# What is Symmetry: Definition and 956 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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41. ### Engineering Applying symmetry to an asymmetrical circuit

Hello everyone, I need to solve a problem applying symmetry and superposition theorem but the problem is that the circuit is almost symetrical but has little differences in both sides (the source in the left side and the unknown impedance in the right side). I couldn't solve the problem using...
42. ### B Could Spontaneous symmetry breaking cause momentum change in an atom?

If you were to fire a single atom from a fixed point into a chamber of perfect vacuum and measure where it collides with the opposite wall. Could Spontaneous symmetry breaking in the sub atomic particles cause momentum change in the atom, changing the part of the wall the atom interacted with?
43. ### How does mirror symmetry for resistance work?

The question is to find the resistance between AF (top 2 points). Let the far right unlabelled vertex of the pentagon be B. Why can we say that points O and C are at the same potential? I get that both points O and C appear to be at 'half the path' if you consider AOF and ABCDF, and so potential...
44. ### Understanding Spherical Symmetry of Electron Clouds in External Fields

The given diagram looks something like this: Electric force on nucleus from external field must balance attraction force from electron cloud and electric force from external field. $$e\vec{E}=\frac{k(\frac{L^3}{R^3}e)}{L^2}\hat{L}$$ where ##\vec{L}## is from center of electron cloud to...
45. ### A Fluid Flow Symmetry: Showing $\pi_b G^b$ is Constant

I don't know where to start with this problem. If ##\pi_a = (\mu + TS) u_a## then show that \begin{align*} u^a \nabla_{a} (\pi_b G^b) = 0 \end{align*}where the field ##G^a## is a symmetry generator. [##S## is entropy/baryon, ##T## is temperature, ##u_a## is a one-form field corresponding to a...
46. ### How does metal sphere determine the potential of the plane by symmetry?

The answer given states that: The entire x-y plane is obviously at the same potential since all the fields are strictly perpendicular to it (draw a diagram if youre confused). Since we choose the sphere to be at potential zero, the point on the sphere which cuts the x-y plane is also at zero...
47. ### A How to systematically find the symmetry operator given a Hamiltonian?

For instance,how to systematically derive the equns 2.2 & 2.5 given a Hamiltonian on the article below?; arxiv.org/pdf/0904.2771.pdf .
48. ### B Symmetry of parity: Mistake in the experiment?

Recently I saw this YouTube video from Veritassium about CPT -Symmetry: In this video an experiment of Prof. Chien-Shiung Wu is presented, which has proven that parity is not symmetric, by observing the emmition of electrons from Co60 atoms with synchronised spin. After thinking about this...
49. ### Symmetry & Field of an Infinite uniformly charged plane sheet

Will translation parallel to x-axis work ? Else please suggest the symmetry? And does symmetry here refer to the symmetry of the sheet which causes the symmetry of the field or something else? Please be kind to help.
50. ### I Broken symmetry in ferromagnetism

Hello, Today I found this paper and this one where P.W. Anderson says that there is no broken symmetry in ferromagnetism because the ground state is an eigenstate of the spin rotation operator. And so we don't have in this system Goldstone's mode for example. But I thought spin waves were...