Most of us are familiar with triangular numbers, such as the arrangement of ten bowling pins in a triangle,
.
. .
. . .
. . . .
or square numbers,
. . . .
. . . .
. . . .
. . . .
but we don't necessarily know how their arithmetic works, or whether we can do the same with, say, pentagons.
Can we learn something by telling a turtle how to make these numbers? Let's try.