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 | [0.0390610991675, 0.0390610991685] | 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": [
[
"0.039061099",
"0.039061099"
],
[
"0.174372716",
"0.039061099"
],
[
"0.309684333",
"0.039061099"
],
[
"0.89302191",
"0.039061099"
],
[
"0.601191278",
"0.039061099"
],
[
"0.444995949",
"0.039061099"
],
[
"0.752159052",
"0.039061099"
],
[
"0.523093614",
"0.041018821"
],
[
"0.676675165",
"0.059192187"
],
[
"0.822590481",
"0.072861864"
],
[
"0.960934995",
"0.078102231"
],
[
"0.242028524",
"0.078122198"
],
[
"0.106716908",
"0.078122198"
],
[
"0.377340141",
"0.078122198"
],
[
"0.482349345",
"0.107674521"
],
[
"0.621499188",
"0.114497607"
],
[
"0.758102445",
"0.116956888"
],
[
"0.893283092",
"0.117182861"
],
[
"0.039061099",
"0.117183298"
],
[
"0.174372716",
"0.117183298"
],
[
"0.309684333",
"0.117183298"
],
[
"0.550009059",
"0.146731715"
],
[
"0.414693536",
"0.146735621"
],
[
"0.6891186",
"0.153621679"
],
[
"0.825627284",
"0.15624396"
],
[
"0.960938901",
"0.15624396"
],
[
"0.242028524",
"0.156244397"
],
[
"0.106716908",
"0.156244397"
],
[
"0.482349345",
"0.18579672"
],
[
"0.347037728",
"0.18579672"
],
[
"0.62116513",
"0.192619091"
],
[
"0.757841262",
"0.19507865"
],
[
"0.893283092",
"0.195305059"
],
[
"0.174372716",
"0.195305496"
],
[
"0.039061099",
"0.195305496"
],
[
"0.550005153",
"0.224857819"
],
[
"0.27938192",
"0.224857819"
],
[
"0.414693536",
"0.224857819"
],
[
"0.688857417",
"0.231743441"
],
[
"0.825627284",
"0.234366158"
],
[
"0.960938901",
"0.234366158"
],
[
"0.106716908",
"0.234366595"
],
[
"0.482349345",
"0.263918918"
],
[
"0.347037728",
"0.263918918"
],
[
"0.211726111",
"0.263918918"
],
[
"0.62116513",
"0.270741289"
],
[
"0.757841262",
"0.273200848"
],
[
"0.893283092",
"0.273427258"
],
[
"0.039061099",
"0.273427694"
],
[
"0.550005153",
"0.302980017"
],
[
"0.144070303",
"0.302980017"
],
[
"0.414693536",
"0.302980017"
],
[
"0.27938192",
"0.302980017"
],
[
"0.688857417",
"0.309865639"
],
[
"0.960938901",
"0.312488357"
],
[
"0.825627284",
"0.312488357"
],
[
"0.347037728",
"0.342041116"
],
[
"0.211726111",
"0.342041116"
],
[
"0.076414495",
"0.342041116"
],
[
"0.482349345",
"0.342041116"
],
[
"0.62116513",
"0.348863488"
],
[
"0.757841262",
"0.351323047"
],
[
"0.893283092",
"0.351549456"
],
[
"0.27938192",
"0.381102216"
],
[
"0.550005153",
"0.381102216"
],
[
"0.144070303",
"0.381102216"
],
[
"0.414693536",
"0.381102216"
],
[
"0.688857417",
"0.387987838"
],
[
"0.960938901",
"0.390610555"
],
[
"0.825627284",
"0.390610555"
],
[
"0.039061099",
"0.410654539"
],
[
"0.347037728",
"0.420163315"
],
[
"0.211726111",
"0.420163315"
],
[
"0.482349345",
"0.420163315"
],
[
"0.62116513",
"0.426985686"
],
[
"0.757841262",
"0.429445245"
],
[
"0.893283092",
"0.429671654"
],
[
"0.106716908",
"0.449715638"
],
[
"0.27938192",
"0.459224414"
],
[
"0.414693536",
"0.459224414"
],
[
"0.550005153",
"0.459224414"
],
[
"0.688857417",
"0.466110036"
],
[
"0.825623378",
"0.468732753"
],
[
"0.960938901",
"0.468732753"
],
[
"0.039061099",
"0.488776737"
],
[
