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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Level 1 is a standard construction using trigonometry that you can find in many sources.
Level 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.
Level 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.... ).
Level 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:
• Area of a Regular Dodecagon III (visu...
• Area of a Regular Dodecagon (visual p...
• Area of a Regular Dodecagon II (visua...
• Beautiful dodecagon dissection
• Regular dodecagon area (visual proof ...
• Area of dodecagon from a square!
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Watch video Area of a Regular Dodecagon | Proofs without Words Levels 1 to 4 online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 30 March 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 4,532 once and liked it 285 people.