Area of a Regular Dodecagon | Proofs without Words Levels 1 to 4
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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