What is Symmetry: Definition and 955 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.

View More On Wikipedia.org
Recent contents Top users
  1. E

    Symmetry the new Ptolemaic Theory?

    Having watched with interest the "progress" in theory since my retirement, I have come to the conclusion that it well may be in the state that Ptolemaic astromical theory was in its heyday. That is to say since the circle was the most 'perfect' figure everything else could be understood using...
  2. G

    Would forces act with the same symmetry in 4D as it does in 3D?

    Would forces act with the same symmetry in 4D as it does in 3D?
  3. N

    Finding "Dynamical Symmetry Breaking in Quantum Field Theories

    Dear PF, Could anyone advise me where I can find the following book: Dynamical symmetry breaking in quantum field theories - Miransky, V.A. Is itt possible to download from somewhere? Cheers George
  4. N

    Proving Angle Sums in Cyclic Polygons: A Generalization Approach

    Right I have been given the following problem and cannot resolve it. I have had an attempt but without much success. Could anyone help me with this exercise, please? A cyclic hexagon is a hexagon whose vertices all lie on the circumference of a circle. The vertices of a cyclic hexagon are...
  5. N

    Understanding Symmetry Groups of a Pentagon

    Right I have been asked to identify the elements of a full symmetry group of a pentagon and give the order of each element? I have found the elements which I have marked as I, R (Rotation of 72 degrees), R2 (Rotation of 144 degrees), R3 (Rotation of 216 degrees), R4 (Rotation of 288 degrees)...
  6. N

    Discovering Triangle Symmetry: Tips for Solving Angle and Side Length Problems

    Sorry I am not sure if I should put this thread here.. looks like I am going to be told off by the boss :frown: Anyway, here is my question in a triangle ABC, AB = AC and D is a point on AC such that AD = DB = BC. Find the size of the angle BAD? Find the angles of triangle ABC? Just need...
  7. N

    How to Find Angle BAD & ABC in a Symmetrical Triangle: Helpful Hints"

    In a triangle ABC, AB = AC and AD = DB = BC. Find the size of the angle BAD? Find the angles of triangle ABC? Just need a few hints to get this problem started please? :redface:
  8. S

    Solving Partial Derivatives & Symmetry Problems: A Practice Test

    8. Let f : R^3 → R a function all whose first order partial derivatives are continuous and such that f(0, 1, 1) = 0, f_x(0, 1, 1) = 1, f_y(0, 1, 1) = 2, f_z(0, 1, 1) = 3. Find lim t-->0 f(t2, cosh t, et) f(t, cos t, cosh t) 9. Let f : R2 → R such that f(x, y) = f(y,−x) for all (x, y) ∈ R2, and...
  9. D

    October issue of symmetry out today

    New issue of http://www.symmetrymagazine.org/cms/?pid=1000183" is about the Snowmass meeting to work toward designing the International Linear Collider. Other stories: http://www.symmetrymagazine.org/cms/?pid=1000191": An experiment with polarized electrons probed the strength and asymmetry...
  10. R

    Electroweak symmetry breaking

    How is the electroweak symmetry actually broken in the standard model ? Please could you explain the idea to me. Thanks Roger.
  11. A

    Tangent Properties Symmetry, domain, asymptotes, zeroes

    y=-2\tan (3x+\pi) +3 state the following period = \frac {\pi} {3} y-intercept=3 Range = {y: yER} Domain= {x: ?} Symmetry? Vertical Asymptotes? Zeros? Can someone please tell me how to figure out what is left there are so many zeroes and i can't read them off of my...
  12. B

    Showing Symmetry in Real Invertible Matrices and Non-Invertible Cases

    Hi can someone please help me get started on the following question? Q. Let A be a real invertible n * n matrix. Show that \left\langle {\mathop x\limits^ \to ,\mathop y\limits^ \to } \right\rangle \equiv \mathop y\limits^ \to A^T A\mathop x\limits^ \to = \left( {A\mathop y\limits^ \to...
  13. D

    New issue of Symmetry magazine

    Hi all, Reintroducing myself, this is the David who was active here many years ago when Greg started up physics forums. I've been off buried in other projects for some years but hope to become active again here. Some people in this forum might find the magazine I run useful and...
  14. T

    Violation of symmetry and conservation

    Does EM force obey the conservation of strangeness like the strong force?
  15. R

    How does spontaneous breaking symmetry occur in quantum mechanics?

