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 | [0.0365695976365, 0.0365695976375] | 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": [
[
"0.036569598",
"0.036569598"
],
[
"0.1632504",
"0.036569598"
],
[
"0.289931202",
"0.036569598"
],
[
"0.416612004",
"0.036569598"
],
[
"0.543292807",
"0.036569598"
],
[
"0.669973609",
"0.036569598"
],
[
"0.796654411",
"0.036569598"
],
[
"0.923335213",
"0.036569598"
],
[
"0.099909999",
"0.073139195"
],
[
"0.226590801",
"0.073139195"
],
[
"0.353271603",
"0.073139195"
],
[
"0.479952405",
"0.073139195"
],
[
"0.606633208",
"0.073139195"
],
[
"0.73331401",
"0.073139195"
],
[
"0.859994812",
"0.073139195"
],
[
"0.963430402",
"0.097739179"
],
[
"0.036569598",
"0.109708793"
],
[
"0.1632504",
"0.109708793"
],
[
"0.289931202",
"0.109708793"
],
[
"0.416612004",
"0.109708793"
],
[
"0.543292807",
"0.109708793"
],
[
"0.669973609",
"0.109708793"
],
[
"0.796654411",
"0.109708793"
],
[
"0.900090001",
"0.134308777"
],
[
"0.099909999",
"0.146278391"
],
[
"0.226590801",
"0.146278391"
],
[
"0.353271603",
"0.146278391"
],
[
"0.479952405",
"0.146278391"
],
[
"0.606633208",
"0.146278391"
],
[
"0.73331401",
"0.146278391"
],
[
"0.8367496",
"0.170878374"
],
[
"0.963430402",
"0.170878374"
],
[
"0.036569598",
"0.182847988"
],
[
"0.1632504",
"0.182847988"
],
[
"0.289931202",
"0.182847988"
],
[
"0.416612004",
"0.182847988"
],
[
"0.543292807",
"0.182847988"
],
[
"0.669973609",
"0.182847988"
],
[
"0.773409199",
"0.207447972"
],
[
"0.900090001",
"0.207447972"
],
[
"0.099909999",
"0.219417586"
],
[
"0.226590801",
"0.219417586"
],
[
"0.353271603",
"0.219417586"
],
[
"0.479952405",
"0.219417586"
],
[
"0.606633208",
"0.219417586"
],
[
"0.710068798",
"0.24401757"
],
[
"0.8367496",
"0.24401757"
],
[
"0.963430402",
"0.24401757"
],
[
"0.036569598",
"0.255987183"
],
[
"0.1632504",
"0.255987183"
],
[
"0.289931202",
"0.255987183"
],
[
"0.416612004",
"0.255987183"
],
[
"0.543292807",
"0.255987183"
],
[
"0.646728397",
"0.280587167"
],
[
"0.773409199",
"0.280587167"
],
[
"0.900090001",
"0.280587167"
],
[
"0.099909999",
"0.292556781"
],
[
"0.226590801",
"0.292556781"
],
[
"0.353271603",
"0.292556781"
],
[
"0.480216324",
"0.293013901"
],
[
"0.583387996",
"0.317156765"
],
[
"0.710068798",
"0.317156765"
],
[
"0.8367496",
"0.317156765"
],
[
"0.963430402",
"0.317156765"
],
[
"0.036569598",
"0.329126379"
],
[
"0.1632504",
"0.329126379"
],
[
"0.289931202",
"0.329126379"
],
[
"0.416612004",
"0.329126379"
],
[
"0.646728397",
"0.353726363"
],
[
"0.773409199",
"0.353726363"
],
[
"0.900090001",
"0.353726363"
],
[
"0.52044904",
"0.354413036"
],
[
"0.099909999",
"0.365695976"
],
[
"0.226590801",
"0.365695976"
],
[
"0.353271603",
"0.365695976"
],
[
"0.456714444",
"0.390291207"
],
[
"0.710068798",
"0.39029596"
],
[
"0.8367496",
