# Talk:Dividing a circle into areas

Just found this (odd) page.

${\displaystyle f(n)=f(n-1)+\sum _{i=1}^{n-1}\left(2-n+ni-i^{2}\right)}$
${\displaystyle =f(n-1)-n^{2}+3n-2+\sum _{i=1}^{n-1}\left(ni-i^{2}\right)}$

Well, I guess this is like

f(n) - f(n-1) = C(n)

with c(n) cubic, so the answer is a quartic?

Anyone want to go in and sort this out?

Charles Matthews 17:38, 9 Feb 2004 (UTC)

## Regular polygon?

What happens if one divides a circle using an inscribed regular polygon (i.e. "case (a)" as described in the "Lemma" section may occur)? More specifically, given a regular n-gon, what is ${\displaystyle f(n)}$ = <total number of areas created>? - SigmaEpsilonΣΕ 16:38, 15 March 2007 (UTC)

WP:Forum, but I guess it's just 2n... 8.8.202.167 (talk) 02:07, 7 January 2008 (UTC)