What A Polygon!

Number of lines that can be drawn given $\displaystyle n$ points on a plane = $\displaystyle {n\choose 2}$ .

Out of these, $\displaystyle (n)$ lines form the convex polygon. Therefore, the number of diagonals is:

$\displaystyle \Rightarrow {n\choose 2} - n$

$\displaystyle \Rightarrow \frac{n(n-3)}{2}$

$\displaystyle \Rightarrow \frac{(2016)(2013)}{2} = \boxed{2029104}$

The number of diagonals of a convex polygon with side(s) $n$ is given by $\frac{n}{2}(n-3)$ Then a 2016 sided polygon has $\frac{2016}{2}(2016-3)=1008(2013)=2029104$ diagonals.