Noticed something neat tonight! The number of unique lines you can form by connecting the vertices of an n-gon is equal to the (n-1)th triangular number.
(e.g. in a square all 4 veritices make 4 lines (4 sides to a square), and then I can also connect any verticie to another verticie that is not directly to the left or right, assuming that it hasn't already been connected to that one earlier. So on a square the top right can connect to the bottom left (later on the bottom left can't connect to the top right because it already has), and the top left and connect to the bottom right. 6 unique lines (the 3rd triangular number is 6!) This works for any n-gon too!)
I'm wondering if this property has already been known, I couldn't find anything about it online. Also, if so, does it have a name?
I can't think of any real application for it other than, if this is held to be true than those who believe a digon is a circle/ellipsoid/ovaloid would be wrong (and it is currently widely held that a digon is a circle/ellipsoid/ovaloid), because then the 1st triangle-number would be "2", but if a digon was rather just a straight line with 2 end points, then the first triangular number would be "1" (which it is!)
A digon would be two lines (NOT CURVES) that overlap and form a closed polygon with area 0 and perimeter 2*s.
This is actually better known as a result in graph theory and combinatorics as the size of a complete graph on $n$ vertices.