Questions tagged [symmetry]

Question 1

I was unsatisfied with the many proofs of the Pythagorean theorem in which it's not clearly apparent which axioms are specifically needed, or because said axioms seem too geometrically motivated in ...

Question 2

Consider a Cobweb diagram on the following function in the interval $(\frac12,1]$: The function is clearly arranged as a fractal, in fact its most obvious symmetry is $x\cong \dfrac{x+2}4$ By this ...

Question 3

I took the image from the IGCSE maths problem, and the answer key says it has 3 symmetrical lines like this: How come? I think the answer key is incorrect? I even tried to print out it on the paper ...

Question 4

In this lecture, Professor Stephen Boyd begins to draw a commutativity diagram to raise the question of whether transforming a program with strong duality into an equivalent problem and computing its ...

Question 5

I am reading a book on symmetry methods for differential equations and trying to understand what exactly the infinitesimal generator is? (And what it describes geometrically, if it describes ...

Question 6

I am reading about symmetry methods on differential equations. It starts by considering invariant points, then orbits of points and invariant curves. It ends in a method to determine all (w.r.t Lie ...

Question 7

This question is related to my previous posts about overlapping circles, like this one. Another way of overlapping 3 circles looks like this: Once again, my question is, "How can these 3 circles ...

Question 8

When doing homework on algebra, on the symmetries of regular polygons and regular polyhedra, I observed, that mapping vertices of a single edge in regular polygon to another or mapping vertices of a ...

Question 9

I have been studying centrally symmetric shapes (i.e., shapes with a center point $O$ such that for every point $P$ on the shape, there exists a point $P'$ where $O$ is the midpoint of $PP'$). When ...

Question 10

Let $K = \mathbb{R}$ or $\mathbb{C}$ and $n \in \mathbb{N}, n \geqslant 2$. I was thinking about the topology of two subsets of $\mathfrak{M}_n(K)$ we don't talk about very often in Matrix Topology ...

Question 11

The determinant of a matrix is given by the Leibniz formula $$\det(A) = \sum_{\tau \in S_n} \text{sgn}(\tau) \prod_{i = 1}^n a_{i\tau(i)} = \sum_{\sigma \in S_n} \text{sgn}(\sigma) \prod_{i = 1}^n a_{\...

Question 12

I'm reading Invitation to Discrete Mathematics (2nd edition) by Matousek and Nesetril. Page 41, problem #2 asks: Prove that a relation $R$ on a set $X$ satisﬁes $R ◦ R^{-1} = ∆X$ if and only if $R$ ...

Question 13

Let $n \in \mathbb{N}$. I am looking for an explicit example of an open, bounded, symmetric, convex subset $C \subset \mathbb{R}^2$ whose full Euclidean symmetry group (that is, the group of ...

Question 14

This problem is taken form the Hungarian Problem Book III for math olympiads and this is problem 1935.2. In the solution it essentially assumes the existence of two centers of symmetry O and O' and ...

Question 15

Looking for confirmation that the following method constructs a geometric object whose symmetry is described by a finite group $G$. Let $G$ be a finite group which is a subgroup of the symmetric group ...

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Questions tagged [symmetry]

Showing positive definite quadratic forms give the "most symmetrical" metrics over $\mathbb{R}^n$

If a representative part of a fractal-defined function lies entirely below the $y=x$ line, is this sufficient to guarantee no periodic points?

Guessing the Symmetry figure

Graph of Optimization Problem Transformations

What exactly is a infinitesimal generator?

Why do we care about invariant solutions of differential equations (under a one parameter Lie group)?

Smallest overlapping circles containing unit circles in each section - Fifth arrangement

symmetry of a polytope after mapping one facet

Must an inscribed parallelogram's center match the shape's symmetry center？

Topology of projection matrices and symmetry matrices

Is there such a mathematical notion as 'antideterminant'?

Reflexive and Antisymmetric relation question

Symmetric convex set in $\mathbb{R}^2$ with symmetry group exactly $\mathbb{Z}_n$ (no reflections)

Prove that a finite point set cannot have more than one center of symmetry [closed]

Geometric representation of finite groups

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