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 | [0.0384176809735, 0.0384176809745] | 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": [
[
"0.038417681",
"0.038417681"
],
[
"0.171500432",
"0.038417681"
],
[
"0.304583182",
"0.038417681"
],
[
"0.437665933",
"0.038417681"
],
[
"0.570748684",
"0.038417681"
],
[
"0.703831435",
"0.038417681"
],
[
"0.836914185",
"0.038417681"
],
[
"0.959659869",
"0.040340131"
],
[
"0.104959056",
"0.076835362"
],
[
"0.238041807",
"0.076835362"
],
[
"0.371124558",
"0.076835362"
],
[
"0.504207308",
"0.076835362"
],
[
"0.637290059",
"0.076835362"
],
[
"0.77037281",
"0.076835362"
],
[
"0.895040944",
"0.088666589"
],
[
"0.038417681",
"0.115253043"
],
[
"0.171500432",
"0.115253043"
],
[
"0.304583182",
"0.115253043"
],
[
"0.437665933",
"0.115253043"
],
[
"0.570748684",
"0.115253043"
],
[
"0.703831435",
"0.115253043"
],
[
"0.828499568",
"0.12708427"
],
[
"0.961582319",
"0.12708427"
],
[
"0.104959056",
"0.153670724"
],
[
"0.238041807",
"0.153670724"
],
[
"0.371124558",
"0.153670724"
],
[
"0.504207308",
"0.153670724"
],
[
"0.637290059",
"0.153670724"
],
[
"0.761958193",
"0.165501951"
],
[
"0.895040944",
"0.165501951"
],
[
"0.038417681",
"0.192088405"
],
[
"0.171500432",
"0.192088405"
],
[
"0.304583182",
"0.192088405"
],
[
"0.437665933",
"0.192088405"
],
[
"0.570748684",
"0.192088405"
],
[
"0.695416818",
"0.203919632"
],
[
"0.828499568",
"0.203919632"
],
[
"0.961582319",
"0.203919632"
],
[
"0.104959056",
"0.230506086"
],
[
"0.238041807",
"0.230506086"
],
[
"0.371124558",
"0.230506086"
],
[
"0.504207308",
"0.230506086"
],
[
"0.628875442",
"0.242337313"
],
[
"0.761958193",
"0.242337313"
],
[
"0.895040944",
"0.242337313"
],
[
"0.038417681",
"0.268923767"
],
[
"0.171500432",
"0.268923767"
],
[
"0.304583182",
"0.268923767"
],
[
"0.437665933",
"0.268923767"
],
[
"0.562334067",
"0.280754994"
],
[
"0.695416818",
"0.280754994"
],
[
"0.828499568",
"0.280754994"
],
[
"0.961582319",
"0.280754994"
],
[
"0.104959056",
"0.307341448"
],
[
"0.238041807",
"0.307341448"
],
[
"0.371124558",
"0.307341448"
],
[
"0.495792692",
"0.319172675"
],
[
"0.628875442",
"0.319172675"
],
[
"0.761958193",
"0.319172675"
],
[
"0.895040944",
"0.319172675"
],
[
"0.038417681",
"0.345759129"
],
[
"0.171500432",
"0.345759129"
],
[
"0.304583182",
"0.345759129"
],
[
"0.429251316",
"0.357590356"
],
[
"0.562334067",
"0.357590356"
],
[
"0.695416818",
"0.357590356"
],
[
"0.828499568",
"0.357590356"
],
[
"0.961582319",
"0.357590356"
],
[
"0.104959056",
"0.38417681"
],
[
"0.238041807",
"0.38417681"
],
[
"0.362709941",
"0.396008037"
],
[
"0.495792692",
"0.396008037"
],
[
"0.628875442",
"0.396008037"
],
[
"0.761958193",
"0.396008037"
],
[
"0.895040944",
"0.396008037"
],
[
"0.038417681",
"0.422594491"
],
[
"0.171500432",
"0.422594491"
],
[
"0.296168565",
"0.434425718"
],
[
"0.429251316",
"0.434425718"
],
[
"0.562334067",
"0.434425718"
],
[
"0.695416818",
"0.434425718"
],
[
"0.828499568",
"0.434425718"
],
[
"0.961582319",
"0.434425718"
],
[
"0.104959056",
"0.461012172"
],
[
"0.22962719",
"0.472843399"
],
[
"0.362709941",
"0.472843399"
],
[
"0.495792692",
"0.472843399"
],
[
"0.628875442",
"0.472843399"
],
[
"0.761958193",
"0.472843399"
],
[
"0.895040944",
"0.472843399"
],
[
"0.038417681",
"0.499429853"
],
[
"0.163085815",
"0.51126108"
],
[
"0.296168565",
"0.51126108"
],
[
"0.429251316",
