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OEIS A00092: Lattice points in a sphere and the limits of volume estimates

Author
Mike Breault
Published
Sat 04 Jan 2025
Episode Link
None

Explore A00092, the OEIS entry that records the radii (radius squared) where the difference between the actual lattice point count inside a sphere and its volume-based estimate is largest. Learn A(n) (the exact lattice point count), V(n) (the sphere volume-based estimate), and P(n) = A(n) - V(n). We'll discuss the remainder term studied by Bleicher and Knob (NIST, 1965), show how Mathematica and ParaGP code snippets help compute the counts, and reflect on the broader tension between discrete and continuous models, with links to computer graphics, cryptography, and the philosophy of estimation.


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