For questions about visualizing mathematical concepts. This includes questions about visualization of mathematical theorems and proofs without words.
Questions tagged [visualization]
955 questions
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1 answer
Visualizing uncountably-infinite-dimensional spaces
I'm familiar with the advice by Geoffrey Hinton, "To deal with a 14-dimensional space, visualize a 3-D space and say ‘fourteen’ to yourself very loudly. Everyone does it." I'm happy with this to visualize high-dimensional spaces and even…
dkv
- 445
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0 answers
Visualizing n-dimensional landscape versus collection
Much has been written on the topic of visualizing n-dimensional spaces (where n is in general much larger than 3). T-SNE and parallel coordinates are two ways to do it rather effectively. (I'm not interested in the philosophical question of whether…
rwallace
- 245
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vote
2 answers
Visual proof that $\mathbb Z_m × \mathbb Z_n = \mathbb Z_{mn} \iff \gcd(m,n) = 1$
Is there a way of visually proving or demonstrating that $\mathbb Z_m × \mathbb Z_n = \mathbb Z_{mn} \iff \gcd(m,n) = 1$?
Take $Z_4 × Z_3$ for example:
It's not obvious from the Cayley diagram that that group is cyclic, even if we rearrange it into…
Zaz
- 1,466
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2 answers
Description of a 4th dimensional sphere
I have been wondering what a 4th dimensional "sphere" is like, because I already know what a tesseract looks like, and I am wondering if there is a description of a 4th dimensional "sphere".
Andrew Z.
- 33
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visualizing a function from the plane into the reals
If $$(x_1,y_1), (x_2,y_2),(x_3,y_3)$$ are points in the plane and if $a,b$ are fixed real numbers, how can I visualize $$f=(ax_1+b-y_1)^2+(ax_2+b-y_2)^2+(ax_3+b-y_3)^2$$ as a function from the plane into the reals?
I tried looking at what happens in…
The Substitute
- 3,888
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1 answer
What kind of graph was github's impact graph?
Github used to have a graph called an impact graph. It feels almost like a Sankey diagram and almost like a stacked area chart. What is the name of this kind of graph?
I couldn't find a better stackexchange site on which to post this question. …
D. Patrick
- 626
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Visualizing the Commutative Property Beyond Three Numbers
I've been pondering how to intuitively visualize the commutative property of multiplication when dealing with more than three numbers. For two numbers, we can easily conceptualize this with the area of a rectangle, and for three, the volume of a…
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How to construct a harmonic mapping
How to construct a harmonic mapping on the complex plane using the method of "Shear Construction"?
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latex question: comutative diagrams side by side
I would like to put the following two diagrams side be side:
{\Large$$
\begin{tikzcd}
X\arrow{r}{i}\arrow[swap]{dr}{j} & M \arrow{d}{j'}\\
& N
\end{tikzcd}
$$}
and
{\Large$$
\begin{tikzcd}
X\arrow{r}{j}\arrow[swap]{dr}{i} & N \arrow{d}{i'}\\
&…
Rodney Coleman
- 742
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How can I visualize $\lim\limits_{x \rightarrow \pm \infty} f(x) = \lim\limits_{t \rightarrow 0^{\pm}} f(1/t)$?
I'm not asking about the proof, that I already understand. I'm itching to understand this graphically. I use James Stewart's graphs. As you can see, I wrote $1/t$. Then what?
Also I'm trying to visualize how Formula 8 shifts to Formula 9 below,…
user851668
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1 answer
Function that produce a spike in 3D
I am looking for a function that would produce a spike, of any size, in the z-direction at a given x and y coordinate. A little bit like the https://en.wikipedia.org/wiki/Dirac_delta_function but that could be graphed in 3D.
I am not sure if those…
silkAdmin
- 105
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What does a $3D$ Penrose diagram look like?
A quick google search turns up many images of $2D$ Penrose diagrams but no $3D$ ones.
Q: What does a $3D$ Penrose diagram look like?
John Zimmerman
- 1,070
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1 answer
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?
MR. Raindrop
- 141
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- 10
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Any subtraction carryover visualization ideas?
I want to teach my kid carryover by using some sort of visualization. It can be a graph/visualization using a mathematics software or may be some sort of real world object shuffling or anything else.
I have installed sage software and tried to see…
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Time period diagram (bar chart) - what is it's real name?
I want to make a diagram like this to display the career spans of several soccer players one below the next:
I know it's basically a bar chart, but I was hoping this has a more specific name, because I want to search the web to find out whether…
Sridhar Sarnobat
- 253