02-04-2013, 06:11 PM
There are 11 ways to chop a pentagon into pieces by drawing lines between corners & lines that don't intersect.
For a square there are just 3 ways, and for a triangle there's just 1, using no lines at all.
We can count the ways for a polygon with any number of corners, and we get these numbers like 1,3,11,45,197,903,…
These are called the Schroder–Hipparchus numbers.
Hipparchus was one of the best of the ancient Greek astronomers.
He lived around 100 BC, and he discovered the precession of the equinoxes and also invented the stereographic projection.