The visualization tag has no wiki summary.
2
votes
0answers
77 views
Imagining four or higher dimensions and the difference to imagining three dimensions
I’m very interested in how people envision four or higher dimensions.
And I’m especially interested in how geometers and topologists who actually work in four dimensions do.
Now I know of the video ...
11
votes
7answers
303 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 ...
0
votes
0answers
18 views
How to visulize surface link in four dimension?
I am now facing a problem with "surface link" in four dimension. I have heard that three 2-torus can be linked in four dimension. And I have created a movie by cutting four dimensional space with ...
0
votes
1answer
73 views
Can anyone comprehend fourth-dimensional space and higher visually? [closed]
When I look at the "Clifford torus," for example, it just looks like a three dimensional object that's morphing/changing shape as it moves. Can anyone actually comprehend fourth-dimensional objects ...
0
votes
1answer
68 views
Visualizing Gauss-Legendre Quadrature
I'm creating a GUI interface for my Python Computing class that is supposed to showcase a few types of Numerical Integration. One of the ones I want to put in as an option is Gauss-Legendre ...
7
votes
0answers
114 views
Visualizing a Calabi Yau
I would like to understand how I can visualize the quintic threefold
$$ z_1^5 + z_2^5 + z_3^5 + z_4^5 +z_5^5 - 5\psi z_1z_2z_3z_4z_5 = 0$$
For a similar problem, Hanson proposes the following:
...
2
votes
1answer
42 views
visualizing functions invariant (or almost) under modular transformation
In the spirit of Möbius Transformations Revealed, I'd like to make a pair of movies depicting how Klein's absolute invariant $j(\tau)$ and the Dedekind eta function $\eta(\tau)$ transform when ...
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 ...
34
votes
4answers
853 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 ...
0
votes
1answer
36 views
How to represent a bounded function
I am not completely sure whether this question belongs on mathematics.SE but I figured to give it a shot:
I have a function which mathematically looks like this: $f(x)=\max(A,B\cos x)$
This will ...
2
votes
2answers
162 views
Fuzzy Venn diagram regions labeled in ternary
I have a couple of questions about the Venn diagrams object :
Words from the binary alphabet with n letters label each region of an order-n Venn diagram. Is there any more profound connection ...
1
vote
1answer
59 views
Visualizing diffeomorphisms
This is probably a really basic question (hence my asking it here as opposed to MO). In a comment to a question on mathoverflow ...
6
votes
2answers
103 views
An example of a Lie group
I have a trouble learning Lie groups --- I have no canonical example to imagine while thinking of a Lie group. When I imagine a manifold it is usually some kind of a 2D blanket or a circle/curve or a ...
1
vote
0answers
87 views
Which space this space drawn in this picture is homeomorphic?
Based in this question Why this space is homeomorphic to the plane? I would like to know which space this space is homeomorphic, any help or an intuitive idea are welcome.
[Context of Image: ...
6
votes
5answers
200 views
Cayley table group visualization
how can I make graphics like this? random colors. I got a script in GAP that prints rows of numbers but I want it colored
just random colors
...
6
votes
2answers
871 views
This quotient space is homeomorphic to the Möbius strip?
Let $G:\mathbb R \times [-1,1]\to \mathbb R \times [-1,1]$ be a map defined by $G(x,y)=(x+1,-y)$
This space $Q=\mathbb R\times [-1,1]/\sim$, where $(x_1,y_1)\sim (x_2,y_2)$ if and only if there is ...
1
vote
1answer
37 views
Vizualisation about line search in Linear Programming?
I am trying to visualize this recursive algorithm in LP, Wikipedia here. I am looking for references about in which kind of problems is this used and what does it really look like?
I am also ...
0
votes
0answers
43 views
Visualising the derivative/slope $f'(x_0)$ of $f:\mathbb{R} \rightarrow \mathbb{R}$ as a line segment
A function $f:I\subseteq \mathbb{R} \rightarrow \mathbb{R}$ that is differentiable at $x_0 \in I$ obeys the following equality for all $h\in (I-x_0)$ (i.e. for all $h\in \mathbb{R}$ such that $x_0+h ...
