# 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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### 5-cell "4D tetrahedron"

I do not know if this is the right place to ask this. But if I have a 3D object (tetrahedron) I can make a projection of it into 2D space where I use colour as the third dimension to determine height. ...
1 vote
53 views

### Assistance in recognizing & visualizing a specific topology

I’m a bit out of my element asking math questions here, but hopeful someone can point me in the right direction. Thanks in advance! Questions: Do the two tables illustrated below each form a shape in ...
69 views

### Is there a visualization tool that shows matrices transforming (multiplying) ellipses?

Matrices send ellipses to ellipses. Is there any online visualization tool where I can enter a matrix $M$ and see a plot of ellipse $e$ being sent to $Me$? This would be very helpful to visualize ...
1 vote
63 views

### Drawing isosceles right triangle on unit circle for intuitive meaning of √2/2

Have you wondered about the meaning of $\sqrt{2}/2$ on the unit circle? Drawing a unit length line at $45^\circ$ from the origin, reflecting it on the $x$ axis and connecting the points where the ...
115 views

### What is going on with this Taylor Series?

I created a program to find high degree Taylor series approximations for any function, but I notice an interesting behavior as higher order polynomials are included. My understanding is that a ...
55 views

### Visualizing the last two paragraphs of 3.2.3(b) solution.

Here is the question I am trying to understand its solution: Finish the proof of Borsuk-Ulam theorem (Hatcher) I did not understand this part of the solution: Let $\gamma:[0,1]\to \Bbb RP^n$ be a ...
34 views

### Is this visualization of arc connectedness of SO(3) wrong?

The article "Anti-twister mechanism" at Wikipedia has an animation showing Dirac's theorem. The rotation axis of the cube is vertical, so it's the distinguished direction. The four belts ...
1 vote
31 views

### Understanding a figure showing the wedge product

On the wikipedia article explaining exterior algebra, this figure is shown, visualizing the relationship between the wedge product of 2 vectors (or differential forms for that matter), and the "...
45 views

### Immersion of $\mathbb RP^2$: explanation of Kirby's article on the Boy's surface

I am trying to understand Rob Kirby's AMS notice https://www.ams.org/notices/200710/tx071001306p.pdf on Boy's surface. From this blogpost https://divisbyzero.com/2020/04/08/make-a-real-projective-...
38 views

### Intuition of Homotopy in Non-Euclidean Spaces

Please note that I am a beginner in Algebraic Topology. I am struggling with the intuition of homotopy equivalence in non-Euclidean spaces. To be more specific, we know that any two loops with the ...
26 views

### Visualisation of the cubic curve $C: y^2 z − x^3 − x^2z − xz^2 − z^3$

To get some insight on the zero locus of the cubic curve, I've tried a couple of online visualisers on Google and mostly failed to generate the plot (run time errors...) except Wolfram Alpha which ...
14 views

### Determine shape of marginal gaussian given 2D gaussian contour lines

Given a 2D multivariate Gaussian contour lines and a point $x_0$, is it possible to draw the marginal distribution $f(y)=\mathbb{P}((X,Y)=(x,y)|x=x_0)$. From the picture, it seems the mean of the ...
121 views

1 vote
103 views

### Correct visualization of a probability density function of 3 continuous random variables

I am reading Rice's book of mathematical statistics, and I have understood that if we visualize a joint probability density function (pdf) of 2 continuous random variables, then in 3D space they ...
95 views

### Understanding projective change of coordinates.

An affine change of coordinates on $\mathbb A^n$ ,the affine $n$-space is defined to be a polynomial map $T:\mathbb A^n\to \mathbb A^n$ which is given by linear homogeneous polynomials and is also ...
31 views

### How to plot/visualize the inverse image of a set using computer software?

Question Let $f: \mathbb C \rightarrow S^2$ be a holomorphic map and $E\subset S^2$ be a geodesic line segment in $S^2$. I would like to plot/visualize $f^{-1}(E)\subset \mathbb C$ on the plane. What ...
184 views

### How can I improve my comprehension of mathematical notation and avoid getting lost in the details, when there's no obvious visualization to rely on?

For context, I'm an engineering student nearing the end of my degree and I've been tutoring algebra, calculus, and statistics for years, so I'm not a newbie to math. It's only really been an issue in ...