"0.39029596"
],
[
"0.963430402",
"0.39029596"
],
[
"0.583789441",
"0.390982634"
],
[
"0.036569598",
"0.402265574"
],
[
"0.1632504",
"0.402265574"
],
[
"0.289931202",
"0.402265574"
],
[
"0.393374043",
"0.426860805"
],
[
"0.773409199",
"0.426865558"
],
[
"0.900090001",
"0.426865558"
],
[
"0.52044904",
"0.427552231"
],
[
"0.647129842",
"0.427552231"
],
[
"0.099909999",
"0.438835172"
],
[
"0.226590801",
"0.438835172"
],
[
"0.330033642",
"0.463430402"
],
[
"0.456714444",
"0.463430402"
],
[
"0.8367496",
"0.463435156"
],
[
"0.963430402",
"0.463435156"
],
[
"0.583789441",
"0.464121829"
],
[
"0.710470243",
"0.464121829"
],
[
"0.036569598",
"0.475404769"
],
[
"0.1632504",
"0.475404769"
],
[
"0.266693241",
"0.5"
],
[
"0.393374043",
"0.5"
],
[
"0.900090001",
"0.500004753"
],
[
"0.52044904",
"0.500691427"
],
[
"0.647129842",
"0.500691427"
],
[
"0.773810644",
"0.500691427"
],
[
"0.099909999",
"0.511974367"
],
[
"0.203352839",
"0.536569598"
],
[
"0.330033642",
"0.536569598"
],
[
"0.456714444",
"0.536569598"
],
[
"0.963430402",
"0.536574351"
],
[
"0.583789441",
"0.537261024"
],
[
"0.710470243",
"0.537261024"
],
[
"0.837151046",
"0.537261024"
],
[
"0.036569598",
"0.548543965"
],
[
"0.140012438",
"0.573139195"
],
[
"0.266693241",
"0.573139195"
],
[
"0.393374043",
"0.573139195"
],
[
"0.52044904",
"0.573830622"
],
[
"0.647129842",
"0.573830622"
],
[
"0.773810644",
"0.573830622"
],
[
"0.900491447",
"0.573830622"
],
[
"0.076672037",
"0.609708793"
],
[
"0.203352839",
"0.609708793"
],
[
"0.330033642",
"0.609708793"
],
[
"0.456714444",
"0.609708793"
],
[
"0.583789441",
"0.61040022"
],
[
"0.710470243",
"0.61040022"
],
[
"0.837151046",
"0.61040022"
],
[
"0.963430402",
"0.611086893"
],
[
"0.140012438",
"0.646278391"
],
[
"0.266693241",
"0.646278391"
],
[
"0.393374043",
"0.646278391"
],
[
"0.52044904",
"0.646969817"
],
[
"0.647129842",
"0.646969817"
],
[
"0.773810644",
"0.646969817"
],
[
"0.900090001",
"0.647656491"
],
[
"0.036569598",
"0.670873621"
],
[
"0.203352839",
"0.682847988"
],
[
"0.330033642",
"0.682847988"
],
[
"0.456714444",
"0.682847988"
],
[
"0.583789441",
"0.683539415"
],
[
"0.710470243",
"0.683539415"
],
[
"0.8367496",
"0.684226088"
],
[
"0.963430402",
"0.684226088"
],
[
"0.099909999",
"0.707443219"
],
[
"0.266693241",
"0.719417586"
],
[
"0.393374043",
"0.719417586"
],
[
"0.52044904",
"0.720109012"
],
[
"0.647129842",
"0.720109012"
],
[
"0.773409199",
"0.720795686"
],
[
"0.900090001",
"0.720795686"
],
[
"0.036569598",
"0.744012817"
],
[
"0.1632504",
"0.744012817"
],
[
"0.330033642",
"0.755987183"
],
[
"0.456714444",
"0.755987183"
],
[
"0.584053359",
"0.75713573"
],
[
"0.710068798",
"0.757365284"
],
[
"0.8367496",
"0.757365284"
],
[
"0.963430402",
"0.757365284"
],
[
"0.099909999",
"0.780582414"
],
[
"0.226590801",
"0.780582414"
