A random approximation for Pi (pi day short)

In this short, we randomly sample 5000 pairs of positive integers and use the pairs to plot points in the plane. If a pair is relatively prime, we shade the dot red; otherwise we shade the dot blue. The theory behind this process says that roughly 6/pi*pi of the dots will be red. So we can use this simulation to get an approximation for 6/pi*pi and in turn use that to get an approximation for Pi. We get 3.142, which is not that bad, but not really good either.

For more information about why this works, check out the wikipedia site:

For more Pi-related videos, check out my playlist:

#manim #approximation #relativelyprime #zetafunction #baselproblem #irrational #Pi #mathvideo​ #math​ #mtbos​ ​ #animation​​​ #iteachmath #mathematics #piday

To learn more about animating with manim, check out:

[lgooch]

Fun fact: the probability that two numbers are coprime is 1/zeta(2)

[RafaelCouto]

TIL: two numbers are said to be relatively prime when they have only 1 as the common factor

[pengin]

Will you do a proof for that and the more general fact for the probability of n numbers being coprime being 1/zeta(n)?

[iamdigory]

So plotting them wasn't really part of it (you had me thinking they'd make a pattern on the plot)

[tuansuri]

Do u have any videos for conic sections????

[robertcampomizzi]

What does "relatively prime" mean??