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4
votes
2answers
243 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 ...
6
votes
3answers
2k 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 ...
2
votes
2answers
403 views

Visualization of Cantor set by Mathematica or Maple!

We all know what it is the Cantor set. The Cantor set is created by repeatedly deleting the open middle thirds of a set of line segments. One starts by deleting the open middle third $(\frac{1}{3}, ...
0
votes
0answers
74 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
77 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 ...
5
votes
3answers
258 views

Can one construct a “Cayley diagram” that lacks only an inverse?

My group theory text asks for an example of a Cayley-like diagram that exhibits all the properties of a group except (only) that at least some elements lack an inverse. Is it possible to construct ...
1
vote
1answer
1k 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 ...
0
votes
0answers
182 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 ...
11
votes
2answers
1k 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
376 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
350 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
142 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?
4
votes
1answer
153 views

Is there any way to give sense to a geometric/visual proof?

Suppose one is given the following visual proof that $$\lim\limits_{n \to \infty} \sum_{k=1}^n \frac{1}{2^k} = 1$$ which is the following construction over $[0,1]\times[0,1]$ What this is ...
2
votes
2answers
146 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
626 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
208 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 ...
3
votes
1answer
131 views

What's this type of chart called?

What's the name of this type of chart?
6
votes
1answer
257 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
408 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
500 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
189 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 ...
6
votes
1answer
310 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
132 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, ...
1
vote
1answer
291 views

Visualize 3 parameters in a graph

How would one visualize 3 parameters, where 1 parameters depends on the other 2? I want to display the time on the y-axis which depends on the input value of two different types. I can only think of ...
2
votes
7answers
621 views

Software to display 3D surfaces

What are some examples of software or online services that can display surfaces that are defined implicitly (for example, the sphere $x^2 + y^2 + z^2 = 1$)? Please add an example of usage (if not ...
5
votes
1answer
384 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 ...
4
votes
8answers
2k views

Techniques for visualising $n$ dimension spaces

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 ...
2
votes
2answers
804 views

a visual route to learning Galois theory

I really like the ideas of Galois theory: that you can think about all the algebraic numbers you can make starting with some set of them that there is some structure to this set of "algebraically ...
0
votes
1answer
444 views

3D correlation visualization?

Incomer per person (x axis) correlates with life expectancy (y axis). These two indicators change over time (z axis). x correlates with y. Moreover, x and y both correlate with z. The question is: ...
3
votes
1answer
1k views

How to visualize the Gaussian curvature of a 3D surface?

I have a 3D surface. I want to visualize color-coded Gaussian Curvature. Is there any software (e.g. MATLAB, Mathematica) which can be used for calculating and visualizing the curvature in color code ...
5
votes
2answers
323 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 of $S$ from a perspective camera within the space ...
15
votes
3answers
2k 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 ...
0
votes
2answers
201 views

Proof Visualization

I'm working through Apostol's 'Calculus, Vol 1', with a focus on learning the theory behind calculus. If you are not familiar, Apostol starts with analysis of the real line and works his way through ...
4
votes
1answer
149 views

Intuitive understanding a theorem in analysis

Is there a way to intuitively understand/visualize the following theorem in analysis? Let $(f_n)$ be a sequence of real functions differentiable in a finite/infinite open interval $(a,b)$. Suppose ...
4
votes
0answers
270 views

Visualizing the domain of the square root

I would like to show someone the domain of the complex square root function (the 2-sheeted riemann surface). Is there a good interactive visualization software for this? I would like some sort of ...
70
votes
17answers
5k views

Proving the identity $\sum\limits_{k=1}^n {k^3} = {\Large(}\sum\limits_{k=1}^n k{\Large)}^2$ without induction

I recently proved that $$ \sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k \right)^2 $$ Using mathematical induction. I'm interested if there's an intuitive explanation, or even a combinatorial ...
2
votes
1answer
256 views

general (asymmetric) real rank-2 tensor visualization in 3d

I have general rank-2 real tensor in 3d space represented as a 3x3 real matrix $M$ (it is gradient of a vector field). I am writing some code to visualize it in several isolated points, this is what I ...
18
votes
3answers
1k views

Interesting implicit surfaces in $\mathbb{R}^3$

I have just written a small program in C++ and OpenGl to plot implicit surfaces in $\mathbb{R}^3$ for a Graphical Computing class and now I'm in need of more interesting surfaces to implement! Some ...
7
votes
3answers
431 views

Reconciling 'intersecting planes' and 'linear transformation' interpretations of matrices

I've learned in linear algebra class that an $n \times m$ augmented matrix can be thought of as a collection of n planes in $\mathbb {R}^m$ . If the matrix is invertible, the planes all intersect at a ...
3
votes
3answers
625 views

Visualization of complex roots for quadratics

I read that if a parabola has no real roots, then its complex roots can be visualized by graphing the same parabola ($ax^2 + bx + c$) with $-a$ and then finding the roots of that, then using those ...
0
votes
1answer
349 views

Mathematical permutation drawing/visualization tool

I'm writing software and need to document an existing mathematical permutation in our code. I thought the folks here would know where I can find a drawing/visualization tool to draw a permutation ...
2
votes
2answers
700 views

calculate location on an isometric world map

I want to display a point with a latitude and a longitude value in an isometric world map using JavaScript and jQuery. For a rectangular map, I use the following code to calculate the x and y ...
2
votes
0answers
130 views

Turning real roots into curves (for visualisation)

One can obviously map a set of real numbers $x_1, x_2, \ldots x_N$ to a curve in 2-D via $y=(x-x_1)(x-x_2)\ldots(x-x_N)$. Thinking about data visualisation, one can portray a set of $N$ observations ...
5
votes
1answer
230 views

FLOSS tool to visualize 2- and 3-space matrix transformations

I'm looking for a FLOSS application (Windows or Ubuntu but preferably both) that can help me visualize matrix transformations in 2- and 3-space. So I'd like to be able to enter a vector or matrix, ...
8
votes
3answers
947 views

Is there a geometric interpretation of the exponential function of real numbers?

I can visualize the exponential function with the graph $y = e^x$, but I can do that for almost any function. In addition to its graph, the function $f(x) = x^n$ can be visualized as the volume of a ...
7
votes
1answer
127 views

Visualising a specific orbifold

Let $1 < k \in \mathbb N$ and $M = \{(z_1, z_2) \in \mathbb C^2 : k|z_1|^2 + |z_2|^2 = 1\}$. Let $S^1$ act on $M$ via $e^{i\theta}(z_1,z_2) = (e^{ik\theta} z_1, e^{i\theta} z_2)$. Then I am told ...
4
votes
3answers
540 views

Trying to draw the tautological line bundle ($\subseteq \mathbb{CP}^1\times \mathbb{C}^2$)

In order to learn about vector bundles, I would like to draw the tautological vector bundle over the complex projective line $$ E = \{(x,v) \in \mathbb{CP}^1 \times \mathbb{C}^2 : v \in x \} .$$ ...
6
votes
2answers
692 views

How to draw a complex line bundle?

The most basic example of a topologically non-trivial real line bundle is the well-known Möbius strip. Everyone who learns about vector bundles will be confronted by it, if only because it has the ...
0
votes
1answer
247 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 ...
9
votes
2answers
901 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?