],
[
"0.393374043",
"0.792556781"
],
[
"0.52044904",
"0.793248208"
],
[
"0.773409199",
"0.793934881"
],
[
"0.900090001",
"0.793934881"
],
[
"0.647773213",
"0.795687627"
],
[
"0.036569598",
"0.817152012"
],
[
"0.1632504",
"0.817152012"
],
[
"0.289931202",
"0.817152012"
],
[
"0.456714444",
"0.829126379"
],
[
"0.583421793",
"0.830447324"
],
[
"0.8367496",
"0.830504479"
],
[
"0.963430402",
"0.830504479"
],
[
"0.711113614",
"0.832257225"
],
[
"0.099909999",
"0.853721609"
],
[
"0.226590801",
"0.853721609"
],
[
"0.353271603",
"0.853721609"
],
[
"0.519720036",
"0.86638377"
],
[
"0.888639742",
"0.888639742"
],
[
"0.036569598",
"0.890291207"
],
[
"0.1632504",
"0.890291207"
],
[
"0.289931202",
"0.890291207"
],
[
"0.416612004",
"0.890291207"
],
[
"0.661909699",
"0.892296702"
],
[
"0.811597803",
"0.899182925"
],
[
"0.738464233",
"0.900090001"
],
[
"0.586819866",
"0.903507539"
],
[
"0.963430402",
"0.903643674"
],
[
"0.099909999",
"0.926860805"
],
[
"0.226590801",
"0.926860805"
],
[
"0.353271603",
"0.926860805"
],
[
"0.480748148",
"0.928275076"
],
[
"0.848167401",
"0.962523326"
],
[
"0.036569598",
"0.963430402"
],
[
"0.1632504",
"0.963430402"
],
[
"0.289931202",
"0.963430402"
],
[
"0.416612004",
"0.963430402"
],
[
"0.544884292",
"0.963430402"
],
[
"0.62875544",
"0.963430402"
],
[
"0.701894635",
"0.963430402"
],
[
"0.77503383",
"0.963430402"
],
[
"0.921300971",
"0.963430402"
]
],
"radius": "0.036569597"
}{
"n": 201
}{
"centers": [
[
"0.036569598",
"0.036569598"
],
[
"0.1632504",
"0.036569598"
],
[
"0.289931202",
"0.036569598"
],
[
"0.416612004",
"0.036569598"
],
[
"0.543292807",
"0.036569598"
],
[
"0.669973609",
"0.036569598"
],
[
"0.796654411",
"0.036569598"
],
[
"0.923335213",
"0.036569598"
],
[
"0.099909999",
"0.073139195"
],
[
"0.226590801",
"0.073139195"
],
[
"0.353271603",
"0.073139195"
],
[
"0.479952405",
"0.073139195"
],
[
"0.606633208",
"0.073139195"
],
[
"0.73331401",
"0.073139195"
],
[
"0.859994812",
"0.073139195"
],
[
"0.963430402",
"0.097739179"
],
[
"0.036569598",
"0.109708793"
],
[
"0.1632504",
"0.109708793"
],
[
"0.289931202",
"0.109708793"
],
[
"0.416612004",
"0.109708793"
],
[
"0.543292807",
"0.109708793"
],
[
"0.669973609",
"0.109708793"
],
[
"0.796654411",
"0.109708793"
],
[
"0.900090001",
"0.134308777"
],
[
"0.099909999",
"0.146278391"
],
[
"0.226590801",
"0.146278391"
],
[
"0.353271603",
"0.146278391"
],
[
"0.479952405",
"0.146278391"
],
[
"0.606633208",
"0.146278391"
],
[
"0.73331401",
"0.146278391"
],
[
"0.8367496",
"0.170878374"
],
[
"0.963430402",
"0.170878374"
],
[
"0.036569598",
"0.182847988"
],
[
"0.1632504",
"0.182847988"
],
[
"0.289931202",
"0.182847988"
],
[
"0.416612004",
"0.182847988"
],
[
"0.543292807",
"0.182847988"
],
[
"0.669973609",
"0.182847988"
],
[
"0.773409199",
"0.207447972"
],
[
