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Math Proofs

Classic proofs, one step at a time. Each diagram responds to the sliders, so you can check that the argument does not depend on one lucky picture.

Circle area from a triangle

To prove A circle of radius rrr has area πr2\pi r^2πr2.

r

8 rings of thickness r/8. The strips’ areas always add to exactly πr²; more rings just smooth the jagged edge.

Slice the circle into thin rings

Cut the circle into nnn concentric rings, each of thickness Δ=r/n\Delta = r/nΔ=r/n. Drag the slider to use more rings.