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

# Questions tagged [visualization]

864 questions

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### Visualisation of the reciprocal of an continued fraction?

If: $$a=\cfrac{l}{m+\cfrac{n}{o+\cfrac{p}{q+\cdots}}}$$
Then could you help me visualize $1/a$? I really don't understand it. Thank you so much!

user253055

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### How do I visualize this quotient space?

If $V = [0,1] \times [0,1] \subset \mathbb{R}^2$. We define the equivalence relation $\sim$ on $V$ as follows: every element $(x,y) \in V$ is equivalent with itself and besides that the three elements $(0,x), (1,x)$ and $(1-x,0)$ are equivalent for…

Nescrio

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### How common is it to plot linear transforms on continuous spaces?

I came across a question asking how the proof that the transform $f(g) = g(x-a) + g(x+a)$ was Hermitian worked. I was a bit surprised that the proof was symbolic, because if you plot out the coefficients it's obvious.
By "plot out the coefficients"…

Craig Gidney

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### Help with Diagram of the Standard Lift of Projective Plane

I am posting here because I need help finding (or making) a visual aid for a presentation.
I am giving a short presentation about Projective Geometry next week, and I am building a beamer for it. One such slide talks about the Standard Lift of the…

Ilan Weinschelbaum

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### Visualizing a volume with MATLAB

I have a rational function $\phi: [0,1]^3 \to \mathbb R^3$ (A NURBS, to be precise) and I want to visualize the image of $\partial [0,1]^3$ using a surface plot (patch, for example). To do this I have chosen equidistant discretisation along each…

AlexR

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### Diagram to depict dependencies/prerequisites of activities

A long time ago in a business course I was taught about diagrams that help plan activities, and determine estimates of time required to complete a project: activities in the project were drawn as little circles; lines connected them to show…

CL22

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### How to visualize(inside ones brain) the Four-dimensional_space

Can the fourth dimension https://en.wikipedia.org/wiki/Four-dimensional_space be visualized intuitively by the humans.
Does the professional mathematicians can do this ? If so what are the things to be learned to acquire this ability.

Talespin_Kit

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### Looking for intuïtive explanation why contour integral of $\frac{dz}{z} $equals $2\pi i$ in complex analysis

$$\oint \frac{dz}z = 2\pi i$$
I've seen the derivation of it using the parametrisation.
Since this result is used all the time in my complex analysis course, i'd like to understand this intuïtively. I tried making sense of it like this:
$$\oint…

ultraking x2

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### Cauchy's Generalized Mean Value Theorem. Required function. (S.A. pp 140 t5.3.5)

Cohen, Henle. Calculus pp 827, (http://www.vias.org/calculus/09_infinite_series_10_06.html)
I revised the footnote in pp 14 http://math.uga.edu/~pete/2400calc2.pdf. This theorem can be illustrated by plotting the parametric equations $x = g(t), y =…

NNOX Apps

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### Graphic of function similar to Sin(x) but with scaled size

I wont to build a graphical representation of numbers, as "waves":
Similar as the graphic of sin x but for each number N it gets bigger and bigger
crosses the x axes in the multiples of N,
with y from -N to +N
and repeating every 2N.
I found this…

d.raev

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### How to visualize the graph of multivariable functions, namely functions from R^2 to R?

I'd like to get a graphical approach to Analysis in higher dimension vector spaces, such as $\mathbb{R^n}$. To make this easier, my goal is to be able to visualize the graph of functions from $\mathbb{R^2}$ to $\mathbb{R}$. If you take one of the…

sleepydrmike

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### Soft-Question: Is it possible to visualize, or make concrete, progressively more abstract mathematics? Are there mathematicians who can?

This is my first post! I'm really not good at math, and I'm trying to re-learn on Khan Academy. As I'm progressing, this question came up for me.
Learning math concepts that I can visualize in my mind or relate to some observable phenomenon in life…

JBR

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### Does the graph of a function $f(x)$ versus its derivative $f'(x)$ have a special purpose?

I can't find any insights online on how useful the graph of function $f(x)$ (on the $y$ axis) versus it's derivative $f'(x)$? (on the $x$ axis) does it provide some useful informations if any?
For example, I see that when I plot $\sin(x)$ against…

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### Can the bijection for the Lost Boarding Pass Probability Problem, be formulated or pictured?

The two proofs below moot "bijection", but I don't see a formula. 1. Does the bijection have an explicit formula?
Can this bijection be pictorialized? My 16 y.o. kid doesn't understand the abstract, Daedalian phrasing below.
hunter's answer dated…

user851668

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### How do I describe this graph with an equation?

Spawn Graph
I need to describe this graph as an equation for my game in unity 3D, it describes the spawn of enemies in time. At first is kind of like a sigmoidal/power curve, but after some time it turns into a spline that goes up and down but…

Pastille

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