Trinomial triangle
The trinomial triangle is like a special kind of number pyramid that has three numbers in each row. Each number in the triangle is made by adding up three other numbers from the row above it.
For example, let's start with the first row of the triangle, which has just one number - the number 1. The next row has three numbers, which are each made by adding up two numbers from the row above. So the first number in the second row is 1 (because there's only one choice of two numbers to add together in the row above - two 1's), the second number is 2 (adding the two choices of one 1 and one 2), and the third number is 1 (adding two 2's).
Then we keep going to build the rest of the triangle. Each number in a row is made by adding up three numbers from the row above it. So the third row has four numbers, and each one is the sum of three numbers from the row above. For example, the first number in the third row is 1 (because there's only one way to add three 1's together), the second number is 3 (adding up two choices of a 1 and a 2, plus one choice of a 3), the third number is 3 (adding up three choices of a 1 and a 2), and the last number is 1 (adding up two choices of a 2 and a 1).
We can keep going to build more rows in the trinomial triangle, each time adding up three numbers from the row above to get the numbers in the new row. It might seem complicated, but it's actually just a way of organizing numbers in a pattern, and it's fun to see how the triangle grows and changes as we add more rows.
For example, let's start with the first row of the triangle, which has just one number - the number 1. The next row has three numbers, which are each made by adding up two numbers from the row above. So the first number in the second row is 1 (because there's only one choice of two numbers to add together in the row above - two 1's), the second number is 2 (adding the two choices of one 1 and one 2), and the third number is 1 (adding two 2's).
Then we keep going to build the rest of the triangle. Each number in a row is made by adding up three numbers from the row above it. So the third row has four numbers, and each one is the sum of three numbers from the row above. For example, the first number in the third row is 1 (because there's only one way to add three 1's together), the second number is 3 (adding up two choices of a 1 and a 2, plus one choice of a 3), the third number is 3 (adding up three choices of a 1 and a 2), and the last number is 1 (adding up two choices of a 2 and a 1).
We can keep going to build more rows in the trinomial triangle, each time adding up three numbers from the row above to get the numbers in the new row. It might seem complicated, but it's actually just a way of organizing numbers in a pattern, and it's fun to see how the triangle grows and changes as we add more rows.