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 | [0.0421454659005, 0.0421454659015] | 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": [
[
"0.042145466",
"0.042145466"
],
[
"0.190711606",
"0.042145466"
],
[
"0.331473075",
"0.042145466"
],
[
"0.477475148",
"0.042145466"
],
[
"0.623422545",
"0.042145466"
],
[
"0.769371304",
"0.042145466"
],
[
"0.915367481",
"0.042145466"
],
[
"0.116428536",
"0.081982467"
],
[
"0.404474111",
"0.084285825"
],
[
"0.842369393",
"0.084290932"
],
[
"0.696396925",
"0.08433197"
],
[
"0.550448847",
"0.084333148"
],
[
"0.26109234",
"0.088529875"
],
[
"0.957854534",
"0.11494527"
],
[
"0.042145466",
"0.126436398"
],
[
"0.47744781",
"0.126473506"
],
[
"0.769395013",
"0.126477436"
],
[
"0.623423226",
"0.126519652"
],
[
"0.18680927",
"0.128366877"
],
[
"0.334096743",
"0.130675341"
],
[
"0.884856446",
"0.157090736"
],
[
"0.550422189",
"0.16866001"
],
[
"0.696421314",
"0.168665118"
],
[
"0.113900025",
"0.17066585"
],
[
"0.261098655",
"0.172820807"
],
[
"0.407070442",
"0.172863023"
],
[
"0.957854534",
"0.199236202"
],
[
"0.81181071",
"0.199318838"
],
[
"0.623423226",
"0.210810583"
],
[
"0.186898113",
"0.212811316"
],
[
"0.042145466",
"0.214895302"
],
[
"0.334072353",
"0.215008489"
],
[
"0.480044821",
"0.215049527"
],
[
"0.884856446",
"0.241381668"
],
[
"0.738763694",
"0.241549163"
],
[
"0.115143554",
"0.257040768"
],
[
"0.2610499",
"0.257111725"
],
[
"0.407046733",
"0.257194993"
],
[
"0.553042714",
"0.25719533"
],
[
"0.957854534",
"0.283527134"
],
[
"0.81181071",
"0.283609769"
],
[
"0.665765606",
"0.283694629"
],
[
"0.042145466",
"0.299186234"
],
[
"0.188076193",
"0.299299392"
],
[
"0.334024959",
"0.299299407"
],
[
"0.480044626",
"0.299340796"
],
[
"0.884856446",
"0.3256726"
],
[
"0.738763694",
"0.325840095"
],
[
"0.588851019",
"0.333502123"
],
[
"0.115078105",
"0.341444858"
],
[
"0.261050572",
"0.341485898"
],
[
"0.407046343",
"0.341485924"
],
[
"0.957854534",
"0.367818065"
],
[
"0.81181071",
"0.367900701"
],
[
"0.665765606",
"0.367985561"
],
[
"0.515852931",
"0.375647589"
],
[
"0.188052484",
"0.383631364"
],
[
"0.33404845",
"0.383631728"
],
[
"0.042145466",
"0.383703483"
],
[
"0.884856446",
"0.409963531"
],
[
"0.738763694",
"0.410131027"
],
[
"0.442854769",
"0.417792928"
],
[
"0.588851019",
"0.417793054"
],
[
"0.261050361",
"0.425777194"
],
[
"0.115119845",
"0.425889988"
],
[
"0.957854534",
"0.452108997"
],
[
"0.81181071",
"0.452191633"
],
[
"0.665765606",
"0.452276493"
],
[
"0.369856754",
"0.45993852"
],
[
"0.515852931",
"0.45993852"
],
[
"0.188117722",
"0.468035818"
],
[
"0.042145466",
"0.468076494"
],
[
"0.884856446",
"0.494254463"
],
[
"0.738763694",
"0.494421958"
],
[
"0.296858666",
"0.502083986"
],
[
"0.442854842",
"0.502083986"
],
[
"0.588851019",
"0.502083986"
],
[
"0.115143344",
"0.510222324"
],
[
"0.957854534",
"0.536399929"
],
[
"0.81181071",
"0.536482565"
],
[
"0.665765606",
"0.536567424"
],
[
"0.369856754",
"0.544229452"
],
[
"0.515852931",
"0.544229452"
],
[
"0.223926027",
"0.544342611"
],
[
"0.042145466",
"0.552368154"
],
[
"0.884856446",
"0.578545395"
],
[
"0.738763694",
"0.57871289"
],
[
"0.442854842",
"0.586374918"
],
[
"0.588851019",
"0.586374918"
],
[
"0.296924115",
"0.586488077"
],
[
"0.150951648",
"0.586529116"
],
[
"0.957854534",
"0.620690861"
],
[
"0.81181071",
"0.620773497"
],
[
"0.665765606",
"0.620858356"
],
[
"0.515852931",
"0.628520384"
],
[
"0.369922203",
"0.628633542"
],
[
"0.223949736",
"0.628674582"
],
[
"0.07795377",
"0.628674947"
],
[
"0.884856446",
