Here is a paper I wrote a while back in 2003 and wanted to publish to a math magazine:
Smaller discs to cover the unit circle
MathWorld cites the best known solutions for n=9 as 0.422 and n=10 as 0.398. My solution is better with n=9 as 0.414 and n=10 as 0.381.
Just when I finished, I looked around for more references and related work, after MathWorld and all those sources. Well, it turns out that two other people:
- D. Nagy, Fedesek es alkalmazasaik, M.Sc. thesis, Eötvös Loránd Univ., Budapest, 1974.
- S. Krotoszyski, “Covering a disk with smaller disks,” Studia Sc. Math. Hungar., vol. 28, 1993, pp. 277–283. MR 95c:52035.
both had published the same solution I came up with. Really, who would spend the time to solve such an esoteric problem? Nerds!
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