文献中也称circle packing in a squarepacking equal circles in a unit squarecsq
在边长 1 的正方形内放置 n 个半径相同、互不重叠的圆，使共同半径尽可能大。
| 纪录 | 数值 / 区间 | 作者 / 持有人 | 来源 |
|---|---|---|---|
| 外部已知最好 | [0.0370473729445, 0.0370473729455] | 见来源署名 | packomania.com ↗ |
| 本站纪录 | 暂无选手纪录 | — | — |
当前展示：起步布局
最优构形是「卡死」的接触结构：圆彼此顶住、顶住边界，常出现斜排、错位、以及不碰任何邻居的游离圆。规整的网格摆法几乎从不最优。
n = 1–30 已证明最优，适合观察经典接触结构；n = 31–300 接入 Packomania 的公开前沿，除 n = 36 外最优性仍未知。大规模部分集中成一张表，供算法批量挑战。
查看来源
查看构型、求解笔记与纪录历史。
容器是边长 1 的正方形，左下角是原点 (0, 0)，右上角是 (1, 1)。坐标和长度用同一个单位，直接写成小数，例如 "0.5"，最多九位小数。
提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。
{
"centers": [
[
"0.037047373",
"0.037047373"
],
[
"0.165700681",
"0.037047373"
],
[
"0.294353989",
"0.037047373"
],
[
"0.423007297",
"0.037047373"
],
[
"0.551660604",
"0.037047373"
],
[
"0.680313703",
"0.037047373"
],
[
"0.808927589",
"0.037047373"
],
[
"0.883022334",
"0.037047373"
],
[
"0.962952627",
"0.037047373"
],
[
"0.101374027",
"0.073818462"
],
[
"0.230027335",
"0.073818462"
],
[
"0.358680643",
"0.073818462"
],
[
"0.48733395",
"0.073818462"
],
[
"0.615987154",
"0.073818644"
],
[
"0.744620646",
"0.073852923"
],
[
"0.922987481",
"0.099439828"
],
[
"0.813239531",
"0.111034103"
],
[
"0.037047373",
"0.111142119"
],
[
"0.165700681",
"0.111142119"
],
[
"0.294353989",
"0.111142119"
],
[
"0.423007297",
"0.111142119"
],
[
"0.551660604",
"0.111142119"
],
[
"0.680313703",
"0.111142119"
],
[
"0.101374027",
"0.147913207"
],
[
"0.230027335",
"0.147913207"
],
[
"0.358680643",
"0.147913207"
],
[
"0.48733395",
"0.147913208"
],
[
"0.615987154",
"0.14791339"
],
[
"0.744620646",
"0.147947669"
],
[
"0.877876007",
"0.158218959"
],
[
"0.962952627",
"0.161832283"
],
[
"0.808788578",
"0.184995042"
],
[
"0.037047373",
"0.185236865"
],
[
"0.165700681",
"0.185236865"
],
[
"0.294353989",
"0.185236865"
],
[
"0.423007297",
"0.185236865"
],
[
"0.551660604",
"0.185236865"
],
[
"0.680313703",
"0.185236865"
],
[
"0.101374027",
"0.222007953"
],
[
"0.230027335",
"0.222007953"
],
[
"0.358680643",
"0.222007953"
],
[
"0.48733395",
"0.222007954"
],
[
"0.615987154",
"0.222008136"
],
[
"0.744620646",
"0.222042415"
],
[
"0.888991744",
"0.231475166"
],
[
"0.962952627",
"0.235927029"
],
[
"0.814931247",
"0.259262125"
],
[
"0.037326303",
"0.259331086"
],
[
"0.165979611",
"0.259331086"
],
[
"0.294632919",
"0.259331086"
],
[
"0.423286227",
"0.259331086"
],
[
"0.551939534",
"0.259331086"
],
[
"0.680592634",
"0.259331086"
],
[
"0.101652957",
"0.296102174"
],
[
"0.230306265",
"0.296102174"
],
[
"0.358959573",
"0.296102174"
],
[
"0.48761288",
"0.296102175"
],
[
"0.616266084",
"0.296102356"
],
[
"0.744899576",
"0.296136635"
],
[
"0.877195962",
"0.30462495"
],
[
"0.951156846",
"0.309076813"
],
[
"0.037047373",
"0.333425306"
],
[
"0.165700681",
"0.333425306"
],
[
"0.294353989",
"0.333425306"
],
[
"0.423007297",
"0.333425306"
],
[
"0.551660604",
"0.333425306"
