چکیده (انگلیسی):

Proofs that the area of a circle is πr
2
can be found in mathematical literature dating as far back as
the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges
and then fitting the wedges together in a way to approximate a rectangle. Later more
sophisticated proofs relied on arguments involving infinite sequences and calculus. Generally
speaking, both of these approaches are difficult to explain to unsophisticated non-mathematics
majors. This paper presents a less known but interesting and intuitive proof that was introduced in
the twelfth century. It discusses challenges that were made to the proof and offers simple rebuttals
to those challenges.