"0.174372716",
"0.488776737"
],
[
"0.482349345",
"0.498285513"
],
[
"0.347037728",
"0.498285513"
],
[
"0.62116513",
"0.505107884"
],
[
"0.757813707",
"0.507567438"
],
[
"0.893283092",
"0.507793853"
],
[
"0.242028524",
"0.527837836"
],
[
"0.106716908",
"0.527837836"
],
[
"0.414693536",
"0.537346612"
],
[
"0.550005153",
"0.537346612"
],
[
"0.688829861",
"0.544232229"
],
[
"0.825627284",
"0.546854952"
],
[
"0.960938901",
"0.546854952"
],
[
"0.174372716",
"0.566898935"
],
[
"0.309684333",
"0.566898935"
],
[
"0.039061099",
"0.566898935"
],
[
"0.482349345",
"0.576407712"
],
[
"0.621137575",
"0.583230078"
],
[
"0.757841257",
"0.585689632"
],
[
"0.893283092",
"0.585916051"
],
[
"0.242028524",
"0.605960035"
],
[
"0.377340141",
"0.605960035"
],
[
"0.106716908",
"0.605960035"
],
[
"0.549989715",
"0.615495538"
],
[
"0.688857411",
"0.622354423"
],
[
"0.960938901",
"0.62497715"
],
[
"0.825627284",
"0.62497715"
],
[
"0.444995949",
"0.645021134"
],
[
"0.039061099",
"0.645021134"
],
[
"0.309684333",
"0.645021134"
],
[
"0.174372716",
"0.645021134"
],
[
"0.621165124",
"0.661352271"
],
[
"0.757841257",
"0.66381183"
],
[
"0.893283092",
"0.664038249"
],
[
"0.377340141",
"0.684082233"
],
[
"0.242028524",
"0.684082233"
],
[
"0.106716908",
"0.684082233"
],
[
"0.512681285",
"0.684133421"
],
[
"0.688857411",
"0.700476621"
],
[
"0.960938901",
"0.703099348"
],
[
"0.825627284",
"0.703099348"
],
[
"0.174372716",
"0.723143332"
],
[
"0.309684333",
"0.723143332"
],
[
"0.444995949",
"0.723143332"
],
[
"0.039061099",
"0.723143332"
],
[
"0.578237914",
"0.726623494"
],
[
"0.757841257",
"0.741934029"
],
[
"0.893283092",
"0.742160448"
],
[
"0.106716908",
"0.762204431"
],
[
"0.242028524",
"0.762204431"
],
[
"0.377340141",
"0.762204431"
],
[
"0.510552578",
"0.765633405"
],
[
"0.645930159",
"0.765747817"
],
[
"0.960938901",
"0.781221547"
],
[
"0.824123822",
"0.78382562"
],
[
"0.309684333",
"0.80126553"
],
[
"0.039061099",
"0.80126553"
],
[
"0.174372716",
"0.80126553"
],
[
"0.44289677",
"0.804694504"
],
[
"0.578237888",
"0.804745692"
],
[
"0.714823086",
"0.807145338"
],
[
"0.893283092",
"0.820282646"
],
[
"0.242028524",
"0.84032663"
],
[
"0.106716908",
"0.84032663"
],
[
"0.375240961",
"0.843755603"
],
[
"0.510552565",
"0.843755626"
],
[
"0.645871091",
"0.843869993"
],
[
"0.785037939",
"0.852908289"
],
[
"0.960938901",
"0.859343745"
],
[
"0.039061099",
"0.879387729"
],
[
"0.174372725",
"0.879387744"
],
[
"0.307585153",
"0.882816702"
],
[
"0.442896757",
"0.882816725"
],
[
"0.57817882",
"0.882867868"
],
[
"0.712151573",
"0.885221845"
],
[
"0.85605296",
"0.88896303"
],
[
"0.106716908",
"0.918448828"
],
[
"0.239929358",
"0.921877824"
],
[
"0.375270502",
"0.921928967"
],
[
"0.511980805",
"0.924351607"
],
[
"0.960938901",
"0.937465943"
],
[
"0.656196439",
"0.939738823"
],
[
"0.808906796",
"0.951255221"
],
[
"0.03945171",
"0.96054829"
],
[
"0.581005784",
"0.960938901"
],
[
"0.307585179",
"0.960938901"
],
[
"0.172273536",
"0.960938901"
],
[
"0.442955825",
"0.960938901"
],
[
"0.886426498",
"0.960938901"
],
[
"0.731387094",
"0.960938901"
