Com-PI-lation: 10 Pi Visualizations!

In this video, I show and describe at least 10 of my favorite Pi visualizations. Please let me know your favorite or what I should/could add! If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to see. more pi visualizations, check out my pi playlist: https://youtube.com/playlist?list=PLZh9gzIvXQUsGRDvzvXc02lDIKHaVeFwq&si=VP6Ff6bpVfcp4T6d If you want to know more about these visuals, here they are below: 1) Pi as almost 3 diameters - this is the definition and not based on any known published visual proof. 2) Pi epicycloid: this is also a classical notion and not documented. 3) Pi as a sum of arctangents in a rectangle is due to Rex Wu and comes from the March 2003 issue of The College Mathematics Journal (https://www.jstor.org/stable/3595783 ) see pages 115 and 138. 4) The pi from coprime integers is a classic: https://en.wikipedia.org/wiki/Coprime_integers 5) This visualization of peeling circumferences was inspired by several other similar visuals: from @MinutePhysics : https://youtu.be/whYqhpc6S6g For more information about this construction, see https://personal.math.ubc.ca/~cass/courses/m446-03/exhaustion.pdf or check out this nice survey article by David Richeson from the May 2015 issue of The College Math Journal: https://doi.org/10.4169/college.math.j.46.3.162 . 6) The area via wedges proof can be traced to both Satō Moshun and Leonardo da Vinci (see Smith, David Eugene; Mikami, Yoshio (1914), A history of Japanese mathematics, https://archive.org/details/historyofjapanes00smituoft, page 130-132 and Beckmann, Petr (1976), A History of Pi, St. Martin's Griffin, page 19). You can also read more about this in a great NYT article by Steven Strogatz: https://archive.nytimes.com/opinionator.blogs.nytimes.com/2010/04/04/take-it-to-the-limit/ 7) The Madhava series visualization was inspired by an article from Mitsuo Kobayashi that appeared in the April 2014 issue of Mathematics Magazine (https://www.jstor.org/stable/10.4169/math.mag.87.2.145 ) see pages 145-150. That article features this dissection proof attributed to Viggo Brun. 8) The pi in a 3-4-5 triangle visual is based on a visual proof from Proofs without Words II by Roger B. Nelsen (MAA, 2000) (https://bookstore.ams.org/clrm-14/) page 14 9) This false argument was suggested to me by Jeff Stuart as a nice alternative to the more classic Pi = 4 argument, which can be found many places. 10) The pi as simulated by dartboards is also a classic and has been done many times in many videos. #manim #irrational #Pi #mathvideo​ #math​ #mtbos​ ​ #animation​​​ #iteachmath #mathematics #piday #shorts #trigonometry #tangent #triangle #rectangle #identities #infiniteseries #series #dissectionproof #dissection #leibniz #leibnizformula #infinitesum #calculus #integral #proofwithoutwords #visualproof To learn more about animating with manim, check out: https://manim.community