Area of a Circle, the BEST COMPLETE PROOF by Archimedes | Tricky Parts of Calculus, Part 3
I give a complete proof that the area of a circle is pi r^2, or 1/2 C r, where C is the circumference, based on the original proof by Archimedes. I also provide some historical notes and commentary on this proof and other proofs.
This is the third episode in a series called Tricky Parts of Calculus, which covers the subtle points of the subject of calculus that are rarely treated in detail in a calculus class.
Tricky Parts of Calculus, Episode 1: • Derivative of sin(x), CAREFUL PROOF |...
Tricky Parts of Calculus, Episode 2: • Sin(x), x, tan(x) inequalities and Ar...
3blue1brown video with circle area formula proof: • The essence of calculus
Eddie Woo video with circle area formula proof: • Quick Visual Proof: Area of a Circle
Veritasium video with discussion of approximation of pi: • The Discovery That Transformed Pi
Check out my podcast for interesting conversations about math and other topics. Especially this conversation about the historical development of mathematics: • Philosophy of Math: What math would a...
Exercise from lecture: Prove that a point of intersection of two tangent lines to a circle is equidistant from the points of tangency.