2
votes
2answers
145 views
Lie group and SO3 visualisation
Maybe I'm asking a very vague question but I'd like to know if there are some visualisation tools available already that explain lie algebra exponential map or logarithm? I'd like to be able to ...
2
votes
0answers
60 views
Visualizing and manipulating 4-dimensional data with 3D technology
It is possible to visualize 3 dimensional data (like a scatter plot) by projecting it on a 2 dimensional screen in a way that allows to interact with it in an intuitive way.
Is it possible to ...
2
votes
1answer
161 views
visual proof of the chinese remainder theorem?
I have seen visual proofs for fermats little theorem, gauss sum and many other things. I find them very useful. Is there a visual proof for the chinese remainder theorem? Thanks in advance.
2
votes
2answers
229 views
Why is it that I cannot imagine a tesseract?
I try hard to "visualise" (say "imagine") a tesseract but I can't.
Why is it that I can't?
This may be a question for a scholar of some other discipline and not for a mathematician, e.g. ...
1
vote
1answer
106 views
Kerning on the fly -algorithm [closed]
Do anyone know any algorithm which would calculate automatically kerning of characters based on glyph shapes when user types text?
I don't mean trivial calculation of advance widths or similar, I ...
5
votes
0answers
121 views
Visualizing Exterior Derivative
How do you visualize the exterior derivative of differential forms?
I imagine differential forms to be some sort of (oriented) line segments, areas, volumes etc. That is if I imagine a two-form, I ...
2
votes
0answers
56 views
Help me to vizualise this falling ball on spinning Earth
The earth rotates. The ball falls in an latitude, not equator, let say in Germany. I am trying to understand how to express the ball in terms of the angular velocity on the planet. The constant ...
2
votes
1answer
202 views
Visualizing Infinity discerning countable and uncountable
This is rather a philosophical question. Although it uses topological notions, it isn't any precise mathematics, so maybe one cannot take it very seriously.
Sometimes I try to picture an infinite set ...
3
votes
4answers
152 views
Proof-without-words for $\bar a\times (\bar b\times\bar c)=\bar b (\bar a\cdot\bar c)-\bar c (\bar a\cdot \bar b)$ or some visual-biased explanation?
Griffiths' Introduction to Electromagnetism -book has equations called 20.10 below.
I have proved this equation d) pretty much on the first mathematics -course I had but I have not yet understood a ...
3
votes
0answers
105 views
Illustrations of a line and a curve intersecting for complex field
Are there nice illustrations on the Net of say $y=a·x+b$ and $y=x^2$ intersecting where x and y are complex? I'm thinking of the amplitude of y being depicted as height above the complex plane with ...
0
votes
2answers
110 views
Visualizing $L_2$ or an infinite dimensional Hilbert space
I need to explain abstract objects in an infinite dimensional Hilbert space. What is the best way to visualize it for an engineering audience? Does anybody have a good example?
2
votes
1answer
202 views
Is there a geometric projection for every complex function
I was wondering about the best way to visualize complex functions. As they're $$ R^2 \rightarrow R^2$$ i think best way are complex plane image/grid transforms like they used in the Dimensions movie ...
4
votes
2answers
176 views
software tool for accurate visualization of algebraic curves
First of all, I apologize since this is not strictly speaking a "mathematical" question but I could not find a better place for it.
For a work presentation I need a tool for accurate visualization of ...
5
votes
3answers
345 views
Visualizing quotient groups: $\mathbb{R/Q}$
I was wondering about this. I know it is possible to visualize the quotient group $\mathbb{R}/\mathbb{Z}$ as a circle, and if you consider these as "topological groups", then this group (not ...
0
votes
0answers
54 views
Xi function plotter ??
i would like to know what software i need to plot the RIemann Xi function
$ \xi(s)= \frac{1}{2}s(s-1)\Gamma (s/2)\zeta (s) $ on a given interval , for example
from $ s=0 , s=1000 $ or from $ s=0 , ...
2
votes
1answer
57 views
What do you call a graph of value vs rank of the value?
