PPL 097 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
Prize Problem LedgerKimberling rewardsPPL 097Kimberling #10 · Curve closest to a sphere

Permanent problem IDPPL 097

Verified openIndependentexistence

Geometry

Kimberling #10 · Curve closest to a sphere

Find and prove optimal parametric equations for a simple closed curve of length 4π on the unit sphere that minimizes mean spherical distance from the sphere to the curve; ideally solve the version for every length L > 2π.

sphereclosed curvesoptimization
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The problem

Find and prove optimal parametric equations for a simple closed curve of length 4π on the unit sphere that minimizes mean spherical distance from the sphere to the curve; ideally solve the version for every length L > 2π.

Open sinceUnknowndate not stated by sponsor
Last checked2026.07.27Catalog verification
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Reward offers

Offer 01$50–$100Clark Kimberling
Personal offer

Be first to publish a solution in a refereed journal, or submit a short proof that Kimberling accepts as correct and complete. For solutions after 1 January 2025, Kimberling says the stated amount will be donated in the solver’s name to the Online Encyclopedia of Integer Sequences; it is not direct cash to the solver. The page lists “$50 or $100”; the applicable amount depends on whether the special or general version is resolved and should be confirmed with the sponsor.

Current post-2025 form: a donation to OEIS in the solver’s name.

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Sources & reading

1 unique reference linksSponsor’s live rewards page