    Does anybody have an enough simple example and explanation of spontaneous breaking symmetry in quantum mechanics? When does the process of breaking take place? After or before some small perturbation appears?
  16. N

    Referencess on Dynamical Symmetry Breaking

    I would much appreciate if anyone could give me some tips/referencess on Dynamical Symmetry Breaking. Namely detailed referrence on Namby Jona-lasinio model of mass for particles.
  17. A

    Symmetry Testing: Solutions to 2 Equations

    Here's 2 more I am having difficulty with, I'll show you what I came up with or what I think the answer is 1. 2x = 3y^2 (sqrt 2x/3) = 3y/3 y = sqrt (2x/3) Symmetric to the X-axis 2. x^2 + 4y^2=16 not symmetric to any axis
  18. M

    Applying gauss' law to planar symmetry, finding E question

    I'm looking at how you find E in a Nonconducting sheet. It all makes sense until the last part. Visualize a thin, infinite, nonconducting heet with a uniform positive surface charge density \delta . A sheet of thin plastic wrap, uniformily charged on one side, can serve as a simple model...
  19. CarlB

    What is the Lie symmetry of this potential?

    The potential function: V(x_r,y_r,\theta_r,x_g,y_g,\theta_g,x_b,y_b,\theta_b) = 3 - exp(-x_r^2-y_r^2)(cos(\theta_r) + \sqrt{3}sin(\theta_r)) - exp(-x_g^2-y_g^2)(cos(\theta_g) + \sqrt{3}sin(\theta_g)) - exp(-x_b^2-y_b^2)(cos(\theta_b) + \sqrt{3}sin(\theta_b)) where the nine variables...
  20. D

    An odd sort of symmetry about E=MC^2

    You sacrifice mass to create energy (energy is just mass with a velocity), and the faster mass moves (relativity) the more massive the mass gets, is there some sort of significance to that? I hate riddles.
  21. D

    Symmetry, groups and gauge theories in the standard model

    This is my (limited) understanding of particle physics: In particle physics gauge symmetries play an important role. To allow for massive gauge bosons this symmetry is broken. The theory of weak interactions can be derived from a local SU(2) symmetry, and quantumchromodynamics from a local SU(3)...
  22. G

    Equation is a parabola with a vertical axis of symmetry

    Determine the restrictions on the constants A, C and E such that the following equation is a parabola with a vertical axis of symmetry. Ax^2+Cy^2+x+Ey=0 a) A=0, C cannot=0, E cannot=0 b) A=0, C cannot=0, E=0 c) A cannot=0, C=0, E=0 d) A cannot=0, C=0, E cannot=0 i know that A cannot=0...
  23. B

    Symmetry Analysis of Partial Differential Equations

    I'm currently taking a symmetry analysis course. It is really interesting. I would recommend it to any math major or anyone interested in ODE's and PDE'S. I am enjoying it very much.
  24. S

    Is there a fundamental connection between energy, momentum, and mass in physics?

    Mass-energy equivalence is fundamental in relativity, but it seems like energy and momentum are also different aspects of the same thing. They've each got very important conservation laws. In SR, the space coordinates of the four-momentum give the momentum while the time coordinate gives...
  25. maverick280857

    Symmetry Method in Electric Circuits

    Hi Could someone point me to a comprehensive resource (either book or website or both) which explains the method of symmetry for the solution of simple resistive electric circuits? Thanks and cheers Vivek
  26. F

    Crossing Symmetry and Mandelstam Variables; and (unrelated) external photons

    Greetings--a few further questions and thoughts from Peskin and Schroeder An Introduction to Quantum Field Theory. (I'll do my best to keep the discussion self-contained, but I'll provide references as well.) Is there an easy way to produce Feynman diagrams in LaTeX? (Maybe Daniel has a...
  27. C

    Symmetry in crystal structures-

    Symmetry in crystal structures- please help! Hi there, I was hoping someone here could help explain a few things about crystal symmetry to me cos it hs me so confused (we've been doing crystals for 2 weeks and things up til now have been ok, I'm just getting myself muddled as usual!). The...
  28. C

    Symmetry in crystal structures-

    Symmetry in crystal structures- please help! Hi there, I was hoping someone here could help explain a few things about crystal symmetry to me cos it hs me so confused (we've been doing crystals for 2 weeks and things up til now have been ok, I'm just getting myself muddled as usual!). The...
  29. cepheid

    Gauss's Law: Cylindrical Symmetry

    Problem : A long coaxial cable carries a uniform volume charge density \rho on the inner cylinder (radius a ), and a uniform surface charge density on the outer cylindrical shell (radius b ). The surface charge is negative and of just the right magnitude so that the cable as a whole is...
  30. Mk

    Vector field, and Lorentz Symmetry

    What are they? "A fundamental property of the natural world that is of supreme importance for physics. It has two components: rotational symmetry, and boost symmetry." :confused:
  31. M

    Information, symmetry, and QM

    I'm considering how the 2nd law of thermodynamics (2LT) might necessitate quantum mechanics. For it would seem that QM effects always consist of a superposition of states. Each state has a particular structure, and there is a number of these states that must be in quantum mechanical...
  32. K

    Is electromagnetism's symmetry affected by the composition of particles?

