The Curious Mathematics of Domino Chain Reactions

From the article: Today, J M J van Leeuwen at Leiden University in The Netherlands takes this problem by the scruff of the neck and gives it a good mathematical shaking. It turns out that the answer-the maximum growth factor- isn't quite as simple as the problem might suggest.

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So van Leeuwen makes a series of simplifications in his mathematical analysis. He assumes that the friction between the ground and the dominoes is effectively infinite so that they cannot slide. He assumes the collisions are fully inelastic so the dominoes stay in contact with each other when they collide. He also assumes that once in contact with each other, the dominoes slide frictionlessly over each other.

Given these assumptions, he then shows that with optimal spacing, each succeeding domino can be no more than about twice as big as the previous one, which is maximum growth factor of no more than about 2.

"No more than about 2"?? Well, I'm glad we've got that nailed down precisely now. Next in our series on Physics Done By Mathematicians, J M J van Leeuwen will show how an atomic bomb packs the wallop of about a truckload of dynamite.

Alternatively, you can think of it as a taunt, like Fermat's Last Theorem, only clumsy. Possibly, like that famous theorem's author, he doesn't really have a proof either... :)