Area of a Circle: Index

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 C(r) = 2 \pi r is the derivative of the area function A(r) = \pi r^2.

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 A(r) = \pi r^2 to geometry students by slicing a circle into pieces and rearranging the pieces as a parallelogram (approximately).




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