    Quarks can't exist in isolation and the electric charge on quarks can't exist in isolation from the electric charges of other quarks either.The electric charge of leptons like the electron can exist in isolation.Isn't electromagnetism showing a kind of asymmetry here: symmetry could be restored...
  33. K

    How does non-abelian gauge symmetry affect quark interactions?

    How does a non-abelian gauge symmetry lead to asymptotic freedom for quarks?
  34. K

    Conservation of energy in GR and symmetry

    Experiment shows that many physical quantities are conserved and that the associated conservation laws can be linked to symmetries. However it seems strange that general relativity is a theory built from principles of symmetry and yet energy might not be conserved in general relativity.Surely...
  35. T

    Understanding U Symmetry: Exploring Its Meaning and Importance

    could someone explain this
  36. T

    Symmetry Breaking: How Does It Occur?

    How does symmetry breaking occur?
  37. K

    How Fast Can a Mass-Charge Swapped Sun Generate Electromagnetic Waves?

    If I take a large mass such as the sun and change its negative electric charges (half the total number of charges) into positive charges, so all electric charges are positive, and I transform the electric force so that like charges attract, the charges would be behaving like masses.If I take the...
  38. R

    So, what are the properties of space at the Planck length?

    What are the properties of "space" at the Planck length? http://physicsweb.org/article/world/17/3/7
  39. O

    Is Blackhole Symmetry Proportional to Information Exchange?

    Is the amount of information taken in by a Blackhole, proportional to the amount given out?
  40. H

    Partitioning Symmetry Groups: Exploring the Multiplication Table Method

    I reading a great book called Symmetry by Roy McWeeny. For those that love Dover Books this one's a gem. Anyway, I have a question. How do you partiton a particular group into distinct classes? The author was discussing the symmetry group C3v the rotation, and reflection of a...
  41. M

    Axis of Symmetry of y=a(x-r_1)(x+r_2)

    Problem 1. Consider the equation y=a(x-r_1)(x+r_2) Write the equation of the axis of symmetry.
  42. M

    Symmetry breaking, what is it?

    What is this symmetry breaking process I keep hearing about?
  43. R

    Residual conformal symmetry in GSW

    Hello, I hope you don't mind this elementary question, but I got stuck with it this evening: GSW state in their equ. (2.1.44) that a combined reparametrisation and a Weyl scaling obeying d^aA^b + d^bA^a = Gamma n^ab don't change the choosen gauge h^ab=n^ab. Now I tried to proof this. The...
  44. Antonio Lao

    Perfect Symmetry: The Perfect Universe

    Perfect Symmetry Heinz R. Pagels wrote about it. I have read it. But I don’t remember enough to say for sure that what I will discuss in the following is not just echoes of what he said. In any event, my understandings of perfect symmetry are the following. In a perfect universe...
  45. Antonio Lao

    Is Time's Symmetry Essential for Validating Physical Experiments?

    Subtitle: Fallacy of all physical experiments If the symmetry of time is broken then all physical experimentations are fallacious. Take one experiment, a bias is unavoidably embedded into it. This bias is time. All experiments are always done in looking backward in the time direction. A...
  46. M

    Why is there no symmetry in space vs. time dimensions?

    If there are three spatial dimensions, why is there only one time dimension? Why can't there be three temporal dimensions parallel to the spatial ones. If there are, perhaps this is what they would resemble. The fourth dimension could be temporal linear - the easiest way to view time...
  47. Loren Booda

    Physical asymmetry from symmetry

    I recall that in their most basic form, quantum mechanics and relativity do not distinguish between past and future. That is, they are each symmetric with respect to time. How then does a unified theory account for temporal assymetries in nature without introducing new physics? Can one...
  48. Loren Booda

    Does each superstring extradimension correspond to a gauge symmetry?

    Does each superstring extradimension represent a (gauge) symmetry?
  49. W

    Is symmetry the key to understanding our relativistic universe?

    Please, anyone who wants to rant about symmetry or relativity, please feel free. Here's my rant. In relativistic terms, whether or not something is moving at all through space or time depends upon your frame of reference. This includes not least of all the entire universe. To a photon...
  50. M

    Dielectric boundaries and symmetry

    I have been reviewing the method of images for electrostatic problems and noticed the following: Textbooks point out that to use Gauss' Law successfully there must be geometric symmetry that makes the Efield constant over some reasonable surface. I thought this was just to make the math...
Back
Top