Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [visualization]

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

955 questions
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10 answers

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 navigated? Sorry this question seems a bit vague,…
Preet Sangha
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5
votes
1 answer

Mental Math Visual Retention

I have always been good at math but even I struggle with visualizing numbers in my head. I am seeking help on this forum to see if any mathematicians here have experienced the same issue I currently have and overcame this problem. If someone where…
jessica
  • 1,002
5
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3 answers

Visual proof for $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$

I've found visualizations of simple mathematical concepts to be a really useful tool in building intuition for more complex mathematical concepts. For example, this visualization of $(a + b)(c + d) = ac + ad + bc + bd$ can be used to visualize the…
Frank
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4
votes
1 answer

How to visualize $\frac{a}{b} \div \frac{c}{d} \equiv \frac{a}{b} \times \frac{d}{c}$?

I read https://matheducators.stackexchange.com/q/7837, but it doesn't answer my question because the Multiplicand is a whole integer there. The trick is to rationalize the denominator, to enable me to compare the numerator. I'm just using …
user851668
3
votes
1 answer

Soft Question: Difficult to Visualize Areas of Mathematics

Yesterday I came across this webpage, which describes a recent (successful) attempt to visualize isometric embeddings of flat tori in 3D Euclidean space. The webpage and associated paper discuss the difficulty in creating this visualization, which…
Jeffrey Rogers
  • 133
3
votes
2 answers

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 those confuse me. I'm looking for Something where…
Henry
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2
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0 answers

arbitrary transformation of data between linear and log-like scales

[I'm not very sure on how to formulate this question (or if it belongs here btw), so apologies in advance and I'd be happy to get feedback on other sites this question may fit better] Suppose that I have a dataset of scores (from Min to Max). I can…
emepyc
  • 129
2
votes
0 answers

Patterns emerging from striped yarns in knitting

There's an interactive tool on this page that shows what happens when you knit a symmetrical striped yarn back-and-forth at different stitch counts (you can drag the stitch counter and it changes the picture). What body of maths covers this kind of…
ᴇʟᴇvᴀтᴇ
  • 151
2
votes
2 answers

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 at a loss as to how to approach this...Is there a…
ZeeKay
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2
votes
1 answer

Can we put the mathematics of paradoxes in visual art into perspective?

(Pun definitely intended.) Dear MSE-Community, If I were to choose one artist that has made interesting works of art not only because of their beauty but also because of their connections to Mathematics, I would choose Escher. His works have always…
Max Muller
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2
votes
0 answers

I seek Visual illustrations of Concepts of Mathematics as animated videos for students of Higher Mathematics

There are some very good animated videos explaining concepts of mathematics on youtube, like videos of website " why U" but most of these deal with elementary mathematics. I am searching for videos explaining concepts of advanced mathematics…
Mathseeker
  • 21
1
vote
1 answer

How to picture $x^n−y^n \equiv (x−y)(x^{n−1}+x^{n−2}y+...+xy^{n−2}+y^{n−1})$?

Many students fail to intuit $x^n−y^n \equiv (x−y)(x^{n−1}+x^{n−2}y+...+xy^{n−2}+y^{n−1})$ , as substantiated by the glut of duplicates. How can students pictorialize it? After substituting $z = \dfrac xy$, this identity follows from $z^n−1 \equiv…
user1211588
1
vote
2 answers

How can you behold that a 45 degree line's |x-intercept| = |y-intercept|?

I'm not asking for an algebraic explanation...I can do algebra. I know $f(x) = x - c = 0 \iff x = c$. Right now, I have to make my mind process four steps. First, a line with slope $|1|$ must angle 45° with the y-intercept. Second, I must consider…
user851668
1
vote
0 answers

How can I visualize dividing by a fraction as partial and full groups?

I can't visualize all these "full groups" and "partial groups." Can someone please picture them? Please see my questions red in-line. Please don't use the identity that $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c}…
user851668
1
vote
1 answer

Picture for the Straddle Lemma, in Bartle's Introduction to Real Analysis (2011 4 ed), 6.1.17, p 171?

Can anyone please picture the Saddle Lemma in Introduction To Real Analysis (2011 4 ed) by Robert G. Bartle & Donald R. Sherbert, Section 6.1, Exercise 17, p 171? I'm not asking proofs. Let $f \colon I \to \mathbb{R}$ be differentiable at $c \in…
user53259
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