Circle Area By Unrolling Into A Triangle
A circle is sliced into thin concentric rings which are cut and laid out side by side, forming a triangular shape whose base equals the circle's circumference and whose height equals the radius. The animation shows this triangle's area, one half base times height, simplifying to pi r squared. Useful for students learning where the circle area formula comes from rather than just memorizing it.
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.
Make the next one in this series
- Show the same unrolling idea used to derive the circumference formula C = 2 pi r
- Animate slicing a circle into wedges and rearranging them into a parallelogram to find area
- Demonstrate how increasing the number of rings makes the triangle approximation more exact
