# 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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71 views

### How to visualize this modular arithmetic problem?

In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 ...
144 views

### Visualisation of ordinal vs cardinal arithmetic

I came around a nice article talking about large countable ordinals with examples such as: Let's have a book with $\omega$ pages (each 1/2 the thickness of previous so we can fit them in a book of ...
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### Visualization of an algebraic stack

I am interested in thinking visually about algebraic stacks (also higher and derived stacks, but let´s start from the beginning). As the visuallization of an algebraic stack is virtually impossible I ...
35 views

### Kerr metric in SageMath causal visualization

I am studying the Kerr Metric via the SageMath manifolds module and would like to visualize the casual surfaces generated by light cones. Like the circles in this picture: Can anybody provide clues ...
187 views

### How can you mathematically define a “wobbly” function?

There are a lot of functions that look wobbly. For example $x^4 + x^3$ looks a little wobbly when it gets near the x axis. The function $\sin(x)$ is extremely wobbly. The function $\sin(x) + x$ is ...
43 views

### I attempted to visualize dot product of complex vectors. What do you advice?

I am an electronics undergraduate student currently learning wavelets. In the book A First Course in Wavelets with Fourier Analysis authors first introduce complex vectors and their dot products. Then ...
35 views

### Visual Intuition: Gaussians closed under addition

I'm trying to develop some intuition for the fact that the family of Gaussian distributions is closed under addition. I.e. if $X_i \sim \mathcal{N}(\mu_i, \sigma_i^2)$, then $Y = \sum_iX_i$ is also ...
129 views

### What's the geometric interpretation of the square root of a matrix?

Question: If I have a matrix $A$, I know that its square root is a matrix that has the same eigenvectors as $A$ but its eigenvalues are the square roots of the eigenvalues of $A$. What does this ...
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### Closed expression and physical interpretation of the median

Opposed to the arithmetic mean there is no immediate closed expression for the median of a distribution $n(x)$ of a variable $x\in\mathbb{N}$ over a population of $N$ items, at least not when ...
25 views

### Area of revolution of a square

A square of side length 1 is rotated 360 degrees about one of its vertices. What is the area of the region the square covers while rotating? I don't know how to visualize this as a geometric shape ...
93 views

### Asymptotic expansion of $Li^{-1}$ and zeros of $F(s)$ and $G(s)$

If you downvote please leave some constructive feedback. I would like to compare and visualize/gain insight about the zeros of two functions, $F(s)$ and $G(s).$ $\pi(m)$ is the prime counting ...
79 views

### A summation of the multiplication of reflected Mobius functions and their behavior for different values of $k$

$$\Psi_k(N)=\sum_{n=1}^{N} \mu(n)\mu(k-n)$$ where $\mu(n)$ is the Mobius function. This function is interesting to me because for the case of $k=N$ it has the symmetric property of being odd with ...
239 views

### How to see if a subgroup is normal from Cayley graph

Let be a Cayley diagram of group $G$. Let $H$ be the orbit of element p. Is $H$ a normal subgroup of $G$? Is there a simple way to check that because going by definition seems complicated. I tried ...
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### Enigmatic patterns in Archimedean spirals

Distributing the natural numbers as circles evenly along the Archimedean spiral yields surprising patterns when changing the radius of the circles: they cover more and more of the plane, finally ...
268 views

Consider two vector fields: $$\vec F_1=(\sin(x),\sin(y))$$ $$\vec F_2=(\sin(1-x),\sin(y)),$$ where $x,y \in(0,\pi).$ Does adding the two superimposed vector fields produce a net vertical flow, ...
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### Conic sections in addition and multiplication graphs of $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$

Compare two kinds of addition and multiplication graphs of the cyclic groups $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$: group tables (with colored circles on a rectangular grid) line graphs (with ...
263 views

### Compute fundamental group _visually_ by the polygonal representation of the space

Some time ago, before I learnt about covering spaces and Seifert-Van Kampen theorem, I tried to compute visually the fundamental group of some spaces. For example I figure out by myself that the ...
133 views

### $\operatorname{Spec}(\mathbb{Z}[x])$ as a ''classical'' topological space?

I've read recently the definition of the prime spectrum associated to a ring and how it can be made into a topological space. I've read that $\operatorname{Spec}(\mathbb{Z}[x])$ is really important ...
### Visualized group tables for $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
Let me share a kind of visualization of group tables which is especially well suited for cyclic groups like $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$. In these groups you can easily give colors to ...