All Questions

Suppose $n$ air molecules (infinitesimal points) are bouncing around in a unit $d$-dimensional cube, with perfectly elastic wall collisions. Let $k=n^{\frac{1}{d}}$. For example, in 3D, $d=3$, with $n=...

Or: Stabbing rolling disks. Imagine there are $n$ unit-diameter disks rolling between $x=0$ and $x=d$, reflecting off either end. The disk centers start at a random location within $[\frac{1}{2}, d-\...

Define a process to start with a unit-area equilateral triangle, and at each step glue on another unit-area triangle.                     $50$ ...

Imagine that an $\epsilon$-radius hole is punched in the plane centered on every integer-coordinate point. Now a point "ball" is dropped on the plane at a random spot $p$. If $p$ has not already ...

A quincunx or Galton board consists of staggered pegs from which ping-pong balls bounce and eventually display a binomial / normal distribution in catch-bins. I am wondering if the downward progress ...