# Questions tagged [visualization]

For questions about visualizing mathematical concepts. This includes questions about visualization of mathematical theorems and proofs without words.

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### How to get equations of fluid flow velocity with vorticies

I am looking for the equation of the velocity field $\textbf{u} = u(x,y)\hat{i} + v(x,y)\hat{j}$ of a two-dimensional steady flow, which streamlines look similarly to this image: example image of the ...
38 views

### Can we visualize the action of $L_A$ easily?

(1) Let $A$ be an $n\times n$ real symmetric matrix. Then, $P^{-1}AP$ is a diagonal matrix for some orthogonal matrix $P$. Let $L_A:\mathbb{R}^n\ni x\mapsto Ax\in\mathbb{R}^n$. In this case, we can ...
• 6,093
1 vote
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### Is there a program or website for visualization of 2d and 3d matrix transformations?

Is there a program or website for visualization of 2d and 3d matrix transformations? Hello everyone !!! How to look at the transformation (when multiplying two matrices or a matrix by a vector) of ...
439 views

### How can you visualize Independence with Venn Diagrams?

Imagine two events $A$ and $B$ that are not mutually exclusive, such that $P(A) = 0.3$ and $P(B)=0.4.$ Consider the Venn diagram of the two overlapping sets, and visualize moving them closer together ...
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### Plotting Spherical Harmonics - Phase Coloring?

Looking at the wikipedia table of spherical harmonics, I'm trying to figure out how they are computing phase and using it set the hue on the plots. I can't figure this out for either the real plots (...
89 views

### What is the Cayley graph for alternating group A6?

According to ATLAS of Group Representations, the alternating group $A_6$ is a group of order 360 which has presentation $$\langle a,b \mid a^2 = b^4 = (ab)^5 = (ab^2)^5 = 1 \rangle.$$ If we draw its ...
• 717
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### Drawing a line from n-dimension in 3D by preserving angles!!

I am brainstorming on something. There might be a standard method for my problem, but I always like to rethink stuff. Here is the problem: I am working on a program mapping my data into a line in a ...
68 views

### How do two tori glued along the identity of $S^1 \times S^1$ look like?

I have got trouble imagining the outcome of gluing two solid tori $D^2 \times S^1 \sqcup_{\text{id}}S^1 \times D^2$ along the identity of $S^1 \times S^1$. If I understand correctly, the tori are ...
• 2,429
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### diagram of inner product - generalization?

Consider a sort of graphical language of linear algebra...tensor network diagrams. So consider the space of $n$ non-intersecting paths connecting a node $A$ to a node $B.$ This "picture" is ...
• 723
1 vote
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I'm currently exploring the meaning, intuition and differences of the various types of Fourier transforms. I can't say everything is ok, but I think I got most of them (hopefully, Dunning Kruger is ...
97 views

### Visually intriguing unsolved problems which are easy to explain

I have come across a list of visual proofs which are wrong (Visually deceptive "proofs" which are mathematically wrong) visual proofs which are not wrong (Proofs without words) visually ...
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