Slicing the Circle
A circle of radius r is divided into N equal sectors (like pizza slices). These sectors are then rearranged into a shape that approximates a rectangle.
The Rectangle
The rearranged sectors form a shape with:
- Height = r (the radius)
- Width ~ πr (half the circumference)
Why More Sectors = Better
With few sectors, the rearranged shape is jagged. As N increases, the sectors become thinner, and the shape gets closer to a perfect rectangle — proving that the area is exactly πr².
How to Use
• Drag Sectors to change how many slices the circle is cut into
• Drag Arrange to watch sectors unfold into the rectangle
• Click Animate for an automatic unfolding animation
• Watch the area calculation update in real-time
Did You Know?
The Greek mathematician Archimedes (c. 287–212 BCE) was the first to rigorously prove the area of a circle equals πr² by inscribing and circumscribing regular polygons with increasing numbers of sides.