(ISNS) — Could a domino small enough to hold in your hand cause a chain reaction that could topple something as big as 112-meter tall tower? It sounds like a plot hatched by a kooky domino-themed super villain, but a new mathematical model shows it’s theoretically possible.
A typical domino is just under 2 inches tall, 1 inch wide, and about one-quarter of an inch thick. These dimensions create a thin block that’s just stable enough to stand upright yet unstable enough to fall over with the slightest nudge.
“If you make them too thick, for instance if you had dominoes like cubes, they would never [fall],” said physicist Hans van Leeuwen of Leiden University in the Netherlands.
Each upright domino is also full of potential energy. When the first domino falls, the force of gravity turns that potential energy into enough kinetic energy to topple a domino larger than itself. That taller, heavier domino stores even more potential energy, and that energy will continue to mount so long as each falling domino’s kinetic energy can overcome the potential energy of their more massive neighbors.
Mathematicians have traditionally assumed that no domino could knock over a neighboring domino more than about one-and-a-half-times its own width, height, and thickness, or a “growth factor” of 1.5. But there was no overarching mathematical model. So, when last year’s annual Dutch National Science Quiz TV Show, run by public broadcaster VPRO, asked how many dominoes it would take to topple a domino the size of the 112-meter-tall Domtoren — the tallest church tower in the Netherlands — van Leeuwen set out to calculate just how much punch a falling domino packs.
But falling dominoes are deceptively complex.
The above video from The National Dutch Science Quiz demonstrates how a sequence of dominoes can be arranged to topple a very large block.