Dominoes and the Cascade

When one domino topples, it triggers a chain reaction that causes adjacent dominoes to fall. This chain, known as a cascade, continues until every domino has fallen or all the players have run out of tiles. Dominoes are a fun way to explore the concept of probability, and they can also be used as a tool for mathematical investigation.

Domino, from the Latin for “little bone,” is twice as long as it is wide and has a line in the middle dividing it into two squares. Each side of a domino has either a number or a blank space. The number on the domino tells you how many dots are present, and the blank spaces represent the numbers zero through nine. The value of a domino is the sum of the values of its two sides. Dominoes are typically used to play positional games. In these, a player moves dominoes from edge to edge so that their values match (e.g., 5 to 5) or form some other total (e.g., 6 to 1).

The first domino that falls starts the cascade. Once it has, all of the other dominoes in its row have to fall too, or the entire set is lost. Dominoes have the potential energy to keep falling for a long time, but they lose this energy over time as they slide against each other and slip against the surface on which they rest. When a domino has enough potential energy to continue falling, it is said to be on its “last legs.”

Once the first domino has fallen, all of its potential energy becomes kinetic energy—energy that gives the tile movement. The rest of the dominoes will have a little kinetic energy because they will still be sliding against each other and slipping against the surface on which they are resting. However, the domino that has the most kinetic energy will have more momentum and will move faster than the others.

Before Hevesh sets out to create an elaborate domino track, she tests each section separately. This allows her to correct any parts that don’t work before she assembles them into the final arrangement. For large and complex arrangements, she also uses special blockages to prevent the premature toppling of more than a small part of the setup.

Dominoes are also used to make art, with straight lines, curved lines, grids that form pictures when they fall, and 3D structures like towers and pyramids. You can even use them to design a domino art display on a flat surface, such as a wall or tabletop.

Dominos are often seen in schools as a way to help students learn basic math skills, such as addition and subtraction. They can practice their skills by creating equations for the dots on each end of a domino. For example, students can discover that the sum of the dots on each end is always equal to the total number of dots on both ends. This activity supports Common Core State Standards, particularly Mathematical Practice Standard 8, Look for and express regularity in repeated reasoning.