The visualization tag has no wiki summary.
5
votes
2answers
383 views
How to Visualize points on a high dimensional (>3) Manifold?
Are there any ways to visualize(plot/draw) points on a high dimensional (ex: dimension = 5) manifold?
10
votes
2answers
262 views
What are all these “visualizations” of the 3-sphere?
a 2-sphere is a normal sphere. A 3-sphere is
$$
x^2 + y^2 + z^2 + w^2 = 1
$$
My first question is, why isn't the w coordinate just time? I can plot a 4-d sphere in a symbolic math program and ...
13
votes
3answers
889 views
Cutting a Möbius strip down the middle
Why does the result of cutting a Möbius strip down the middle lengthwise have two full twists in it? I can account for one full twist--the identification of the top left corner with the bottom right ...
4
votes
1answer
276 views
Intuition about the size of $\aleph_k$ with $k>1$
Assuming CH for simplicity, I know of some more or less intuitive way to think about difference in sizes of $\aleph_0$ and $\aleph_1$. The most straightforward is the distinction of natural/rational ...
34
votes
4answers
851 views
Algebra: Best mental images
I'm curious how people think of Algebras (in the universal sense, i.e., monoids, groups, rings, etc.). Cayley diagrams of groups with few generators are useful for thinking about group actions on ...
4
votes
7answers
800 views
Techniques for visualising $n$-dimensional space
Can you guys point me to the types of things I should read about (I'm a maths lay person really) if I want to learn about the current thinking how $n$ dimensional spaces can be visualised and thus ...
4
votes
1answer
80 views
The complement of a torus is a torus.
Take $S^3$ to be the three-sphere, that is, $S^3=\lbrace (x_1,x_2,x_3,x_4):x_1^2+x_2^2+x_3^2+x_4^4=1\rbrace$. Using the stereographic projection, $S^3=\mathbb{R}^3\cup \lbrace \infty \rbrace.$ Can ...
4
votes
2answers
177 views
Computing the projection of an infinite 3D grid of points
Consider the subset $S$ of $\mathbb{R}^3$ consisting of points whose coordinates are integers (compare Gaussian integers, Euclid's orchard). The view from the origin has interesting structure; it has ...
0
votes
0answers
144 views
Visualization of 2-dimensional function spaces
As a follow-up question to what is the norm measuring in function spaces
I just had an idea: How about visualizing function spaces as normal planes. What I have in mind is to have an orthogonal ...
11
votes
7answers
300 views
$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? [duplicate]
If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed ...
