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

# Questions tagged [visualization]

864 questions

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votes

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### A way to directly see that the interior angles of triangle sum to $180^\circ$?

I'm looking for a way to look at a triangle, and perhaps visualize a few extra lines, and be able to see that the interior angles sum to $180^\circ$.
I can visualize that supplementary angles sum to $180^\circ$. I'd like to be able to see the…

hyperpallium

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### Is there an intuitive way of visualising complex roots?

Consider the function $f(x)$ such that $f(x) = x^2-4x+13$. By considering the discriminant, it can immediately be seen that the function has no real roots, since $b^2-4ac = (-4)^2-4(13) = -36$ and $-36 < 0 $, and hence the graph looks as…

joshuaheckroodt

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### Textbooks for visual learners

Perhaps this question has already been asked (if so, please let me know) but I am looking for books that appeal to visual learners.
I discovered that I am able to understand concepts much quicker and better when they are explained/taught in a…

qmd

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### Trying to visualize the hierarchy of mathematical spaces

I was inspired by this flowchart of mathematical sets and wanted to try and visualize it, since I internalize math best in that way. This is what I've come up with so far:
Version 1 (old diagram)
Version 2:
Is there anything that I'm missing, or…

Patch

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### Can I represent groups geometrically?

I have just taken up abstract algebra for my college and my professor was giving me an introduction to groups, but since I like geometric definitions or ways of looking at stuff, I kept thinking, "How do you represent a group geometrically in a…

user210387

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**1**answer

### Geometric representation of Euler-Maclaurin Summation Formula

In Tom Apostol's expository article (here's a free link), upon seeing the figure below (or this from the Wolfram project) I was expecting more diagrams to come to continue the error decomposition of the shaded regions in the shape of "curved…

Lee David Chung Lin

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### A random walk on a finite square with prime numbers

This question is following two similar questions that you can find here and here.
The idea is to walk on a square of length $n\times n$, following some rules. We will identify the opposite sides.
Formally, the square with the opposite sides…

E. Joseph

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### Visualization of Lens Spaces

I am trying to visualize lens spaces geometrically.
While I am aware of the fact that most manifolds which cannot be embedded in $\mathbb{R}^3$ are hard to visualize because of the obvious limitations, some of them are not too complicated; For…

Pandora

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### Are there any visual proofs for $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$?

I was flipping through Proofs Without Words (PWW) and saw many visual proofs for sequences and series. However, I saw none for $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$$
Are there any visual proofs for the above series?

zerosofthezeta

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### Interesting implicit surfaces in $\mathbb{R}^3$

I have just written a small program in C++ and OpenGl to plot implicit surfaces in $\mathbb{R}^3$ for a Graphical Computing class and now I'm in need of more interesting surfaces to implement!
Some that I've implemented are:
Basic surfaces like…

Leonardo Fontoura

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### Visualizing the Partition numbers (suggestions for visualization techniques)

So Ken Ono says that the partition numbers behave like fractals, in which case I'd like to try to find an appropriately illuminating way of visualizing them. But I'm sort of stuck at the moment, so here I'm asking for suggestions for visualization…

graveolensa

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### Can Number Theory be visualized?

So I was thinking about a hard euclidean geometry problem, when it hit me just how much more difficult it would become without the aid of a diagram. This got me thinking: Wouldn't it be great if we could somehow find corresponding diagrams for…

user45220

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### Visualizing the factorial

Often in basic mathematics, we can visualize things very easily, which I believe helps understanding (instead of just working out a number theoretical proof). For example:
$$(n+1)^2 - n^2 = (n+1) +n$$
can be visualized by squares. Remove a square…

Krijn

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### A prime number random walk

This question came to my mind thanks to this question which I found really interesting (and beautiful! Like the mathematician Philippe Caldero said in his book Histoires Hédonistes de Groupes et de Géométries (roughly translated) "Let us stop for a…

E. Joseph

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### An enigmatic pattern in division graphs

Draw the numbers $1,2,\dots,N$ on a circle and draw a line from $n$ to $m>n$ when $n$ divides $m$:
For larger $N$ some kind of stable structure emerges
which remains perfectly in place for ever larger $N$, even though the points on the circle get…

Hans-Peter Stricker

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