What do you call a graph of value vs rank of the value?
For example, say I make a census of the 2010 net income for a bunch of people.
The graph of net income vs age gives me a: scatterplot
The ...
1
vote
1answer
614 views
Visualize a difference equation with Matlab [closed]
I have a difference equation for a Single Pole Infinite Impulse Response Filter, defined on a discrete time-series:
$y[n]-(1-\alpha)*y[n-1]=\alpha*x_n$
While the []s brackets refer to a position n ...
1
vote
0answers
165 views
The geometry of functions $\mathbb{R}^2\rightarrow \mathbb{R}$ that satisfy the norm axioms
What are constraints on the "looks" of a function $f:\mathbb{R}^2\rightarrow \mathbb{R}$, if $f$ satisfies $$f(x_1+x_2)\leq f(x_1) + f(x_2), \ \quad x_1,x_2\in \mathbb{R}^2 \quad \quad (1)$$i.e. the ...
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 ...
0
votes
1answer
174 views
Visualizing solids of revolution
Can someone shed a little bit of light on the problem of volumes of revolution about the $x$-axis and the $y$-axis of the same shapes? Take for example $f(x)=x^2$. If we want to find the volume ...
8
votes
3answers
218 views
Three-dimensional art galleries
The well-known art gallery problem starts with an "art gallery" (a simple polygon in the plane, not necessarily convex) and asks for the minimum number of "guards" (points on the polygon) required to ...
4
votes
3answers
98 views
Visualizing identity $m\le3n-6$ for simple connected finite planar graphs
How can I visualize the identity $m\leq3n-6$ (where $m$ is the number of edges, $n$ the number of vertices) for simple connected finite planar graphs?
2
votes
2answers
117 views
Visualization of 4D Expanded form of $f(x,y) = y/x - x/y$
I have a (not so) simple question: how do I visualize the following:
$$f(x,y,z) = ((yz)/x - x/(yz)) + (y/(xz) - (xz)/y) + (y/x - x/y)?$$
I am a csci person, but not a big math person, so I'm a bit ...
1
vote
1answer
312 views
Problem involving drawing a diagram with belts and elevators and specific directions on a given floor/belt
Today, while reading A Practical Guide to Problem Solving in Mathematics by Carol Meyer and Tom Sallee, I came across a problem I was unsure of how to solve except by brute forcing possibilities and ...
3
votes
2answers
134 views
Programs for visualizing math designed for laymen?
I'm looking for interactive applications that are for university topics (designed for windows) in mathematics only , preferably something that doesn't include programming languages to use because ...
2
votes
1answer
108 views
6
votes
1answer
167 views
Visualize operator algebras?
It seems to me that to study mathematics is to convert the abstract language into diagrams, graphs and images. It does depend on the subject how much this technique can ease the struggle yet most of ...
6
votes
3answers
237 views
Favourite proofs with a visualization
As a fan of 'visual' proofs, I love the book Visual Complex Analysis by Tristan Needham.
For example, this picture http://en.wikipedia.org/wiki/File:Pythagoras_algebraic2.svg leads quickly to ...
5
votes
2answers
243 views
continuum between linear and logarithmic
A friend and I are working on a heatmap representing some population numbers. Initially we used a linear color scale by default. Then, because the numbers covered a wide range, I tried using a log ...
5
votes
2answers
168 views
linearly arranging the group tables of groups of order 128
I'm planning to make a video that shows color coded group tables for all 2328 groups of order 128 -- at 128$\times$128 pixels at 24 frames a second I think I get 97 seconds of video. Is there some ...
3
votes
1answer
226 views
Ways to visualize the real numbers?
I was just wondering if there are any diagrams for visualizing subsets of the real numbers, or totally 'radically' different ways of looking at them as a real line? The model of the line relies on ...
3
votes
1answer
80 views
Visualizing SPD cone for $3\times3$ matrices
Can anyone see a good way to visualize the SPD cone for 3x3 symmetric matrices?
I'm interested in something that would highlight it's special structure, like non-smoothness.
Here's one attempt, ...
