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Currently Playing: Four Wordless Dodecagon Proofs

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. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! 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. https://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 (https://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) (https://bookstore.ams.org/clrm-14/) See these videos for standalone versions of these dissections: https://youtu.be/LbCghvu6G5w https://youtu.be/aSdo2ug4EyE https://youtu.be/7lCJDdD_fHs https://youtube.com/shorts/uxL7K2IZBf8 https://youtube.com/shorts/f_y-V75O93c https://youtube.com/shorts/AgdgwQbWFvM #math​ #manim​ #visualproof​ ​ #geometry #dodecagon #mathshorts​​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #proof​ #iteachmath #area #dissection To learn more about animating with manim, check out: https://manim.community