MathDB

1999 Calculus #10: Inscribing and Circumscribing to Infinity

Source:

June 21, 2012

calculusgeometrycircumcircle

Problem Statement

Let

A_n

be the area outside a regular

n

-gon of side length

1

but inside its circumscribed circle, let

B_n

be the area inside the

n

-gon but outside its inscribed circle. Find the limit as

n

tends to infinity of

\dfrac{A_n}{B_n}