# Questions tagged [visualization]

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

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### plotting 2 x 2 matrix visually. What it represents?

Hello I am engineering student. I need help understanding basic of matrix plotting. Currently I am learning about vectors and I wonder how they are represented by a matrix. Suppose we have a 2D vector ...
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### Can you explain combination with tree data structure [closed]

I can use tree data data structure to understand permutation .Is it possible to understand combination using tree data structure.If so can you please explain it.
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### Name for the surface formed by taking a filled in square and identifying diagonal vertices?

Consider the surface formed by taking a filled in square and identifying diagonal vertices. For example, $(0,0)\sim(1,1)$ and $(0,1)\sim(1,0).$ Image courtesy of @robjohn: Is there a name for this ...
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### How do people visualise Algebraic varieties?

The usual way I used to imagine Differentiable Manifolds are, as locally Euclidean spaces, with some nice enough properties. Intuitively speaking, instead of just looking at the manifolds from '...
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### Visual proof of $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} + … = 1$

I am trying to find a visual way of proving that $$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} + ... = 1$$ I am familiar with algebraic methods of proving ...
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### Intuition or Geometric model for Dicyclic Groups?

When studying groups of order 12, I learned about dicyclic groups, of which the quaternion group is the first example, and there is one of every order $4n$ for $n > 1$. I can do the basic ...
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### Visualizing $\mathbb{S}^{3}$ as consisting of two “polar” great circles together with a family of nested Clifford tori interpolating between them.

The following text describes a construction of the unit sphere $\mathbb{S}^{3}$. To consider the next example, it is helpful to practice visualizing $\mathbb{S}^{3}$ as consisting of two "polar&...
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### Using PlotGraph command from JupyterViz in MyBinder [closed]

I am executing a program "Newprogram.gap" in GAP file in My Binder. There, I have an output which is an adjacency matrix, $A$ corresponding to a Cayley graph. 1). I need to add the command &...
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### Calculating the rate of convergence from a plot of a limit.

The rate of convergence represents how quickly a sequence approaches its limit. $$\lim _{n \rightarrow \infty} \frac{\left|x_{n+1}-x^{*}\right|}{\left|x_{n}-x^{*}\right|^{q}}=\mu$$ Here, the rate of ...
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### Property of Determinant

If any two rows or columns of a determinant are interchanged, the sign of the value of the determinant is changed. What is the intuition of this? I can see from algebra perspective thats right, but I ...
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### functions that are good “half way log scales” to visualize exponential distribution

I'm making graphs based on frequencies of data -- this is data from the internet and like most things on the internet frequency follows an exponential curve - the most frequent item is orders of ...
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### 3-variable 3-equations problem

For positive reals $x,y,z$, if $xy+yz+xz=\sqrt{\frac pq}$, given $$x^2+xy+y^2=2$$ $$y^2+yz+z^2=1$$ $$z^2+zx+x^2=3$$ find $p-q$, where $p$ and $q$ are relatively prime integers. I tried grouping the ...
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### Can you help me understand barycentric coordinates visually?

This is my first question here so I'm sorry if it is not a well written/formatted one. I love maths but I have always had a lot of trouble following long equations. It always helps me when visuals are ...
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### Creating a complete number diagram once and for all

Background I have been recently searching for a good number diagram I could save for future reference. I was looking for a picture that would show different types or real numbers, and also ...
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### Is there a graphical proof that $9n+1$ is triangular if $n$ is?

It is straightforward to prove that if $n$ is a triangular number then $9n+1$ must be. Is there a systematic decomposition of a triangle made of $9n+1$ dots into nine triangles of $n$ dots plus one ...
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### How to visualize $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c}$?

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 ...
Because $10 \div \dfrac{4}{3}$ isn't an integer, I changed the numbers in this Reddit post. My $X = 6, A = 2, B = 3$. Undoubtedly, I know $6 \div \dfrac{2}{3} = 6 \times \dfrac{3}{2} = 9$, but don'...