Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry
Questions tagged [symmetry]
1533 questions
1
vote
1 answer
Reading the sphere diagrams in point groups on wikipedia
How do you read/make sense of the sphere diagrams shown here: http://en.wikipedia.org/wiki/List_of_spherical_symmetry_groups
What do the yellow shaded areas represent?
What are the red triangle/arrows?
Why are the curves drawn like so?
Can you…
ina
- 455
1
vote
2 answers
Symmetry in Space
Is it possible for a non-co-planar set of points to be symmetric about a point but not symmetric about a plane?
I am pretty sure this is true but I can't think of an example.
Things that I think don't…
Zachooz
- 169
- 7
1
vote
1 answer
Farthest points in asymmetric 2D closed curve
Is there a mathematically proper name for the two points that are located farther away from each other in a 2D asymmetric closed curve? See the image below to get an idea of what I mean.
Gabriel
- 1,355
1
vote
2 answers
Property on glide reflections
I need to prove that the conjugate of a glide reflection is a glide reflection.
What I have tried: Let $m: X= \begin{pmatrix} x_1\\ x_2 \end{pmatrix} \mapsto \begin{pmatrix} \cos \phi & \sin \phi \\ \sin \phi & -\cos \phi \end{pmatrix}…
amir
- 1,311
1
vote
1 answer
Question on a lemma related to isometries
$\textbf{Lemma:}$ An isometry $f$ that has the form $m=t_a \rho_{\theta} $, with $\theta \neq 0$, is a rotation through the angle $\theta$ about a point in the plane.
$\forall x \in M_{2,1}(\mathbb{R}) , t_a(x)=x+a$ (translation)
$\forall x=…
amir
- 1,311
1
vote
0 answers
Is there a dictionary/encyclopedia/thesaurus of equivalent equations?
I had heard from Barry Barish that (paraphrased from Lex Fridman podcast): In 1916, Einstein noticed that if he wrote the formulas for general relativity in a particular way, they looked a lot like the formulas for electricity and magnetism. He knew…
Hmm
- 131
1
vote
1 answer
What is the formal definition of a symmetry of a subset of the real plane?
Consider a set $S \subseteq \mathbb{R}^2$. What does it mean for a function $f$ to be a symmetry of $S$? After all, there are usually infinitely many bijections on $\mathbb{R}^2$ that send $S$ to $S$. I would very much like some clarification of…
user107952
- 20,508
1
vote
1 answer
Using symmetry to calculate the centroid
How can I show (without calculating the triple integral) that the $y$ centroid of a $\mathbb R^3$ region enclosed by $z=x$, $x^2+y^2 =1$ and $x^2+y^2 =4$ equals $0$.
All I know is the plane $z=x$ holds for all values of $y$ so it should not have an…
mathnoob123
- 1,373
1
vote
2 answers
Symmetry notation
Does pure mathematics bring a good, concise, straightforward, standard notation to express a symmetry argument?
I will give an example but as you can see, the example is too long—which is exactly my point. Is there not a much shorter, clearer, more…
thb
- 449
1
vote
1 answer
Layman symmetry versus mathematical symmetry
I'm reading Edward Frenkel's Love & Math and he talks about the mathematical concept of symmetry. He says a symmetry is a transformation of an object that, in the end, leaves the object unchanged or brings it back to a state indistinguishable from…
147pm
- 920
1
vote
1 answer
Determine the formulas that represent the decomposition of vertices/edges/faces into orbits.
I've taken a basic stab at this problem. I feel like I am missing something big. Please help. Thanks!
Q: Let $G$ be the group of rotational symmetries of a cube, let $G_v, G_e, G_f$ be the stabilizers
of a vertex $v$, an edge $e$, and a face $f$ of…
clay
- 2,713
- 23
- 34
0
votes
2 answers
What is a "unique" mirror line of symmetry?
What is a "unique" mirror line of symmetry? For example why does an equilateral triangle have three mirror lines but only one "unique"mirror line of symmetry?
pirsquare
- 721
0
votes
1 answer
Symmetry Definition and Equation
I need some help to understand Inversian Symmetry, Conformal Symmetry, and Scale Symmetry. Could you give me some guideline?
TBBT
- 347
0
votes
0 answers
The relationship between proportionality and symmetry
In this post Matt Strassler talks about proportionalities and symmetry in the context of massless photons.
I asked this question
«x and y are not invariant, but the equation which relates them is invariant! »
This sounds like the definition of a…
zeynel
- 365
0
votes
1 answer
Symmetry point of experimental data
I have the experimental data of some measurement as a function of angle. Since this is an experimental data, I have the measurements at every 1.8 degree. From the physics, I do know that the data should be symmetric with respect to some angle. But…
