# Questions tagged [symmetry]

Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry

875 questions
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### Rigid motions taking a regular $n$-gon back to itself carry vertices to vertices

I have been reading Keith Conrad's expository paper Dihedral groups I and I have two questions about Theorem $2.2$, which deals with the size of $D_n$. In the first part of the proof you can read ...
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### Determining Graph Automorphisms by Determining Ways of Permuting Edges

Here is an example from the book Groups, Graphs, and Trees (Ignore example 1.15; I accidently included it in my snippet of the pdf): From my understanding, the symmetry group of a graph $\Gamma$ ...
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### Lie symmetry methods of differential equations.

If we have a differential equation $$y^{(n)} = H( x, y, y', ...y^{(n-1)}) .$$ And say we have its two infinitesimal generators admitted by this equation. What do I mean by the invariance of this ...
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### center of symmetry formula

How to prove that $I(0,-1)$ is the center of symmetry of the function $$F(x)= x - \dfrac{2e^x}{(e^x -1)}$$ Is there any formula that I can directly apply?