I’m using the Twelve Days of Christmas (with a week-long head start) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on the formula for the area of a circle.
Part 1: Why the circumference function is the derivative of the area function .
Part 2: Finding the area of a circle via integration by trigonometric substitution.
Part 3: Finding the area of a circle via a double integral.
Part 4: Justifying the formula to geometry students by slicing a circle into pieces and rearranging the pieces as a parallelogram (approximately).