Leibniz Formula for Pi/4 - A Pi Day Visualization/Dissection

In this video, we explore a wonderful dissection of the unit circle (with area Pi) into regions that have areas given by differences of reciprocals of consecutive odds. When the diagram is complete, we get a visualization of the famous Madhava-Gregory-Leibniz series, or Leibniz formula, for Pi/4. We explain how this dissection comes about by investigating a family of regions bounded by two special polar curves, coming from powers of tangents of half angles. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks! This animation 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/... ) see pages 145-150. That article features this dissection proof attributed to Viggo Brun. For more Pi-related videos, check out my playlist:    • Pi   #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 To learn more about animating with manim, check out: https://manim.community