For Reimy
posted by Keira .
Math (Reimy)  Reiny, Thursday, June 25, 2009 at 4:46pm
You are welcome
Just as an afterthought...
There is also a set of numbers called the pyramidal numbers, they are ...
1 4 10 20 ....
Can you figure out the pattern?
(Let their name be a hint.)

http://en.wikipedia.org/wiki/Tetrahedral_number
look at the rotating triangular pyramids and count the number of balls for the different layers
top layer: 1 ball
top two layers: 4 balls
top three layers: 10 balls
etc.
you can figure out the number of balls for any number of layers n by
n(n+1)(n+2)/6
e.g. if n=3
3(4)(5)/6 = 10