A rough Pi approximation from coprime integers
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.
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For more information about why this works, check out the wikipedia site:
https://en.wikipedia.org/wiki/Coprime...
For more Pi-related videos, check out my playlist:
• Pi
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