Ball Pyramid

Put the four pieces together to form a pyramid. Hint: Where can you place the long pieces?

A pyramid (tetrahedron) of side length 4 contains 20 balls. How many balls would be in a pyramid of side length 5?

How many balls would be in a pyramid of side length 12? Is there a general way to work it out?

We want to make a pyramid (tetrahedron) of side length 4. Each face is a triangle, made from a row of 4, a row of 3, a row of 2 and a row of 1. There is only one way the pieces can be stacked to make these rows.

Starting from the top, the number of balls in each layer is: 1 ball; 3 balls; 6 balls; 10 balls. These are called triangle numbers, and each triangle number is the sum of consecutive numbers: 1; 1 + 2 = 3; 1 + 2 + 3 = 6; 1 + 2 + 3 + 4 = 10. The next triangle number is 15, making a pyramid of 35 balls.

The first twelve triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78.