],
[
"0.680313703",
"0.333425306"
],
[
"0.808927589",
"0.333425306"
],
[
"0.101374027",
"0.370196395"
],
[
"0.230027335",
"0.370196395"
],
[
"0.358680643",
"0.370196395"
],
[
"0.48733395",
"0.370196396"
],
[
"0.615987154",
"0.370196577"
],
[
"0.744620646",
"0.370230856"
],
[
"0.888991744",
"0.377774734"
],
[
"0.962952627",
"0.382226597"
],
[
"0.811219569",
"0.407484595"
],
[
"0.037326303",
"0.407519527"
],
[
"0.165979611",
"0.407519527"
],
[
"0.294632919",
"0.407519527"
],
[
"0.423286227",
"0.407519527"
],
[
"0.551939534",
"0.407519527"
],
[
"0.680592634",
"0.407519527"
],
[
"0.101652957",
"0.444290616"
],
[
"0.230306265",
"0.444290616"
],
[
"0.358959573",
"0.444290616"
],
[
"0.48761288",
"0.444290617"
],
[
"0.616266084",
"0.444290798"
],
[
"0.744899576",
"0.444325077"
],
[
"0.876299388",
"0.450774292"
],
[
"0.950260271",
"0.455226155"
],
[
"0.037047373",
"0.481613748"
],
[
"0.165700681",
"0.481613748"
],
[
"0.294353989",
"0.481613748"
],
[
"0.423007297",
"0.481613748"
],
[
"0.551660604",
"0.481613748"
],
[
"0.680313703",
"0.481613748"
],
[
"0.808927589",
"0.481613748"
],
[
"0.101374027",
"0.518384837"
],
[
"0.230027335",
"0.518384837"
],
[
"0.358680643",
"0.518384837"
],
[
"0.48733395",
"0.518384838"
],
[
"0.615987154",
"0.518385019"
],
[
"0.744620646",
"0.518419298"
],
[
"0.888991744",
"0.52377385"
],
[
"0.962952627",
"0.528225713"
],
[
"0.813165647",
"0.555589398"
],
[
"0.037047373",
"0.555708494"
],
[
"0.165700681",
"0.555708494"
],
[
"0.294353989",
"0.555708494"
],
[
"0.423007297",
"0.555708494"
],
[
"0.551660604",
"0.555708494"
],
[
"0.680313703",
"0.555708494"
],
[
"0.101374027",
"0.592479583"
],
[
"0.230027335",
"0.592479583"
],
[
"0.358680643",
"0.592479583"
],
[
"0.48733395",
"0.592479584"
],
[
"0.615987154",
"0.592479765"
],
[
"0.744620646",
"0.592514044"
],
[
"0.875128174",
"0.596560063"
],
[
"0.949089058",
"0.601011926"
],
[
"0.808788578",
"0.629561417"
],
[
"0.037047373",
"0.62980324"
],
[
"0.165700681",
"0.62980324"
],
[
"0.294353989",
"0.62980324"
],
[
"0.423007297",
"0.62980324"
],
[
"0.551660604",
"0.62980324"
],
[
"0.680313703",
"0.62980324"
],
[
"0.101374027",
"0.666574329"
],
[
"0.230027335",
"0.666574329"
],
[
"0.358680643",
"0.666574329"
],
[
"0.48733395",
"0.66657433"
],
[
"0.615987154",
"0.666574511"
],
[
"0.744620646",
"0.66660879"
],
[
"0.888991744",
"0.669346276"
],
[
"0.962952627",
"0.673798139"
],
[
"0.809993114",
"0.703653031"
],
[
"0.037047373",
"0.703897986"
],
[
"0.165700681",
"0.703897986"
],
[
"0.294353989",
"0.703897986"
],
[
"0.423007297",
"0.703897986"
],
[
"0.551660604",
"0.703897986"
],
[
"0.680313703",
"0.703897986"
],
[
"0.101374027",
"0.740669074"
],
[
"0.230027335",
"0.740669074"
],
[
"0.358680643",
"0.740669074"
],
[
"0.48733395",
"0.740669075"
],
[
"0.615987154",
"0.740669257"
],
[
"0.744620646",
"0.740703536"
],
[
"0.873589683",
