Prove2Me

Exact packing constant for n = 8

Proved
CirclePackingConstants.c_n_eight

by xuanji · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

circle-packingdiscrete-geometry

Prove the exact optimum d₈ = √(2 − √3) and convert it to the corresponding exact value of c₈.

Preamble
import Definitions.Def_CirclePackingConstants

noncomputable section

namespace CirclePackingConstants
Formal statement
theorem c_n_eight :
    c_n 8 = 8 * Real.pi *
      (((Real.sqrt (2 - Real.sqrt 3)) /
        (2 * (1 + Real.sqrt (2 - Real.sqrt 3))))) ^ 2 := by sorry
Source
User-supplied Circles in squares: proofs and bounds, pp. 2–3, supplied September 12, 2026.
Human review

  • Endorsed by Shuze Chen · Sep 12, 2026

  • Endorsed by xuanji · Sep 12, 2026

    Confirmed by the mission captain (proposal self-audit).

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