# Category Archives: featured

## Dancing with the Spheres

In my latest American Scientist column I’m packing spheres again. The goal this time is to maximize the number of contact points where spheres touch each other. For example, four spheres in a tetrahedral cluster have six contacts; this is … Continue reading

## The abc game

Five years ago I wrote about a rumored proof of the abc conjecture, an idea from the 1980s that stands at the juncture between the additive and the multiplicative parts of number theory. Now there’s more abc news, and this … Continue reading

## Statistical mechanics of magnet balls

They come out of the can in a gleaming 6 × 6 × 6 cubic crystal. It took me a day to figure out how to get them back into the can. But that’s not the deepest mystery about these … Continue reading

## World3, the public beta

Forty years ago I had my first close encounter with mathematical models of doomsday. The Limits to Growth, published in the spring of 1972, offered a grim vision of environmental and economic collapse, based on the implacable logic of a … Continue reading

## The n-ball game

The area enclosed by a circle is πr2. The volume inside a sphere is 4∕3πr3. These are formulas I learned too early in life. Having committed them to memory as a schoolboy, I ceased to ask questions about their origin … Continue reading