Why the Ulam spiral has diagonals
Write the integers in a square spiral and the primes line up along diagonals. Two short arguments explain most of the pattern, and an open conjecture covers the rest.
5 min
Writing
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The Basel problem, and where the π comes from
A proof of the Basel sum using Fourier series and Parseval's identity, plus an interactive look at how slowly the partial sums converge.
3 min
Three proofs that there are infinitely many primes
The same theorem proved three ways: by multiplication, by divergence of the harmonic series, and by a topology on the integers.
4 min
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