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The video traces how counting lattice points in circles leads through Gaussian integers, sums of squares, and prime factorization to an alternating infinite series for π. It offers a conceptual look at the intersection of algebraic and analytic number theory.
Syllabus
- Introduction.
- Counting lattice points.
- Gaussian integers.
- The lattice point recipe.
- Counting on one ring.
- Exploiting prime regularity.
- Combining the rings.
- Branches of number theory.
Taught by
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