# 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 >>

# Ulps Plots Reveal Math Function Accuracy2

Posted by Cleve Moler,

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... read more >>

# Season’s Greetings Fractal6

Posted by Cleve Moler,

I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can shed any light on either of these questions.... read more >>

# The Ziggurat Random Normal Generator

Posted by Cleve Moler,

This is the third in a multi-part series on the MATLAB random number generators. MATLAB has used variants of George Marsaglia's ziggurat algorithm to generate normally distributed random numbers for almost twenty years. ... read more >>