]
],
"radius": "0.039061098"
}{
"n": 175
}{
"centers": [
[
"0.039061099",
"0.039061099"
],
[
"0.174372716",
"0.039061099"
],
[
"0.309684333",
"0.039061099"
],
[
"0.89302191",
"0.039061099"
],
[
"0.601191278",
"0.039061099"
],
[
"0.444995949",
"0.039061099"
],
[
"0.752159052",
"0.039061099"
],
[
"0.523093614",
"0.041018821"
],
[
"0.676675165",
"0.059192187"
],
[
"0.822590481",
"0.072861864"
],
[
"0.960934995",
"0.078102231"
],
[
"0.242028524",
"0.078122198"
],
[
"0.106716908",
"0.078122198"
],
[
"0.377340141",
"0.078122198"
],
[
"0.482349345",
"0.107674521"
],
[
"0.621499188",
"0.114497607"
],
[
"0.758102445",
"0.116956888"
],
[
"0.893283092",
"0.117182861"
],
[
"0.039061099",
"0.117183298"
],
[
"0.174372716",
"0.117183298"
],
[
"0.309684333",
"0.117183298"
],
[
"0.550009059",
"0.146731715"
],
[
"0.414693536",
"0.146735621"
],
[
"0.6891186",
"0.153621679"
],
[
"0.825627284",
"0.15624396"
],
[
"0.960938901",
"0.15624396"
],
[
"0.242028524",
"0.156244397"
],
[
"0.106716908",
"0.156244397"
],
[
"0.482349345",
"0.18579672"
],
[
"0.347037728",
"0.18579672"
],
[
"0.62116513",
"0.192619091"
],
[
"0.757841262",
"0.19507865"
],
[
"0.893283092",
"0.195305059"
],
[
"0.174372716",
"0.195305496"
],
[
"0.039061099",
"0.195305496"
],
[
"0.550005153",
"0.224857819"
],
[
"0.27938192",
"0.224857819"
],
[
"0.414693536",
"0.224857819"
],
[
"0.688857417",
"0.231743441"
],
[
"0.825627284",
"0.234366158"
],
[
"0.960938901",
"0.234366158"
],
[
"0.106716908",
"0.234366595"
],
[
"0.482349345",
"0.263918918"
],
[
"0.347037728",
"0.263918918"
],
[
"0.211726111",
"0.263918918"
],
[
"0.62116513",
"0.270741289"
],
[
"0.757841262",
"0.273200848"
],
[
"0.893283092",
"0.273427258"
],
[
"0.039061099",
"0.273427694"
],
[
"0.550005153",
"0.302980017"
],
[
"0.144070303",
"0.302980017"
],
[
"0.414693536",
"0.302980017"
],
[
"0.27938192",
"0.302980017"
],
[
"0.688857417",
"0.309865639"
],
[
"0.960938901",
"0.312488357"
],
[
"0.825627284",
"0.312488357"
],
[
"0.347037728",
"0.342041116"
],
[
"0.211726111",
"0.342041116"
],
[
"0.076414495",
"0.342041116"
],
[
"0.482349345",
"0.342041116"
],
[
"0.62116513",
"0.348863488"
],
[
"0.757841262",
"0.351323047"
],
[
"0.893283092",
"0.351549456"
],
[
"0.27938192",
"0.381102216"
],
[
"0.550005153",
"0.381102216"
],
[
"0.144070303",
"0.381102216"
],
[
"0.414693536",
"0.381102216"
],
[
"0.688857417",
"0.387987838"
],
[
"0.960938901",
"0.390610555"
],
[
"0.825627284",
"0.390610555"
],
[
"0.039061099",
"0.410654539"
],
[
"0.347037728",
"0.420163315"
],
[
"0.211726111",
"0.420163315"
],
[
"0.482349345",
"0.420163315"
],
[
"0.62116513",
"0.426985686"
],
[
"0.757841262",
"0.429445245"
],
[
"0.893283092",
"0.429671654"
],
[
"0.106716908",
"0.449715638"
],
[
"0.27938192",
"0.459224414"
],
[
"0.414693536",
"0.459224414"
],
[
"0.550005153",
"0.459224414"
],
[
"0.688857417",
"0.466110036"
],
[
"0.825623378",
"0.468732753"
],
[
"0.960938901",
"0.468732753"
],
[
"0.039061099",
"0.488776737"
],
[
"0.174372716",
"0.488776737"
],
[
"0.482349345",
"0.498285513"
],
[
"0.347037728",
"0.498285513"
