Four Dodecagon Area Proofs in Sixty Seconds @MathVisualProofs

Uploaded January 2026 | Updated September 2026, 2 weeks ago

This is a compilation of four animated visual proofs demonstrating that the area of a regular dodecagon inscribed in the unit circle has an area of exactly 3.

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Proof 1 is a standard construction using trigonometry that you can find in many sources.

Proof 2 is based on a dissection from the book The Penguin Book of Curious and Interesting Puzzles by David Wells. amzn.to/3O4CnUF : I may receive commissions from this link

Thanks to Matthew Scroggs for pointing me to the source.

Proof 3 is based on a proof by Roger B. Nelsen from the January 2015 issue of The College Mathematics Journal page 10 (doi.org/10.4169/college.math.j.46.1.10 ).

Proof 4 is based on a dissection by J. Kürschák that appears in the following sources:

Mathematical Morsels by Ross Honsberger (MAA, 1978)

Proofs without Words II by Roger B. Nelsen (MAA, 2000) (bookstore.ams.org/clrm-14/)

See these videos for standalone versions of these dissections:
youtu.be/LbCghvu6G5w
youtu.be/aSdo2ug4EyE
youtu.be/7lCJDdD_fHs
youtube.com/shorts/uxL7K2IZBf8
youtube.com/shorts/f_y-V75O93c
youtube.com/shorts/AgdgwQbWFvM

#math #manim #visualproof #geometry #dodecagon #mathshorts #animation #theorem #pww #proofwithoutwords #proof #iteachmath #area #dissection

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Four Dodecagon Area Proofs in Sixty Seconds

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