Prove that $\pi>3$ using geometry I was asked this question today in an interview.
Question: Prove that $\pi>3$ using geometry.
They gave me hints about drawing a unit circle and then inscribing an equilateral triangle and then proceeding. But I could not follow. Can anyone help?

The inscribed $12$-gon in the unit circle has area $\frac{12}{2}\sin (2\pi/12)=3$. The area of the unit circle is $\pi$. Hence $\pi\ge 3$. 
