Questions about symmetry, in group theory, geometry or elsewhere in mathematics. See https://en.wikipedia.org/wiki/Symmetry
Questions tagged [symmetry]
1533 questions
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Square cut into 2 parts, point reflection
There is following statement: if a square is cut into 2 congruent parts (i.e. equal area and shape), then the cut line (not necessarily straight) will have point reflection around the center of the square, in particular, it will pass through it. I…
user3798254
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Can one imagine spaces where point reflections are not bijective?
Not a mathematician, and the question probably does not make sense but asking it anyway:
In usual euclidian spaces, central inversion through O(0,...,0) of point M(x1,...,xN) gives you one and only one point M'(-x1,...,-xN). I would write…
DarkBulle
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Finding point of symmetry of function $y=2x^3-bx^2+cx$
may I know how to find the point of symmetry of the function $y=2x^3-bx^2+cx$. I have checked some resources, it said that the point of symmetry is $(\frac{b}{6},f(\frac{b}{6})$, due to the fact that $\frac{b}{6}=\frac{p+q}{2}$, where p is the…
Henry Cai
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When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers?
When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers? Because the vertices of square also gives the same symmetries.
user629838
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Symmetry problem involving functions
I was given a definition.
A symmetry of a plane figure $F$ is an isometry that maps $F$ to itself, that is, an isometry $f:R^2 \to R^2$ such that $f(F)=F$.
I don't really understand this because is $F$ not a collection of points and the domain of…
hitherematey
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How to calculate and compare symmetry between two objects?
I need to figure out how symmetrical two objects are. Is there an equation that will generate numerical values in regards to symmetry?
I.e object 1 has 0.5 symmetry while object 2 has 0.6 symmetry so therefore these two objects have similar…
RustyShackleford
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Abstract Branch of Math Covering Symmetry?
If anyone could point me in the direction of a branch of mathematics that focuses on symmetry (or abstracting symmetry), I would greatly appreciate it. Not just in terms of functions and shapes, but at a higher-level than that.
Samuel
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Why do two symmetrical points form a perpendicular line to their reflection axis?
Question is the title. I know that this is the case, but I don't know why.
You can take two points that are at the same distance from an axis but whose line doesn't form a 90° angle to the axis and they wouldn't be symmetrical, so why is this?
Jose
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Infinitesimal transformation of Lagrangian
I am trying to find three independent infinitesimal transformations that leave my lagrangian invariant.
$$\mathcal{L}=-\frac{1}{2}\partial_{\mu}\phi_I\partial^{\mu}\phi^I-\frac{1}{2}m^2\phi_I\phi^I $$
The indecis $I=1,2,3$ represent three…
user405158
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Proving that expectation equals point of symmetry without calculus
In my Probability book I have come across the following passage: "Since the PMF is symmetric around 3.5, we conclude that E[X] = 3.5". The PMF in question is one of a binomial random variable uniformely distributed around 3.5. My doubt is: is it…
daniels
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2D figure with a nontrivial rotational symmetry
I am stuck with following problem, could anyone help me?
(1) Can a finite 2D figure with a nontrivial rotational symmetry can have exactly one reflection symmetry?
thanks
Myshkin
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Does $y=(ax^{2}+bx+c)/(dx+e)$ have any lines of symmetry?
Does $y = \dfrac{ax^2 + bx + c}{dx + e}$ have any lines of symmetry. If it does, what are they, and if not, how would one prove that it doesn't have any lines of symmetry?
(Please consider the general case. And please ignore trivial cases where the…
user46234
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Does $y=2/x$ have any lines of symmetry?
Lines of symmetry for $y=1/x$ are $y=x$ and $y=-x$.
Does $y=2/x$ likewise have lines of symmetry?
user46234
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Show $d(x,y) = d(y,x)$
If
$$\mu (x,y) = \min\{n\in\mathbb{N} \ | \ x_n \not= y_n \}$$
and
$$d(x,y) = \frac{1}{\mu(x,y)}$$
How can I show that
$$d(x,y)=d(y,x)$$
For me it's pretty obvious, but I don't know how to show it mathematically.
Stranqer95
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Describe the orbits of poles for the group of rotations of an octahedron.
Can anyone review my work on this problem and tell me if I'm missing anything major? Thanks!
Q: Describe the orbits of poles for the group of rotations of an octahedron.
There are $|G|=N=24$ rotational symmetries for an octahedron. These can be…
clay
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