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Draw $n$ random chords in a circle, where each chord connects two independent uniformly random points on the circle. As $n\to\infty$, which kind of polygon (triangle, quadrilateral, pentagon, etc.) o …

This question was posted on MSE. It received some interesting responses, but no definite answer. Let's build a variation of Pascal's triangle. We write $1$'s going down the sides, as usual. Then for …

Suppose we choose $n$ uniformly random points in a disk, then draw the smallest circle that encloses all of those points. There is evidence suggesting that the probability that the enclosing circle is …

In my MSE question, "Conjectured connection between $e$ and $\pi$ in a semidisk", the answer included $$\prod_{k=1}^\infty\left[1-\big((k+1)^{1/3}-k^{1/3}\big)^3\right]\approx 0.96454\ldots.$$ Does th …

Consider the sequence $a_1=1$ and $a_n=\sec (a_{n-1})$ for $n>1$. What does the proportion of positive terms approach, as $n\to\infty$? At first I thought the limiting proportion might be $\frac{1} …