],
[
"0.62116513",
"0.505107884"
],
[
"0.757813707",
"0.507567438"
],
[
"0.893283092",
"0.507793853"
],
[
"0.242028524",
"0.527837836"
],
[
"0.106716908",
"0.527837836"
],
[
"0.414693536",
"0.537346612"
],
[
"0.550005153",
"0.537346612"
],
[
"0.688829861",
"0.544232229"
],
[
"0.825627284",
"0.546854952"
],
[
"0.960938901",
"0.546854952"
],
[
"0.174372716",
"0.566898935"
],
[
"0.309684333",
"0.566898935"
],
[
"0.039061099",
"0.566898935"
],
[
"0.482349345",
"0.576407712"
],
[
"0.621137575",
"0.583230078"
],
[
"0.757841257",
"0.585689632"
],
[
"0.893283092",
"0.585916051"
],
[
"0.242028524",
"0.605960035"
],
[
"0.377340141",
"0.605960035"
],
[
"0.106716908",
"0.605960035"
],
[
"0.549989715",
"0.615495538"
],
[
"0.688857411",
"0.622354423"
],
[
"0.960938901",
"0.62497715"
],
[
"0.825627284",
"0.62497715"
],
[
"0.444995949",
"0.645021134"
],
[
"0.039061099",
"0.645021134"
],
[
"0.309684333",
"0.645021134"
],
[
"0.174372716",
"0.645021134"
],
[
"0.621165124",
"0.661352271"
],
[
"0.757841257",
"0.66381183"
],
[
"0.893283092",
"0.664038249"
],
[
"0.377340141",
"0.684082233"
],
[
"0.242028524",
"0.684082233"
],
[
"0.106716908",
"0.684082233"
],
[
"0.512681285",
"0.684133421"
],
[
"0.688857411",
"0.700476621"
],
[
"0.960938901",
"0.703099348"
],
[
"0.825627284",
"0.703099348"
],
[
"0.174372716",
"0.723143332"
],
[
"0.309684333",
"0.723143332"
],
[
"0.444995949",
"0.723143332"
],
[
"0.039061099",
"0.723143332"
],
[
"0.578237914",
"0.726623494"
],
[
"0.757841257",
"0.741934029"
],
[
"0.893283092",
"0.742160448"
],
[
"0.106716908",
"0.762204431"
],
[
"0.242028524",
"0.762204431"
],
[
"0.377340141",
"0.762204431"
],
[
"0.510552578",
"0.765633405"
],
[
"0.645930159",
"0.765747817"
],
[
"0.960938901",
"0.781221547"
],
[
"0.824123822",
"0.78382562"
],
[
"0.309684333",
"0.80126553"
],
[
"0.039061099",
"0.80126553"
],
[
"0.174372716",
"0.80126553"
],
[
"0.44289677",
"0.804694504"
],
[
"0.578237888",
"0.804745692"
],
[
"0.714823086",
"0.807145338"
],
[
"0.893283092",
"0.820282646"
],
[
"0.242028524",
"0.84032663"
],
[
"0.106716908",
"0.84032663"
],
[
"0.375240961",
"0.843755603"
],
[
"0.510552565",
"0.843755626"
],
[
"0.645871091",
"0.843869993"
],
[
"0.785037939",
"0.852908289"
],
[
"0.960938901",
"0.859343745"
],
[
"0.039061099",
"0.879387729"
],
[
"0.174372725",
"0.879387744"
],
[
"0.307585153",
"0.882816702"
],
[
"0.442896757",
"0.882816725"
],
[
"0.57817882",
"0.882867868"
],
[
"0.712151573",
"0.885221845"
],
[
"0.85605296",
"0.88896303"
],
[
"0.106716908",
"0.918448828"
],
[
"0.239929358",
"0.921877824"
],
[
"0.375270502",
"0.921928967"
],
[
"0.511980805",
"0.924351607"
],
[
"0.960938901",
"0.937465943"
],
[
"0.656196439",
"0.939738823"
],
[
"0.808906796",
"0.951255221"
],
[
"0.03945171",
"0.96054829"
],
[
"0.581005784",
"0.960938901"
],
[
"0.307585179",
"0.960938901"
],
[
"0.172273536",
"0.960938901"
],
[
"0.442955825",
"0.960938901"
],
[
"0.886426498",
"0.960938901"
],
[
"0.731387094",
"0.960938901"
]
],
"radius": "0.039061098"
}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。