# How Far Apart Are Two Random Points in a Hypercube?3

Posted by Cleve Moler,

Two days ago I wrote about random points in a square. At the last minute I added the paragraph asking about the generalization to random points in a cube. I have to admit that I didn't check the Web to see what was known about the question.... read more >>

# How Far Apart Are Two Random Points in a Square?5

Posted by Cleve Moler,

How far apart can you expect two points chosen at random in the unit square to be? I found this problem on the YouTube channel maintained by Presh Talwalkar, Mind Your Decisions. He correctly calls it a very hard puzzle. At first, I guessed the answer might be $1/2$. But the correct answer is more interesting than that.... read more >>

# Modernization of Numerical Integration, From Quad to Integral

Posted by Cleve Moler,

The MATLAB functions for the numerical evaluation of integrals has evolved from quad, through quadl and quadgk, to today's integral. ... read more >>

# The Classic Crossed Ladders Puzzle

Posted by Cleve Moler,

Here is a classic puzzle. A pair of ladders leaning against the sides of an alley form a lopsided cross. Each ladder is propped against the base of one wall and leans against the opposite wall. If one ladder is 30 feet long, the other 20 feet long, and the point where they cross 10 feet above the ground, how wide is the alley?... read more >>

# Surprising SVD, Square Waves, and Pi2

Posted by Cleve Moler,

I am surprised when many of the singular values of a nonsymmetric variant of the Hilbert matrix turn out to be nearly equal to $\pi$. The explanation involves the Fourier series for a square wave.... read more >>