Circle Area By Unrolling Into A Triangle
A circle is sliced into thin pie-shaped sectors that are laid side by side, alternating direction, to form a shape approaching a triangle (or rectangle). The base of this shape equals the circle's circumference, 2πr, and the height equals radius r. Using the triangle area formula, half base times height, gives A = πr². Useful for students meeting the circle area formula for the first time and needing a visual derivation rather than memorization.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Show how the area of a circle emerges by unrolling it into a triangle: circle with radius r, then the unrolled triangle, then the formula A = pi r^2. You know like many little triangles forming a rectangle. Clearly show the rectangle
Make the next one in this series
- Show the same unrolling trick but forming a rectangle instead of a triangle
- Animate how increasing the number of sectors makes the shape approach a perfect rectangle
- Derive the circumference formula 2πr using a similar slicing and unrolling animation
