# Questions tagged [visualization]

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

737 questions
Filter by
Sorted by
Tagged with
152 views

### Distributions of prime numbers

When folding the number line not into a spiral (like Ulam did) but into a zig-zag pattern (like Cantor did) there are other patterns visible in the distribution of prime numbers: [To see these ...
89 views

### Why do we evaluate $-x^{z-1}e^{-x}$ as zero when explaining the gamma function through integration by parts?

The gamma function is the integral of $x^{z-1}e^{-x}$ If you integrate by parts you get two terms. The first one is $-x^{z-1}e^{-x}$ and this is bound by infinity and zero. If you plug in infinity, ...
135 views

128 views

### Geometrical visualization of Tensors

My question is about tensors. I have recently spent some time studying the various definitions of tensors and some tensor calculus. What I am missing now is an intuitive way to represent tensors and I ...
60 views

### Projecting 6D cartesian coordinates to lower dimension

I've got a noisy set of points that lie on/near a unit 6-sphere. I want to visualise their proximity to the sphere in some way. The only way I can come up with now is a histogram of the norm of the ...
50 views

### Would this suffice in a visual type theory to define an abstract List type?

See the image. I got that from: wikipedia article. In that, I don't understand the first function nil : () -> L. What is ()...
72 views

### Efficient visualisation of arrangements

First, I don't know the word for the set. I have n cases and the set I have is 2^n which lists all their "arrangements" present or absent, so a summation of combinations with k from 0 to n. Each ...
94 views

### Geometric intuition of a point in a flag manifold

From Wikipedia According to basic results of linear algebra, any two complete flags in an $n$-dimensional vector space $V$ over a field $F$ are no different from each other from a geometric point ...
227 views

### How can I use kernel density estimation for heat map visualization?

I want to know more about visualization and density estimations. Basically, I have a large sample of location data and every location object has a duration in milliseconds. I want to solve the ...
222 views

### Derivative of Square Root Visual

Derivative formulas through geometry | Essence of calculus, chapter 3 (3Blue1Brown): https://www.youtube.com/watch?v=S0_qX4VJhMQ There is a challenge at 12:23 asking the viewer to arrive at the ...
942 views

298 views

### Row versus column picture

So, we have a system of linear equations.It's preferred that we visualize the column picture, since as dimensions go up we only have to think of vectors moving to more dimensions, instead of ...
44 views

### Visualizing $c-d<a-b \implies b<a+d-c$?

I am wondering if someone can provide some geometric intuition, or some simple way to visualize why $$c-d<a-b \implies b<a+d-c$$ The way I have been trying to do this is to think of $a,b,c,d$ ...
28 views

### How to combine multiple indices?

I'm trying to combine various risk indices e.g. flooding, fire, burglary and structural damage. These values are scored from 1-3. For instance, I could have measures for two different areas as ...
149 views

### Visual proof of isosceles base-angle congruency?

A geometric proof (without algebra or trigonometry), and ideally presented visually (a proof without words). EDITED (I'm especially curious if it's possible without without using triangle congruency.)...
44 views

### Plotting lines, points, planes, triangles for technical documentation

I'm looking for a (free) tool to draw or plot graphics as the one linked below: Maybe a CAD solutions could be the easiest one. But which do you recommend for this certain case? I don't want to deal ...
136 views

39 views

### Questions to test visualization in 4D

Some people claim to be able to visualize four dimensional objects. I have a friend who thinks that these folks are just blowing hot air. I thought it would be fun to test how well people actually ...
116 views

### (Soft) Why do our visual understandings of homotopy equivalence correspond to the definitions?

This may be too soft, and it may be a confusion only about formalism. But seeing why the homotopies equivalences I visualize in my head and that people describe are the same thing as the definition of ...
90 views

### Visualizing the minimization of $\|Ax-b\|_2^2$?

Consider the least-squares problem $$\text{minimize} \quad \|Ax-b\|_2^2$$ where $A$ is an $m \times n$ matrix and $b$ is an $m$-vector. How does it looks like geometrically? Could someone draw a ...
107 views

### Visualization vs memorization of mathematical knowledge [closed]

As far as math research is concerned, what kind of understanding level of mathematical knowledge is required in order to truly master a topic and leverage on it? Can top-level researchers fully ...
24 views

### A question regarding multi variate functions

When we have a simple one variable function $y = f(x)$, $f(x)$ gives the height of function/curve at an arbitrary point $x$, but if we have a multivariate function $u = f(x,y)$, what does it give us?