Finding Formula for Circle Area via Parallelogram
Questions to guide your thinking:
1. Play with the sliders a bit. What does each slider do?
Suppose the circle has radius r.
If we put each slider at its right end (n=80, i=2), the shape we get is nearly, but not quite, a parallelogram. You might even call it a near-rectangle, but I'll call it a "parallelogram". By moving i between 0 and 2, answer these questions:
2. What is the height of the "parallelogram"?
3. What is the width of the "parallelogram"?
Now for the punch line:
4. What is the area of the "parallelogram"?
5. What is the area of the circle?