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If I have a rectangle ABCD such that A and B touch two points of the outer circle and CD's touches one point of the inner circle, how could the maximum dimensions of the rectangle be calculated? Exam …

Why are the homeomorphisms from the unit circle to the unit circle preserving measure affine? The affine is composition of rotation and continue automorphism.

Consider derivative of the convolution of a given function $f(\cdot)$ with a fixed $C^\infty$ function $s(\cdot)$, evaluated say at $1/2$. Is there a measure which generates the functional so defined? …

John Nash and his wife Alicia tragically passed away in 2015. According to Sylvia Nasar's book "A Beautiful Mind", their son is apparently a good mathematician. What works is he known for?

I need it to show that $\displaystyle\sum_{k=1}^\infty \frac{\sin k}{k^3} = \frac{2\pi^2-3\pi+1}{12}$

I found this formula for calculating maximum number of regions created by r hyper-planes in n-dimensional space (n<=r) rC0 + rC1 + ....... + rCn How can this formula be proved?? …

Let $S$ be a compact connected surface. Let $K$ be a compact subset of $S$ and suppose that $K$ has a finite number of connected components. Let $U$ be a connected component of $S \setminus K$ and con …

Can some body help me with some source code for finding automorphism groups of regular maps?. For example: the type of graph is denoted as $\{p, q\}$, which means that they are tessellations of the pl …

Let us have a list of vectors in a $3$D space. Is there a more efficient way to find the greatest difference between any two of them than combining each, computing the size of their difference, and th …

I am trying to figure out the least number of directed edges that would be bi-directional after constructing a graph with $2k-1$ nodes that are each $k$ in-degree. For example, $2(2)-1=3$ nodes that a …

I have a Lottery app and I'm implementing a feature to optimize the number of bets that are necessary to cover a subset of numbers since they can repeat on several bets. What I have: Supposing a lotte …

Let $𝑋_1,𝑋_2, … , 𝑋_𝑛$ be a sequence of independent random variables with $𝑃(𝑋_𝑛 = 4^𝑛) = 𝑃(𝑋_𝑛 = −4^𝑛) = \frac12$. Let $𝑆_𝑛 = 𝑋_1 + 𝑋_2 + ⋯ + 𝑋_𝑛$. If $A_n=\sup\, \{𝑟 ∈ \Bbb R: 𝑃( …

We know that framing structure means the trivialization of tangent bundle of manifold $M$. string structure means the trivialization of Stiefel-Whitney class $w_1$, $w_2$ and half of the first Pontr …

In a triangle with three points A, B, and C. The L2 distance between each pair of points |AB|, |AC|, |BC| is given. For the other two points O and P, the distance to the three points is given, i.e. |A …

I'm trying to determine the nature of this series $ \sum_{n \geq 1} \frac{ \cos(n) \sin(n+1) }{n} $, but I'm not getting anywhere. I've tried using the Abel and trigonometric formulas, but I can't fin …