"0.662836327"
],
[
"0.738763694",
"0.663003822"
],
[
"0.588851019",
"0.67066585"
],
[
"0.442920291",
"0.670779008"
],
[
"0.296947825",
"0.670820048"
],
[
"0.150951859",
"0.670820412"
],
[
"0.042145466",
"0.704981739"
],
[
"0.957854534",
"0.704981793"
],
[
"0.81181071",
"0.705064428"
],
[
"0.665765606",
"0.705149288"
],
[
"0.51591838",
"0.712924474"
],
[
"0.369945913",
"0.712965514"
],
[
"0.223949947",
"0.712965878"
],
[
"0.115143554",
"0.747127205"
],
[
"0.884856446",
"0.747127259"
],
[
"0.738763694",
"0.747294754"
],
[
"0.588910596",
"0.755080109"
],
[
"0.442944001",
"0.75511098"
],
[
"0.296948035",
"0.755111344"
],
[
"0.042145466",
"0.78927267"
],
[
"0.188141642",
"0.78927267"
],
[
"0.957854534",
"0.789272724"
],
[
"0.81181071",
"0.78935536"
],
[
"0.665830314",
"0.7895521"
],
[
"0.369946123",
"0.79725681"
],
[
"0.515936218",
"0.797266614"
],
[
"0.115143554",
"0.831418136"
],
[
"0.261139731",
"0.831418136"
],
[
"0.884856446",
"0.83141819"
],
[
"0.738083861",
"0.832961617"
],
[
"0.588957992",
"0.839371027"
],
[
"0.44293834",
"0.839412445"
],
[
"0.042145466",
"0.873563602"
],
[
"0.188141642",
"0.873563602"
],
[
"0.334137819",
"0.873563602"
],
[
"0.957854534",
"0.873563656"
],
[
"0.811906099",
"0.873646238"
],
[
"0.665203318",
"0.875310025"
],
[
"0.515983614",
"0.881557533"
],
[
"0.115143554",
"0.915709068"
],
[
"0.261139731",
"0.915709068"
],
[
"0.407146136",
"0.91572679"
],
[
"0.882966874",
"0.918981957"
],
[
"0.728154249",
"0.931364832"
],
[
"0.564144175",
"0.950734997"
],
[
"0.042145466",
"0.957854534"
],
[
"0.188141642",
"0.957854534"
],
[
"0.334137819",
"0.957854534"
],
[
"0.480154453",
"0.957854534"
],
[
"0.648133897",
"0.957854534"
],
[
"0.808174602",
"0.957854534"
],
[
"0.957759146",
"0.957854534"
]
],
"radius": "0.042145465"
}{
"n": 150
}{
"centers": [
[
"0.042145466",
"0.042145466"
],
[
"0.190711606",
"0.042145466"
],
[
"0.331473075",
"0.042145466"
],
[
"0.477475148",
"0.042145466"
],
[
"0.623422545",
"0.042145466"
],
[
"0.769371304",
"0.042145466"
],
[
"0.915367481",
"0.042145466"
],
[
"0.116428536",
"0.081982467"
],
[
"0.404474111",
"0.084285825"
],
[
"0.842369393",
"0.084290932"
],
[
"0.696396925",
"0.08433197"
],
[
"0.550448847",
"0.084333148"
],
[
"0.26109234",
"0.088529875"
],
[
"0.957854534",
"0.11494527"
],
[
"0.042145466",
"0.126436398"
],
[
"0.47744781",
"0.126473506"
],
[
"0.769395013",
"0.126477436"
],
[
"0.623423226",
"0.126519652"
],
[
"0.18680927",
"0.128366877"
],
[
"0.334096743",
"0.130675341"
],
[
"0.884856446",
"0.157090736"
],
[
"0.550422189",
"0.16866001"
],
[
"0.696421314",
"0.168665118"
],
[
"0.113900025",
"0.17066585"
],
[
"0.261098655",
"0.172820807"
],
[
"0.407070442",
"0.172863023"
],
[
"0.957854534",
"0.199236202"
],
[
"0.81181071",
"0.199318838"
],
[
"0.623423226",
"0.210810583"
],
[
"0.186898113",
"0.212811316"
],
[
"0.042145466",
"0.214895302"
],
[
"0.334072353",
"0.215008489"
],
[
"0.480044821",
"0.215049527"
],
[
"0.884856446",
"0.241381668"
],
[
"0.738763694",
"0.241549163"
],
[
"0.115143554",
"0.257040768"
],
[
"0.2610499",
"0.257111725"
],
[
"0.407046733",
"0.257194993"
],
[
"0.553042714",
"0.25719533"
],
[
"0.957854534",
"0.283527134"
],
[
"0.81181071",
"0.283609769"
],
[
"0.665765606",
"0.283694629"
],
[
"0.042145466",
"0.299186234"
],
[
"0.188076193",
"0.299299392"
],
[
"0.334024959",
"0.299299407"
],
[
"0.480044626",
"0.299340796"
],
[
"0.884856446",
"0.3256726"
],
[
"0.738763694",
"0.325840095"
],
[
"0.588851019",
"0.333502123"
],
[
"0.115078105",