"0.741822534"
],
[
"0.947550567",
"0.746274397"
],
[
"0.808788578",
"0.777750909"
],
[
"0.037047373",
"0.777992732"
],
[
"0.165700681",
"0.777992732"
],
[
"0.294353989",
"0.777992732"
],
[
"0.423007297",
"0.777992732"
],
[
"0.551660604",
"0.777992732"
],
[
"0.680313703",
"0.777992732"
],
[
"0.101374027",
"0.81476382"
],
[
"0.230027335",
"0.81476382"
],
[
"0.358680643",
"0.81476382"
],
[
"0.48733395",
"0.814763821"
],
[
"0.615987154",
"0.814764003"
],
[
"0.744620646",
"0.814798282"
],
[
"0.888742044",
"0.815616002"
],
[
"0.962952627",
"0.818750654"
],
[
"0.808788578",
"0.851845655"
],
[
"0.037047373",
"0.852087478"
],
[
"0.165700681",
"0.852087478"
],
[
"0.294353989",
"0.852087478"
],
[
"0.423007297",
"0.852087478"
],
[
"0.551660604",
"0.852087478"
],
[
"0.680313703",
"0.852087478"
],
[
"0.101374027",
"0.888858566"
],
[
"0.230027335",
"0.888858566"
],
[
"0.358680643",
"0.888858566"
],
[
"0.48733395",
"0.888858567"
],
[
"0.615987154",
"0.888858748"
],
[
"0.744620646",
"0.888893028"
],
[
"0.871785121",
"0.890851641"
],
[
"0.945879867",
"0.890851641"
],
[
"0.166019311",
"0.926181538"
],
[
"0.29467262",
"0.926181539"
],
[
"0.423326033",
"0.926181722"
],
[
"0.551999224",
"0.926216161"
],
[
"0.037099982",
"0.926355008"
],
[
"0.681624103",
"0.927899014"
],
[
"0.817880215",
"0.941687578"
],
[
"0.101692657",
"0.962952627"
],
[
"0.230345965",
"0.962952627"
],
[
"0.358999274",
"0.962952627"
],
[
"0.487652791",
"0.962952627"
],
[
"0.616345657",
"0.962952627"
],
[
"0.746902549",
"0.962952627"
],
[
"0.888857881",
"0.962952627"
],
[
"0.962952627",
"0.962952627"
]
],
"radius": "0.037047372"
}{
"n": 196
}{
"centers": [
[
"0.037047373",
"0.037047373"
],
[
"0.165700681",
"0.037047373"
],
[
"0.294353989",
"0.037047373"
],
[
"0.423007297",
"0.037047373"
],
[
"0.551660604",
"0.037047373"
],
[
"0.680313703",
"0.037047373"
],
[
"0.808927589",
"0.037047373"
],
[
"0.883022334",
"0.037047373"
],
[
"0.962952627",
"0.037047373"
],
[
"0.101374027",
"0.073818462"
],
[
"0.230027335",
"0.073818462"
],
[
"0.358680643",
"0.073818462"
],
[
"0.48733395",
"0.073818462"
],
[
"0.615987154",
"0.073818644"
],
[
"0.744620646",
"0.073852923"
],
[
"0.922987481",
"0.099439828"
],
[
"0.813239531",
"0.111034103"
],
[
"0.037047373",
"0.111142119"
],
[
"0.165700681",
"0.111142119"
],
[
"0.294353989",
"0.111142119"
],
[
"0.423007297",
"0.111142119"
],
[
"0.551660604",
"0.111142119"
],
[
"0.680313703",
"0.111142119"
],
[
"0.101374027",
"0.147913207"
],
[
"0.230027335",
"0.147913207"
],
[
"0.358680643",
"0.147913207"
],
[
"0.48733395",
"0.147913208"
],
[
"0.615987154",
"0.14791339"
],
[
"0.744620646",
"0.147947669"
],
[
"0.877876007",
"0.158218959"
],
[
"0.962952627",
"0.161832283"
],
[
"0.808788578",
"0.184995042"
],
[
"0.037047373",
"0.185236865"
],
[
"0.165700681",
"0.185236865"
],
[
"0.294353989",
"0.185236865"
],
[
