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  "body": "\n## Summary\n\nA circle packing is an arrangement of circles in the plane, or on a surface, whose discs do not overlap.\nOne studies dense packings of equal circles, where the hexagonal packing is optimal by [[Thue's theorem|3P246RHXMF]].\nOne also studies packings with prescribed tangencies, where the [[circle packing theorem|GR1DDT1B6B]] realizes every planar graph.\nCircle packings give a discrete analogue of [[conformal maps|0YYT36R4YD]], and fractal examples such as the [[Apollonian gasket|8SETG842RX]].\n\n## Explanations\n\n### L1 human\n\nLay coins on a table so that no two coins overlap; that is a circle packing.\nThe coins may all have the same size, as in a tray of identical cans, or different sizes.\nIf the coins are equal, the honeycomb arrangement, where each coin touches six others, wastes the least space.\n",
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