"0.341444858"
],
[
"0.261050572",
"0.341485898"
],
[
"0.407046343",
"0.341485924"
],
[
"0.957854534",
"0.367818065"
],
[
"0.81181071",
"0.367900701"
],
[
"0.665765606",
"0.367985561"
],
[
"0.515852931",
"0.375647589"
],
[
"0.188052484",
"0.383631364"
],
[
"0.33404845",
"0.383631728"
],
[
"0.042145466",
"0.383703483"
],
[
"0.884856446",
"0.409963531"
],
[
"0.738763694",
"0.410131027"
],
[
"0.442854769",
"0.417792928"
],
[
"0.588851019",
"0.417793054"
],
[
"0.261050361",
"0.425777194"
],
[
"0.115119845",
"0.425889988"
],
[
"0.957854534",
"0.452108997"
],
[
"0.81181071",
"0.452191633"
],
[
"0.665765606",
"0.452276493"
],
[
"0.369856754",
"0.45993852"
],
[
"0.515852931",
"0.45993852"
],
[
"0.188117722",
"0.468035818"
],
[
"0.042145466",
"0.468076494"
],
[
"0.884856446",
"0.494254463"
],
[
"0.738763694",
"0.494421958"
],
[
"0.296858666",
"0.502083986"
],
[
"0.442854842",
"0.502083986"
],
[
"0.588851019",
"0.502083986"
],
[
"0.115143344",
"0.510222324"
],
[
"0.957854534",
"0.536399929"
],
[
"0.81181071",
"0.536482565"
],
[
"0.665765606",
"0.536567424"
],
[
"0.369856754",
"0.544229452"
],
[
"0.515852931",
"0.544229452"
],
[
"0.223926027",
"0.544342611"
],
[
"0.042145466",
"0.552368154"
],
[
"0.884856446",
"0.578545395"
],
[
"0.738763694",
"0.57871289"
],
[
"0.442854842",
"0.586374918"
],
[
"0.588851019",
"0.586374918"
],
[
"0.296924115",
"0.586488077"
],
[
"0.150951648",
"0.586529116"
],
[
"0.957854534",
"0.620690861"
],
[
"0.81181071",
"0.620773497"
],
[
"0.665765606",
"0.620858356"
],
[
"0.515852931",
"0.628520384"
],
[
"0.369922203",
"0.628633542"
],
[
"0.223949736",
"0.628674582"
],
[
"0.07795377",
"0.628674947"
],
[
"0.884856446",
"0.662836327"
],
[
"0.738763694",
"0.663003822"
],
[
"0.588851019",
"0.67066585"
],
[
"0.442920291",
"0.670779008"
],
[
"0.296947825",
"0.670820048"
],
[
"0.150951859",
"0.670820412"
],
[
"0.042145466",
"0.704981739"
],
[
"0.957854534",
"0.704981793"
],
[
"0.81181071",
"0.705064428"
],
[
"0.665765606",
"0.705149288"
],
[
"0.51591838",
"0.712924474"
],
[
"0.369945913",
"0.712965514"
],
[
"0.223949947",
"0.712965878"
],
[
"0.115143554",
"0.747127205"
],
[
"0.884856446",
"0.747127259"
],
[
"0.738763694",
"0.747294754"
],
[
"0.588910596",
"0.755080109"
],
[
"0.442944001",
"0.75511098"
],
[
"0.296948035",
"0.755111344"
],
[
"0.042145466",
"0.78927267"
],
[
"0.188141642",
"0.78927267"
],
[
"0.957854534",
"0.789272724"
],
[
"0.81181071",
"0.78935536"
],
[
"0.665830314",
"0.7895521"
],
[
"0.369946123",
"0.79725681"
],
[
"0.515936218",
"0.797266614"
],
[
"0.115143554",
"0.831418136"
],
[
"0.261139731",
"0.831418136"
],
[
"0.884856446",
"0.83141819"
],
[
"0.738083861",
"0.832961617"
],
[
"0.588957992",
"0.839371027"
],
[
"0.44293834",
"0.839412445"
],
[
"0.042145466",
"0.873563602"
],
[
"0.188141642",
"0.873563602"
],
[
"0.334137819",
"0.873563602"
],
[
"0.957854534",
"0.873563656"
],
[
"0.811906099",
"0.873646238"
],
[
"0.665203318",
"0.875310025"
],
[
"0.515983614",
"0.881557533"
],
[
"0.115143554",
"0.915709068"
],
[
"0.261139731",
"0.915709068"
],
[
"0.407146136",
"0.91572679"
],
[
"0.882966874",
"0.918981957"
],
[
"0.728154249",
"0.931364832"
],
[
"0.564144175",
"0.950734997"
],
[
"0.042145466",
"0.957854534"
],
[
"0.188141642",
"0.957854534"
],
[
"0.334137819",
"0.957854534"
],
[
"0.480154453",
"0.957854534"
],
[
"0.648133897",
"0.957854534"
],
[
"0.808174602",
"0.957854534"
],
[
"0.957759146",
"0.957854534"
]
],
"radius": "0.042145465"
}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。