In this short, plot all the points in the positive integer grid up to 101. If a coordinate (x,y) has numbers x and y that are relatively prime, we shade the dot blue; otherwise we shade the dot red. A famous result states that roughly 6/pi*pi of the dots will be blue. So we can use this image to get an approximation for 6/pi*pi and in turn use that to get an approximation for Pi. We get 3.12, which is not really good, but it’s kind of amazing that such a small grid gets us that close. Using a larger grid will give you a better approximation.
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
For more information about why this works, check out the wikipedia site:
https://en.wikipedia.org/wiki/Coprime_integers
For more Pi-related videos, check out my playlist:
https://youtube.com/playlist?list=PLZh9gzIvXQUsGRDvzvXc02lDIKHaVeFwq
#manim #approximation #relativelyprime #zetafunction #baselproblem #irrational #Pi #mathvideo #math #mtbos #animation #iteachmath #mathematics #piday
To learn more about animating with manim, check out:
https://manim.community
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
For more information about why this works, check out the wikipedia site:
https://en.wikipedia.org/wiki/Coprime_integers
For more Pi-related videos, check out my playlist:
https://youtube.com/playlist?list=PLZh9gzIvXQUsGRDvzvXc02lDIKHaVeFwq
#manim #approximation #relativelyprime #zetafunction #baselproblem #irrational #Pi #mathvideo #math #mtbos #animation #iteachmath #mathematics #piday
To learn more about animating with manim, check out:
https://manim.community