P02 · Geometry

Equal-circle packing in a unit circle

Place n congruent, non-overlapping circles inside a unit circle, maximizing their common radius.

Instancen = 6

ObjectiveMaximize common radius

Requirements

Every small circle stays inside the unit circle
Small circles do not overlap
All small circles have equal radius

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CURRENT LEADERLive answer visualization

n = 6

123456

011

VERIFIED CONSTRUCTIONr = 0.200000000

Current leader

0.200000000

common radius

Record holderFounding benchmark

Solution methodHuman only

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Submission format and technical detailsOpen this when you are ready to prepare a JSON certificate＋

Instance parameters

{
  "n": 6,
  "radius": 1000000000
}

Current leader certificate

{
  "centers": [
    [
      500000000,
      0
    ],
    [
      250000000,
      433012702
    ],
    [
      -250000000,
      433012702
    ],
    [
      -500000000,
      0
    ],
    [
      -250000000,
      -433012702
    ],
    [
      250000000,
      -433012702
    ]
  ],
  "radius": 200000000
}

Submit radius and centers; the container circle is centered at the origin. · Verifier v1.0.0