"0.51126108"
],
[
"0.562334067",
"0.51126108"
],
[
"0.695416818",
"0.51126108"
],
[
"0.828499568",
"0.51126108"
],
[
"0.961582319",
"0.51126108"
],
[
"0.096544439",
"0.549678761"
],
[
"0.22962719",
"0.549678761"
],
[
"0.362709941",
"0.549678761"
],
[
"0.495792692",
"0.549678761"
],
[
"0.628875442",
"0.549678761"
],
[
"0.761958193",
"0.549678761"
],
[
"0.895040944",
"0.549678761"
],
[
"0.163085815",
"0.588096442"
],
[
"0.296168565",
"0.588096442"
],
[
"0.429251316",
"0.588096442"
],
[
"0.562334067",
"0.588096442"
],
[
"0.695416818",
"0.588096442"
],
[
"0.828499568",
"0.588096442"
],
[
"0.961582319",
"0.588096442"
],
[
"0.038417681",
"0.59992767"
],
[
"0.22962719",
"0.626514123"
],
[
"0.495792692",
"0.626514123"
],
[
"0.628875442",
"0.626514123"
],
[
"0.761958193",
"0.626514123"
],
[
"0.895040944",
"0.626514123"
],
[
"0.362679606",
"0.626566616"
],
[
"0.104959056",
"0.638345351"
],
[
"0.429251261",
"0.664931804"
],
[
"0.562334067",
"0.664931804"
],
[
"0.695416818",
"0.664931804"
],
[
"0.828499568",
"0.664931804"
],
[
"0.961582319",
"0.664931804"
],
[
"0.296138231",
"0.664984297"
],
[
"0.038417681",
"0.676763031"
],
[
"0.171500432",
"0.676763031"
],
[
"0.495792636",
"0.703349485"
],
[
"0.761958193",
"0.703349485"
],
[
"0.895040944",
"0.703349485"
],
[
"0.362679606",
"0.703401978"
],
[
"0.627774573",
"0.705196094"
],
[
"0.104959056",
"0.715180712"
],
[
"0.238190738",
"0.715439832"
],
[
"0.695348471",
"0.741767136"
],
[
"0.429251261",
"0.741767166"
],
[
"0.828499568",
"0.741767166"
],
[
"0.961582319",
"0.741767166"
],
[
"0.561233171",
"0.743613729"
],
[
"0.038417681",
"0.753598393"
],
[
"0.171500432",
"0.753598393"
],
[
"0.304732114",
"0.753857513"
],
[
"0.761889847",
"0.780184817"
],
[
"0.895036508",
"0.78019253"
],
[
"0.627774573",
"0.782031456"
],
[
"0.493662389",
"0.783816765"
],
[
"0.116049286",
"0.811224915"
],
[
"0.347932507",
"0.817398042"
],
[
"0.424760375",
"0.818471174"
],
[
"0.695348471",
"0.818602498"
],
[
"0.828431222",
"0.818602498"
],
[
"0.961582319",
"0.818602528"
],
[
"0.561233171",
"0.820449091"
],
[
"0.270666806",
"0.824106155"
],
[
"0.193217962",
"0.827300644"
],
[
"0.038417681",
"0.830433755"
],
[
"0.616987985",
"0.879764923"
],
[
"0.772195417",
"0.879764923"
],
[
"0.464292694",
"0.884356442"
],
[
"0.385417081",
"0.884469493"
],
[
"0.856589051",
"0.890092423"
],
[
"0.933424413",
"0.890092423"
],
[
"0.308921566",
"0.891688141"
],
[
"0.232109164",
"0.893566376"
],
[
"0.155275755",
"0.894114278"
],
[
"0.540465554",
"0.89442462"
],
[
"0.693697833",
"0.895420127"
],
[
"0.078463735",
"0.896008037"
],
[
"0.808755938",
"0.950222833"
],
[
"0.4249494",
"0.950354761"
],
[
"0.272141964",
"0.95914875"
],
[
"0.038417681",
"0.961582319"
],
[
"0.118509788",
"0.961582319"
],
[
"0.19534515",
"0.961582319"
],
[
"0.348938777",
"0.961582319"
],
[
"0.500960023",
"0.961582319"
],
[
"0.577795385",
"0.961582319"
],
[
"0.654630747",
"0.961582319"
],
[
"0.73276492",
"0.961582319"
],
[
"0.884746957",
"0.961582319"
],
[
"0.961582319",
"0.961582319"
]
],
"radius": "0.03841768"
}{
"n": 182
}{
"centers": [
[
"0.038417681",
"0.038417681"
],
[
"0.171500432",
"0.038417681"
],
[
"0.304583182",
"0.038417681"
],
[
"0.437665933",
"0.038417681"
],
[
"0.570748684",
"0.038417681"
],
[
"0.703831435",
"0.038417681"
],
[
"0.836914185",
"0.038417681"
],
[
"0.959659869",
"0.040340131"
],
