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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### How do you picture: $\Pr(B|A)$ shrunk down by $\Pr(A)$?

Though understanding these diagrams, I do not understand how to visualise the following explanation:
$\color{green}{[P1.]}$ Suppose you were to grab the edges of $A$ and stretch it out so it covers all of $\Omega$. $B$ stretches out with it. Now…

NNOX Apps

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### The role of visualization and intuition in graduate and postgraduate math and developing it

In Visual Complex Analysis's preface, the author gives an analogy with pseudo-deaf musicians and follows the same to mathematics. Mathmatics today, he argues, is mostly build on abstract symbolic manipulation rather than much more stronger visual…

user185498

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### An image suitable for a skyscraper sheaf?

This question relates to this thread:
Skyscraper sheaf?
Consider one of the diagramms for the representation of a sheaf (and stalks thereof) which are popular on the web:
I just wanted to know whether the representation on each point represents a…

Javier Arias

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### 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 triangle inequality ?
An answer should be…

temo

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### About the classification of linear autonomic differential equations of the plane.

For a linear autonomic differential equation of the plane
$$\dot x = Ax,$$
with $A ∈ \operatorname{Mat}_{2×2} (ℝ)$, say we have a fundamental matrix $Φ \colon ℝ → \operatorname{Mat}_{2×2} (ℝ)$, that is an invertible solution to the differential…

k.stm

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### Some explanation regarding a diagram of homotopy

I found this visualization regarding homotpy in wikipedia:
https://commons.wikimedia.org/wiki/File:Homotopy_curves.png
I would be very grateful if you could explai me all the abbreviations being used. I guess t stands for t and s for space, so that…

Javier Arias

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### Orthogonality in Hilbert Spaces

For the sake of concreteness, let's say that our Hilbert space is the beloved $\mathscr L^2(\Bbb R)$. Suppose that we have $\psi,\phi\in\mathscr L^2(\Bbb R)$, what's the intuitive meaning to a semi-layperson when we say that…

BigbearZzz

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### Slope in algebra I

What is a good project for teaching y=mx + b and having students discover slopes of lines in classroom or on the classroom buildings?

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### Name and explanation of triangular representation of 3 coordinates in 2 dimensions

There is a common two-dimensional graphical representation of three values that are required to sum to a constant. The three values are represented by a point inside an equilateral triangle. More specifically, the values are represented by…

Mars

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### 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 bounded by the parabola and the $x$-axis with axis of…

Milo Wielondek

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### Grothendiek and singular points

My question relates to the following thread I opened some weeks ago:
A question regarding Grothendieck , topos and (adelic??) points
Specifically, consider this paragraph:
At 1:14:30 and after,
Toen presents the new objects emerging from topos…

Javier Arias

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### Visualising a 1-(50,15,15) design.

The problem I have is the visualisation of a 1-(50,15,15) design. That is a set of 50 points and 50 blocks (lines), so that each point is on 15 lines, and each line contains 15 points.
My attempts thus far have been on Mathematica. I have managed to…

Adrian

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### What is the correct equation for "Normal distribution function of continuous random variable"?

I was reading a book and came across with a equation which gives the normal distribution function of continuous random variable. It was used in a software called RapidMiner to visualize data distribution.
$f\left( x \right) = \frac{1}{{\sqrt {2\pi…

Puriney

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### Comparing a function and its estimate

What are some clever ways of comparing (visually) a function with its estimate?
For regions where the function does not cross zero, plotting the ratio of the functions and plotting the relative error of the estimate gives a good idea. However when…

Gappy Hilmore

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### Is there a way to visualize, like a picture in mind, the $n$-th derivative?

Is there a way to visualize (like a picture in mind) the $n$-th derivative ?
For $n=1$ is the tangent line and we can visualize it quite well.
More abstractly is it possible to see the geometric significance of the $n$-th derivative for all $n$?
For…

halfpog

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