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Pi hiding in prime regularities

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Further reading 1

When does a pattern in a picture become a proof? →A tiling suggests a conjecture, a new encoding turns rectangles into collisions, and a plotting rule creates spirals before primes even enter the picture. What work does each picture actually do?This video helps answer · Does the spiral survive when every integer is plotted?

Caption notes

Lattice points in a large disk can be estimated by area or counted ring by ring. The link between π and arithmetic comes from showing that the two routes count the same points.

Video or transcript source ↗
Original passages · 2
how many lattice points of the plane sit inside a big circle
Pi hiding in prime regularities · ▶ 1:51–2:00
count how many lattice points are on a given one of these rings
Pi hiding in prime regularities · ▶ 4:27–4:36

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