"0.900090001",
"0.207447972"
],
[
"0.099909999",
"0.219417586"
],
[
"0.226590801",
"0.219417586"
],
[
"0.353271603",
"0.219417586"
],
[
"0.479952405",
"0.219417586"
],
[
"0.606633208",
"0.219417586"
],
[
"0.710068798",
"0.24401757"
],
[
"0.8367496",
"0.24401757"
],
[
"0.963430402",
"0.24401757"
],
[
"0.036569598",
"0.255987183"
],
[
"0.1632504",
"0.255987183"
],
[
"0.289931202",
"0.255987183"
],
[
"0.416612004",
"0.255987183"
],
[
"0.543292807",
"0.255987183"
],
[
"0.646728397",
"0.280587167"
],
[
"0.773409199",
"0.280587167"
],
[
"0.900090001",
"0.280587167"
],
[
"0.099909999",
"0.292556781"
],
[
"0.226590801",
"0.292556781"
],
[
"0.353271603",
"0.292556781"
],
[
"0.480216324",
"0.293013901"
],
[
"0.583387996",
"0.317156765"
],
[
"0.710068798",
"0.317156765"
],
[
"0.8367496",
"0.317156765"
],
[
"0.963430402",
"0.317156765"
],
[
"0.036569598",
"0.329126379"
],
[
"0.1632504",
"0.329126379"
],
[
"0.289931202",
"0.329126379"
],
[
"0.416612004",
"0.329126379"
],
[
"0.646728397",
"0.353726363"
],
[
"0.773409199",
"0.353726363"
],
[
"0.900090001",
"0.353726363"
],
[
"0.52044904",
"0.354413036"
],
[
"0.099909999",
"0.365695976"
],
[
"0.226590801",
"0.365695976"
],
[
"0.353271603",
"0.365695976"
],
[
"0.456714444",
"0.390291207"
],
[
"0.710068798",
"0.39029596"
],
[
"0.8367496",
"0.39029596"
],
[
"0.963430402",
"0.39029596"
],
[
"0.583789441",
"0.390982634"
],
[
"0.036569598",
"0.402265574"
],
[
"0.1632504",
"0.402265574"
],
[
"0.289931202",
"0.402265574"
],
[
"0.393374043",
"0.426860805"
],
[
"0.773409199",
"0.426865558"
],
[
"0.900090001",
"0.426865558"
],
[
"0.52044904",
"0.427552231"
],
[
"0.647129842",
"0.427552231"
],
[
"0.099909999",
"0.438835172"
],
[
"0.226590801",
"0.438835172"
],
[
"0.330033642",
"0.463430402"
],
[
"0.456714444",
"0.463430402"
],
[
"0.8367496",
"0.463435156"
],
[
"0.963430402",
"0.463435156"
],
[
"0.583789441",
"0.464121829"
],
[
"0.710470243",
"0.464121829"
],
[
"0.036569598",
"0.475404769"
],
[
"0.1632504",
"0.475404769"
],
[
"0.266693241",
"0.5"
],
[
"0.393374043",
"0.5"
],
[
"0.900090001",
"0.500004753"
],
[
"0.52044904",
"0.500691427"
],
[
"0.647129842",
"0.500691427"
],
[
"0.773810644",
"0.500691427"
],
[
"0.099909999",
"0.511974367"
],
[
"0.203352839",
"0.536569598"
],
[
"0.330033642",
"0.536569598"
],
[
"0.456714444",
"0.536569598"
],
[
"0.963430402",
"0.536574351"
],
[
"0.583789441",
"0.537261024"
],
[
"0.710470243",
"0.537261024"
],
[
"0.837151046",
"0.537261024"
],
[
"0.036569598",
"0.548543965"
],
[
"0.140012438",
"0.573139195"
],
[
"0.266693241",
"0.573139195"
],
[
"0.393374043",
"0.573139195"
],
[
"0.52044904",
"0.573830622"
],
[
"0.647129842",
"0.573830622"
],
[
"0.773810644",
"0.573830622"
],
[
"0.900491447",
"0.573830622"
],
[
"0.076672037",
"0.609708793"
],
[
"0.203352839",
