, and/or harmony. In mathematics, symmetry is more akin to something like "constancy," that is, how something can be manipulated without changing its form.

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