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# Questions tagged [visualization]

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4 votes
1 answer
287 views

• 323
281 votes
47 answers
109k views

### Examples of unexpected mathematical images

I try to generate a lot of examples in my research to get a better feel for what I am doing. Sometimes, I generate a plot, or a figure, that really surprises me, and makes my research take an ...
5 votes
2 answers
4k views

### Visualization of the real projective plane [closed]

Consider a closed (compact and without boundary) and non-orientable 2-manifold $M$. By Whitney embedding theorem, one can embed $M$ in $\mathbb{R}^4$. $M$ cannot be embeded in $\mathbb{R}^3$ and just ...
• 1,273
7 votes
4 answers
2k views

### Visualizing functions with a number of independent variables

I need to graph real valued functions (for exposition and analysis). The issue is: there are more independent variables so that the conventional graphing methods can't be used, and furthermore I don't ...
• 841
4 votes
4 answers
1k views

### Picturing a Certain Torus and Klein Bottle

The other day I was explaining orientability to someone and we were walking through some of the statements about orientability on the Wikipedia page on the topic. While I was able to satisfy his ...
• 5,191
37 votes
4 answers
5k views

### Understanding the countable ordinals up to $\epsilon_{0}$

in a recent MO question, link, discussing the current foundations of mathematics, the author linked a video lecture by Prof. Voevodsky, which argues against the principle of $\epsilon_{0}$-induction ...
28 votes
12 answers
3k views

### Creating high quality figures of surfaces

I am not sure if this question is suitable for mo, it is more about visualization than math. Anyway, here it is: What is the best way to visualize a 2-surface in Euclidean space with high quality? ...
19 votes
5 answers
17k views

### Visualization of Riemann–Stieltjes Integrals

The Riemann–Stieltjes integral $\int_a^b f(x)\,dg(x)$ is a generalization of the Riemann integral. It is e.g. heavily used as a starting point for stochastic integration. The approximating Riemann–...
• 5,915
10 votes
5 answers
1k views

### Visual representation of mathematical research interrelationships

I remember seeing a visualization in the form of a 2d (nodal) graph of all areas of academia, with math, physics and engineering over in one section, connecting in an arc to the central area of ...
• 2,383