"0.423007297",
"0.185236865"
],
[
"0.551660604",
"0.185236865"
],
[
"0.680313703",
"0.185236865"
],
[
"0.101374027",
"0.222007953"
],
[
"0.230027335",
"0.222007953"
],
[
"0.358680643",
"0.222007953"
],
[
"0.48733395",
"0.222007954"
],
[
"0.615987154",
"0.222008136"
],
[
"0.744620646",
"0.222042415"
],
[
"0.888991744",
"0.231475166"
],
[
"0.962952627",
"0.235927029"
],
[
"0.814931247",
"0.259262125"
],
[
"0.037326303",
"0.259331086"
],
[
"0.165979611",
"0.259331086"
],
[
"0.294632919",
"0.259331086"
],
[
"0.423286227",
"0.259331086"
],
[
"0.551939534",
"0.259331086"
],
[
"0.680592634",
"0.259331086"
],
[
"0.101652957",
"0.296102174"
],
[
"0.230306265",
"0.296102174"
],
[
"0.358959573",
"0.296102174"
],
[
"0.48761288",
"0.296102175"
],
[
"0.616266084",
"0.296102356"
],
[
"0.744899576",
"0.296136635"
],
[
"0.877195962",
"0.30462495"
],
[
"0.951156846",
"0.309076813"
],
[
"0.037047373",
"0.333425306"
],
[
"0.165700681",
"0.333425306"
],
[
"0.294353989",
"0.333425306"
],
[
"0.423007297",
"0.333425306"
],
[
"0.551660604",
"0.333425306"
],
[
"0.680313703",
"0.333425306"
],
[
"0.808927589",
"0.333425306"
],
[
"0.101374027",
"0.370196395"
],
[
"0.230027335",
"0.370196395"
],
[
"0.358680643",
"0.370196395"
],
[
"0.48733395",
"0.370196396"
],
[
"0.615987154",
"0.370196577"
],
[
"0.744620646",
"0.370230856"
],
[
"0.888991744",
"0.377774734"
],
[
"0.962952627",
"0.382226597"
],
[
"0.811219569",
"0.407484595"
],
[
"0.037326303",
"0.407519527"
],
[
"0.165979611",
"0.407519527"
],
[
"0.294632919",
"0.407519527"
],
[
"0.423286227",
"0.407519527"
],
[
"0.551939534",
"0.407519527"
],
[
"0.680592634",
"0.407519527"
],
[
"0.101652957",
"0.444290616"
],
[
"0.230306265",
"0.444290616"
],
[
"0.358959573",
"0.444290616"
],
[
"0.48761288",
"0.444290617"
],
[
"0.616266084",
"0.444290798"
],
[
"0.744899576",
"0.444325077"
],
[
"0.876299388",
"0.450774292"
],
[
"0.950260271",
"0.455226155"
],
[
"0.037047373",
"0.481613748"
],
[
"0.165700681",
"0.481613748"
],
[
"0.294353989",
"0.481613748"
],
[
"0.423007297",
"0.481613748"
],
[
"0.551660604",
"0.481613748"
],
[
"0.680313703",
"0.481613748"
],
[
"0.808927589",
"0.481613748"
],
[
"0.101374027",
"0.518384837"
],
[
"0.230027335",
"0.518384837"
],
[
"0.358680643",
"0.518384837"
],
[
"0.48733395",
"0.518384838"
],
[
"0.615987154",
"0.518385019"
],
[
"0.744620646",
"0.518419298"
],
[
"0.888991744",
"0.52377385"
],
[
"0.962952627",
"0.528225713"
],
[
"0.813165647",
"0.555589398"
],
[
"0.037047373",
"0.555708494"
],
[
"0.165700681",
"0.555708494"
],
[
"0.294353989",
"0.555708494"
],
[
"0.423007297",
"0.555708494"
],
[
"0.551660604",
"0.555708494"
],
[
"0.680313703",
"0.555708494"
],
[
"0.101374027",
"0.592479583"
],
[
"0.230027335",
"0.592479583"
],
[
"0.358680643",
"0.592479583"
],
[
"0.48733395",
"0.592479584"
],
[
"0.615987154",
"0.592479765"
],
[
"0.744620646",
