# Questions tagged [visualization]

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

198 questions
535 views

### 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 ...
196 views

### The famous prime race and generalizations

So I was messing around with the famous prime race that comes down to this: We make a list of primes. The list has two rows; the top row is for primes $1\mod 4$ and the bottom row for primes $3\mod 4$...
269 views

### Geometric representation of Euler-Maclaurin Summation Formula

When reading Tom Apostol's expository article (or the free link), I was expecting more diagrams to come that follow the figure below (or this from the Wolfram project). It was a disappointment not ...
497 views

### Visualizing Hopf fibration $S^3\to S^2$ as a based map $S^1\to \mathrm{Map}(S^2,S^2)$

A fiber bundle $F\to E\to B$ may be interpreted as $E$ being a bunch of $F$s arranged in the shape of a $B$. For instance, a Mobius band $M$ is a bunch of line segments $[0,1]$ arranged in the shape ...
604 views

### Visual intuition for direct sum vs. tensor product of vector spaces

I completely understand the formal mathematical distinction between the direct sum and the tensor product of two vector spaces. I also understand that the direct sum has a nice visual interpretation (...
215 views

### Seeing symmetries

Preliminaries Let $[n] = \{0,\dots,n-1\}$ and $P([n])$ be the power set of $[n]$. Let the correlation between two subsets $x,y$ of $[n]$ be the number $\kappa(x,y) = 1 - \frac{2}{n}|x\triangle y|$ ...
637 views

### How to visualize cotangent spaces.

I was wondering how to intuitively and visually understand dual vector spaces and one-forms. So my question is (1), how to visualize cotangent spaces and (2), how to intuitively understand them? My ...
188 views

### Figures and Numbers: Relating properties of geometric shapes and their Fourier series

Consider two types of parametrized curves $\gamma:[0,2\pi]\rightarrow \mathbb{R}^2$ open curves $\gamma_\sim(t) = (t,a(t) + b(t))$ closed curves $\gamma_\bigcirc(t) = (a(t),b(t)) = a(t) + ib(t)$ ...
192 views

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### Graph layout that reflects graph symmetries

I am looking for practical computational methods to lay out graphs in such a way that the geometry of the drawing reflects some of the symmetries of the graph. Here are two example drawings of two ...
103 views

### Iterative construction of the real projective space

I can visualize the construction of $\mathrm{RP}^2$ from a disc $B^2$ whose boundary $S^1$ is subjected to the antipodal identification. This can be obtained by glueing the edge of a Möbius strip $M$, ...