# Symmetry Definition and 64 Discussions

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article.
Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music.This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and nature; and in the arts, covering architecture, art and music.
The opposite of symmetry is asymmetry, which refers to the absence or a violation of symmetry.

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1. ### A What is meant when a phase is said to have "symmetry protected"?

What is meant when a phase is said to have "symmetry protected"?
2. ### I The Feynman way of explaining Symmetry in Physical laws

So on this page https://www.feynmanlectures.caltech.edu/I_11.html under heading 11-2 Translations first he tries to proof that there is no origin in space. Joe writes newtons laws after measuring quantities from some origin. $$m(d^2x/dt^2)=F_x$$ $$m(d^2y/dt^2)=F_y$$ $$m(d^2z/dt^2)=F_z$$ We need...
3. ### I Space group symmetry

What does mean spinel structure has F d3m space group? I know F is for face centred cubic, 3 is 3-fold symmetry and m is mirror, but I don't know what means "d"?
4. ### Help with Space Inversion Symmetry Problem

{a} P = identity Matrix w/ -1 on diagonals {b} eigenvalues = +/- 1
5. ### I Symmetry and Finite Coupled Oscillators

For an infinite system of coupled oscillators of identical mass and spring constant k. The matrix equation of motion is \ddot{X}=M^{-1}KX The eigenvectors of the solutions are those of the translation operator (since the translation operator and M^{-1}K commute). My question is, for the...