Randomizing a regular polygon along its "spokes" while maintaining area

Why are picewise continuous functions on $[a,b]$ bounded?

Find all possible positive integers $x$ and $y$ such that the equation: $(x+y)(x-y)=\frac{(y+1)(y-1)}{24}$ is satisfied.

Compute the integral $\int\limits_{0}^{\pi/2} \frac{dx}{\sqrt{1 + \sin x}}$

Evaluate a real integral, e.g. $\int_{0}^{\infty}\frac{x^2}{(x^2+1)(x^2+4)}\:\mathrm dx$ with complex analysis

Can we find a closed-form formula for $a_{n+1}=\frac{a_n}{a_n+1}$, given $a_1=a$?

How to solve this integral with transformation to polar coordinates?

Knights $3\times 3$ riddle

Ahmed integral revisited $\int_0^1 \frac{\tan ^{-1}\left(\sqrt{x^2+4}\right)}{\left(x^2+2\right) \sqrt{x^2+4}} \, dx$

If $\sum_{n=1}^{\infty} a_{n}$ converges, then$\sum_{n=1}^{\infty} \sin(a_{n})$ also converges

What is $\sum_{k=0}^n {n \choose k} p^k (1-p)^{n-k} e^{-s(k - np)^2}$?

Prove: $\sum\limits_{k=0}^{n}\frac{1}{k+1}\binom{2k}{k}\binom{2n-2k}{n-k} = \binom{2n+1}{n}$

Positive continuous supermartingale is a proper martingale

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