"0.609708793"
],
[
"0.330033642",
"0.609708793"
],
[
"0.456714444",
"0.609708793"
],
[
"0.583789441",
"0.61040022"
],
[
"0.710470243",
"0.61040022"
],
[
"0.837151046",
"0.61040022"
],
[
"0.963430402",
"0.611086893"
],
[
"0.140012438",
"0.646278391"
],
[
"0.266693241",
"0.646278391"
],
[
"0.393374043",
"0.646278391"
],
[
"0.52044904",
"0.646969817"
],
[
"0.647129842",
"0.646969817"
],
[
"0.773810644",
"0.646969817"
],
[
"0.900090001",
"0.647656491"
],
[
"0.036569598",
"0.670873621"
],
[
"0.203352839",
"0.682847988"
],
[
"0.330033642",
"0.682847988"
],
[
"0.456714444",
"0.682847988"
],
[
"0.583789441",
"0.683539415"
],
[
"0.710470243",
"0.683539415"
],
[
"0.8367496",
"0.684226088"
],
[
"0.963430402",
"0.684226088"
],
[
"0.099909999",
"0.707443219"
],
[
"0.266693241",
"0.719417586"
],
[
"0.393374043",
"0.719417586"
],
[
"0.52044904",
"0.720109012"
],
[
"0.647129842",
"0.720109012"
],
[
"0.773409199",
"0.720795686"
],
[
"0.900090001",
"0.720795686"
],
[
"0.036569598",
"0.744012817"
],
[
"0.1632504",
"0.744012817"
],
[
"0.330033642",
"0.755987183"
],
[
"0.456714444",
"0.755987183"
],
[
"0.584053359",
"0.75713573"
],
[
"0.710068798",
"0.757365284"
],
[
"0.8367496",
"0.757365284"
],
[
"0.963430402",
"0.757365284"
],
[
"0.099909999",
"0.780582414"
],
[
"0.226590801",
"0.780582414"
],
[
"0.393374043",
"0.792556781"
],
[
"0.52044904",
"0.793248208"
],
[
"0.773409199",
"0.793934881"
],
[
"0.900090001",
"0.793934881"
],
[
"0.647773213",
"0.795687627"
],
[
"0.036569598",
"0.817152012"
],
[
"0.1632504",
"0.817152012"
],
[
"0.289931202",
"0.817152012"
],
[
"0.456714444",
"0.829126379"
],
[
"0.583421793",
"0.830447324"
],
[
"0.8367496",
"0.830504479"
],
[
"0.963430402",
"0.830504479"
],
[
"0.711113614",
"0.832257225"
],
[
"0.099909999",
"0.853721609"
],
[
"0.226590801",
"0.853721609"
],
[
"0.353271603",
"0.853721609"
],
[
"0.519720036",
"0.86638377"
],
[
"0.888639742",
"0.888639742"
],
[
"0.036569598",
"0.890291207"
],
[
"0.1632504",
"0.890291207"
],
[
"0.289931202",
"0.890291207"
],
[
"0.416612004",
"0.890291207"
],
[
"0.661909699",
"0.892296702"
],
[
"0.811597803",
"0.899182925"
],
[
"0.738464233",
"0.900090001"
],
[
"0.586819866",
"0.903507539"
],
[
"0.963430402",
"0.903643674"
],
[
"0.099909999",
"0.926860805"
],
[
"0.226590801",
"0.926860805"
],
[
"0.353271603",
"0.926860805"
],
[
"0.480748148",
"0.928275076"
],
[
"0.848167401",
"0.962523326"
],
[
"0.036569598",
"0.963430402"
],
[
"0.1632504",
"0.963430402"
],
[
"0.289931202",
"0.963430402"
],
[
"0.416612004",
"0.963430402"
],
[
"0.544884292",
"0.963430402"
],
[
"0.62875544",
"0.963430402"
],
[
"0.701894635",
"0.963430402"
],
[
"0.77503383",
"0.963430402"
],
[
"0.921300971",
"0.963430402"
]
],
"radius": "0.036569597"
}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。