The course explores the curious patterns, approximations for pi, and prime distributions related to prime numbers and spirals. The learning outcomes include understanding Dirichlet’s theorem, pi approximations, residue classes, Euler’s totient function, and the significance of prime number distributions. The course teaches analytical skills in interpreting mathematical patterns and relationships. The teaching method involves a combination of visual animations, historical context, and mathematical explanations. The intended audience includes mathematics enthusiasts, students interested in number theory, and individuals curious about the connections between prime numbers and geometric patterns.
Why Do Prime Numbers Make These Spirals? - Dirichlet’s Theorem, Pi Approximations, and More
3Blue1Brown via YouTube
Overview
Syllabus
- The spiral mystery
- Non-prime spirals
- Residue classes
- Why the galactic spirals
- Euler’s totient function
- The larger scale
- Dirichlet’s theorem
- Why care?
: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate. By "allowable", here, I mean a residue class whose elements are coprime to the modulus, as described in the video. What he actually showed is that the sum of the reciprocals of all primes in a given allowable residue class diverges, which proves that there are infinitely many primes in such a sequence.
Taught by
3Blue1Brown
