Arbelos Area Visual Proof @MathVisualProofs

Uploaded September 2025 | Updated September 2026, 2 weeks ago

This is a short, animated visual proof proving that the area of an arbelos is equal to the area of the circle with diameter given by the half circle chord obtained from the arbelos construction (from the tangent point of the two interior circles).

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For the wide-format original of this animation, see
youtu.be/zhriP_4QpJQ?si=kHfZeEFFiHnoQ2XV

For other similar visual proofs check these out:

youtu.be/p3_7bOjiWm8
youtu.be/-IKyUjRcFDw

This animation is based on a visual proof from Roger B. Nelsen that appeared in the April 2002 issue of Mathematics Magazine (jstor.org/stable/3219152 p. 144)

To learn more about animating with manim, check out:
https://manim.community

#math #arbelos #geometry #pythagoreantheorem #thalestheorem #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #area #circle #geometricconstruction

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