"0.592514044"
],
[
"0.875128174",
"0.596560063"
],
[
"0.949089058",
"0.601011926"
],
[
"0.808788578",
"0.629561417"
],
[
"0.037047373",
"0.62980324"
],
[
"0.165700681",
"0.62980324"
],
[
"0.294353989",
"0.62980324"
],
[
"0.423007297",
"0.62980324"
],
[
"0.551660604",
"0.62980324"
],
[
"0.680313703",
"0.62980324"
],
[
"0.101374027",
"0.666574329"
],
[
"0.230027335",
"0.666574329"
],
[
"0.358680643",
"0.666574329"
],
[
"0.48733395",
"0.66657433"
],
[
"0.615987154",
"0.666574511"
],
[
"0.744620646",
"0.66660879"
],
[
"0.888991744",
"0.669346276"
],
[
"0.962952627",
"0.673798139"
],
[
"0.809993114",
"0.703653031"
],
[
"0.037047373",
"0.703897986"
],
[
"0.165700681",
"0.703897986"
],
[
"0.294353989",
"0.703897986"
],
[
"0.423007297",
"0.703897986"
],
[
"0.551660604",
"0.703897986"
],
[
"0.680313703",
"0.703897986"
],
[
"0.101374027",
"0.740669074"
],
[
"0.230027335",
"0.740669074"
],
[
"0.358680643",
"0.740669074"
],
[
"0.48733395",
"0.740669075"
],
[
"0.615987154",
"0.740669257"
],
[
"0.744620646",
"0.740703536"
],
[
"0.873589683",
"0.741822534"
],
[
"0.947550567",
"0.746274397"
],
[
"0.808788578",
"0.777750909"
],
[
"0.037047373",
"0.777992732"
],
[
"0.165700681",
"0.777992732"
],
[
"0.294353989",
"0.777992732"
],
[
"0.423007297",
"0.777992732"
],
[
"0.551660604",
"0.777992732"
],
[
"0.680313703",
"0.777992732"
],
[
"0.101374027",
"0.81476382"
],
[
"0.230027335",
"0.81476382"
],
[
"0.358680643",
"0.81476382"
],
[
"0.48733395",
"0.814763821"
],
[
"0.615987154",
"0.814764003"
],
[
"0.744620646",
"0.814798282"
],
[
"0.888742044",
"0.815616002"
],
[
"0.962952627",
"0.818750654"
],
[
"0.808788578",
"0.851845655"
],
[
"0.037047373",
"0.852087478"
],
[
"0.165700681",
"0.852087478"
],
[
"0.294353989",
"0.852087478"
],
[
"0.423007297",
"0.852087478"
],
[
"0.551660604",
"0.852087478"
],
[
"0.680313703",
"0.852087478"
],
[
"0.101374027",
"0.888858566"
],
[
"0.230027335",
"0.888858566"
],
[
"0.358680643",
"0.888858566"
],
[
"0.48733395",
"0.888858567"
],
[
"0.615987154",
"0.888858748"
],
[
"0.744620646",
"0.888893028"
],
[
"0.871785121",
"0.890851641"
],
[
"0.945879867",
"0.890851641"
],
[
"0.166019311",
"0.926181538"
],
[
"0.29467262",
"0.926181539"
],
[
"0.423326033",
"0.926181722"
],
[
"0.551999224",
"0.926216161"
],
[
"0.037099982",
"0.926355008"
],
[
"0.681624103",
"0.927899014"
],
[
"0.817880215",
"0.941687578"
],
[
"0.101692657",
"0.962952627"
],
[
"0.230345965",
"0.962952627"
],
[
"0.358999274",
"0.962952627"
],
[
"0.487652791",
"0.962952627"
],
[
"0.616345657",
"0.962952627"
],
[
"0.746902549",
"0.962952627"
],
[
"0.888857881",
"0.962952627"
],
[
"0.962952627",
"0.962952627"
]
],
"radius": "0.037047372"
}提交 radius 与 centers。每个数写成十进制字符串，例如 "0.25"。 · 验证器 v1.0.0
聊思路、贴方法、问为什么卡住。所有登录用户都可以发帖；发言公开署名，与纪录使用同一个名字，署名后的 #编号是账号注册序号，冒不了名。新发言经自动审核后公开。
按选手与子题分组，默认展示最新一篇。历史笔记及回复完整保留，点击笔记可查看和回复。笔记随纪录提交发布。