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Circle packing in a circle

mathematical problem

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General referenceInterpretive dossier study · Crown Archives visual atlas
Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionMar 9, 2026
Entity authorityQ5121498 ↗
Source-derived summary

Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle.

Table of solutions, 1 ≤ n ≤ 20

If more than one optimal solution exists, all are shown.

Special cases

Only 26 optimal packings are thought to be rigid (with no circles able to "rattle"). Numbers in bold are prime:

Proven for n = 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 19

Conjectured for n = 15, 16, 17, 18, 22, 23, 27, 30, 31, 33, 37, 61, 91

Of these, solutions for n = 2, 3, 4, 7, 19, and 37 achieve a packing density greater than any smaller number > 1. (Higher density records all have rattles.)

See also

Disk covering problem

Square packing in a circle

References

External links

Mathematical analysis of 2D packing of circles (2022).

Editorial summary

“Circle packing in a circle” enters the record as mathematical problem. Crown Archives preserves that source wording while asking what Circle, packing and circle can confirm, complicate or overturn.

Editorial reviewA dependable orientation record for establishing vocabulary, names and a first evidence trail. The current lead gives the account dated anchors—2022—that can be checked directly. The selected authority fields contribute no independent date. Its strongest next move is a source search built around Circle, packing and circle.
Editorial analysis

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“Circle packing in a circle” is worth following because a concise public description often conceals a longer documentary argument. Here, Circle, packing and circle provides the most credible route into that argument.

Evidence profile

Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Mar 9, 2026. The linked authority identifier is Q5121498. None of the 0 selected statements returned an explicit reference. The first chronological checks are 2022.

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Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.

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Source & attribution

This entry incorporates text from “Circle packing in a circle” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.