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P87 · Packing and covering · Classic · Medium

Equal discs covering a disc · n = 33

Cover the largest possible disc with n unit-radius discs. Maximise the covered disc radius.

Instancen = 33
ObjectiveMaximize covered disc radius

Record comparison

covered disc radius · Higher is better
RecordValue / intervalAuthor / holderSource
External best known——No reference listed
Site record4.754184577NUE_13Record details ↓

Formal definition

  • ContainerThe editor and certificate normalize to the closed unit disc centred at (1,1). This is a coordinate convention only; scores use the literature's unit-piece scale. Boundary contact is allowed.
  • SubmissionSubmit {radius, placements:[{x,y,turn},…]}, with decimal strings of at most nine places. x,y are centres; circles require turn=0, polygons use turn=tan(θ/2). Coordinates and turn lie in ±4; 0 < radius ≤ 4.
  • ConstraintsThe n distinct centres lie in the target disc. Covering discs may overlap and protrude, but must cover every target point.
  • PrecisionInput decimals are exact rationals; regular-polygon vertices are algebraic, not rounded templates. Feasibility has no floating-point tolerance. A finite-decimal certificate is not a continuous optimality proof.
  • ObjectiveCovered disc radius R = 1/r, larger is better.
Open the full editor ↗

Layout shown: site record

VERIFIED CONSTRUCTIONVERIFIED CONSTRUCTION

Getting a feel for it

Source and certificate

External targets are converted with their printed precision; decimal coordinate certificates are separate. Reconstruction loss never lowers the literature target, and a source construction is not automatically an optimality proof.

Source
The record-holding arrangement for Equal discs covering a disc n = 33, 4.754184577
LAYOUT & HISTORY

Record details

Inspect the layout, solver notes and record history.

Record holderNUE_13
Solution methodHuman
Challenge this record ↗Submit a proof / idea ↓Share a proof or idea in the discussion. Accepted contributions can earn proof points.
Record holder's solver noteNo solver note yet (expand)＋

The record holder has not shared a solver note yet.

Record history (1 changes)
  1. NUE_13Human
    4.754169727→4.754184577
ANSWER FORMAT

How to write your answer

the closed unit disc centred at (1,1)

Submit {radius, placements:[{x,y,turn},…]}, with decimal strings of at most nine places. x,y are centres; circles require turn=0, polygons use turn=tan(θ/2). Coordinates and turn lie in ±4; 0 < radius ≤ 4.

The current leader's answer

{
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    {
      "turn": "0.000000000",
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    {
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    {
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    {
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    {
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    {
      "turn": "0.000000000",
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    {
      "turn": "0.000000000",
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    {
      "turn": "0.000000000",
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    {
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    {
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    {
      "turn": "0.000000000",
      "x": "0.390280148",
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    {
      "turn": "0.000000000",
      "x": "1.889991494",
      "y": "0.639518293"
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    {
      "turn": "0.000000000",
      "x": "0.959844669",
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    {
      "turn": "0.000000000",
      "x": "1.881067442",
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    {
      "turn": "0.000000000",
      "x": "0.122712162",
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    {
      "turn": "0.000000000",
      "x": "1.508013825",
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    {
      "turn": "0.000000000",
      "x": "0.111137223",
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    {
      "turn": "0.000000000",
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    {
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    {
      "turn": "0.000000000",
      "x": "1.468590162",
      "y": "1.736902816"
    }
  ],
  "radius": "0.210341013"
}
Submission format and technical detailsOpen this when you are ready to prepare a JSON answer＋

Instance parameters

{
  "n": 33,
  "sides": 5
}

The current leader's answer

{
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}

Submit {radius, placements:[{x,y,turn},…]}, with decimal strings of at most nine places. x,y are centres; circles require turn=0, polygons use turn=tan(θ/2). Coordinates and turn lie in ±4; 0 < radius ≤ 4. · Verifier v1.0.0

DISCUSSION

Discussion

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