Cyclic Regular Polygon Fractals
Calculus
Level
3
The \(n^{\text{th}}\) figure in the above sequence is constructed by the following procedure:
- Draw a blue disc of radius \(\displaystyle\sqrt{\frac{2016}{\pi}}\)
- Remove a regular \(n\)-gon area from the (smallest) disc
- Inscribe a blue disc inside the empty \(n\)-gon space
- Repeat steps 2-4
Let \(A_n\) be the total blue area of the \(n^{\text{th}}\) figure in the sequence.
Compute \(\displaystyle\lim_{n\to\infty}A_n\).
by
Kerry Soderdahl