Triangle Numbers
The total number of pins in a triangular arrangement is called a triangle number.
The total number of pins in a triangular arrangement of 5 rows is 5 plus the
number of pins in 4 rows.
Let us call this number Triangle(5)
Here is a chart that gives the first seven triangle numbers. But it seems not to be complete. Luckily you can fill it in. Click on the figure at right to see the various arrangements.
| Triangle Numbers | ||
|---|---|---|
| Rows | Triangle(Rows) | Formula |
| 1 | base case | |
| 2 | 2 + Triangle(1) | |
| 3 | 3 + Triangle(2) | |
| 4 | 4 + Triangle(3) | |
| 5 | 5 + Triangle(4) | |
| 6 | 6 + Triangle(5) | |
| 7 | 7 + Triangle(6) | |
