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.

If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks!

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!  

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

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