[
"0.104959056",
"0.076835362"
],
[
"0.238041807",
"0.076835362"
],
[
"0.371124558",
"0.076835362"
],
[
"0.504207308",
"0.076835362"
],
[
"0.637290059",
"0.076835362"
],
[
"0.77037281",
"0.076835362"
],
[
"0.895040944",
"0.088666589"
],
[
"0.038417681",
"0.115253043"
],
[
"0.171500432",
"0.115253043"
],
[
"0.304583182",
"0.115253043"
],
[
"0.437665933",
"0.115253043"
],
[
"0.570748684",
"0.115253043"
],
[
"0.703831435",
"0.115253043"
],
[
"0.828499568",
"0.12708427"
],
[
"0.961582319",
"0.12708427"
],
[
"0.104959056",
"0.153670724"
],
[
"0.238041807",
"0.153670724"
],
[
"0.371124558",
"0.153670724"
],
[
"0.504207308",
"0.153670724"
],
[
"0.637290059",
"0.153670724"
],
[
"0.761958193",
"0.165501951"
],
[
"0.895040944",
"0.165501951"
],
[
"0.038417681",
"0.192088405"
],
[
"0.171500432",
"0.192088405"
],
[
"0.304583182",
"0.192088405"
],
[
"0.437665933",
"0.192088405"
],
[
"0.570748684",
"0.192088405"
],
[
"0.695416818",
"0.203919632"
],
[
"0.828499568",
"0.203919632"
],
[
"0.961582319",
"0.203919632"
],
[
"0.104959056",
"0.230506086"
],
[
"0.238041807",
"0.230506086"
],
[
"0.371124558",
"0.230506086"
],
[
"0.504207308",
"0.230506086"
],
[
"0.628875442",
"0.242337313"
],
[
"0.761958193",
"0.242337313"
],
[
"0.895040944",
"0.242337313"
],
[
"0.038417681",
"0.268923767"
],
[
"0.171500432",
"0.268923767"
],
[
"0.304583182",
"0.268923767"
],
[
"0.437665933",
"0.268923767"
],
[
"0.562334067",
"0.280754994"
],
[
"0.695416818",
"0.280754994"
],
[
"0.828499568",
"0.280754994"
],
[
"0.961582319",
"0.280754994"
],
[
"0.104959056",
"0.307341448"
],
[
"0.238041807",
"0.307341448"
],
[
"0.371124558",
"0.307341448"
],
[
"0.495792692",
"0.319172675"
],
[
"0.628875442",
"0.319172675"
],
[
"0.761958193",
"0.319172675"
],
[
"0.895040944",
"0.319172675"
],
[
"0.038417681",
"0.345759129"
],
[
"0.171500432",
"0.345759129"
],
[
"0.304583182",
"0.345759129"
],
[
"0.429251316",
"0.357590356"
],
[
"0.562334067",
"0.357590356"
],
[
"0.695416818",
"0.357590356"
],
[
"0.828499568",
"0.357590356"
],
[
"0.961582319",
"0.357590356"
],
[
"0.104959056",
"0.38417681"
],
[
"0.238041807",
"0.38417681"
],
[
"0.362709941",
"0.396008037"
],
[
"0.495792692",
"0.396008037"
],
[
"0.628875442",
"0.396008037"
],
[
"0.761958193",
"0.396008037"
],
[
"0.895040944",
"0.396008037"
],
[
"0.038417681",
"0.422594491"
],
[
"0.171500432",
"0.422594491"
],
[
"0.296168565",
"0.434425718"
],
[
"0.429251316",
"0.434425718"
],
[
"0.562334067",
"0.434425718"
],
[
"0.695416818",
"0.434425718"
],
[
"0.828499568",
"0.434425718"
],
[
"0.961582319",
"0.434425718"
],
[
"0.104959056",
"0.461012172"
],
[
"0.22962719",
"0.472843399"
],
[
"0.362709941",
"0.472843399"
],
[
"0.495792692",
"0.472843399"
],
[
"0.628875442",
"0.472843399"
],
[
"0.761958193",
"0.472843399"
],
[
"0.895040944",
"0.472843399"
],
[
"0.038417681",
"0.499429853"
],
[
"0.163085815",
"0.51126108"
],
[
"0.296168565",
"0.51126108"
],
[
"0.429251316",
"0.51126108"
],
[
"0.562334067",
"0.51126108"
],
[
"0.695416818",
"0.51126108"
],
[
"0.828499568",
"0.51126108"
],
[
"0.961582319",
"0.51126108"
],
[
"0.096544439",
"0.549678761"
],
[
"0.22962719",
"0.549678761"
],
[
"0.362709941",
"0.549678761"
],
[
"0.495792692",
"0.549678761"
],
[
"0.628875442",
"0.549678761"
],
[
"0.761958193",
"0.549678761"
],
[
"0.895040944",
"0.549678761"
],
[
"0.163085815",
"0.588096442"
],
[
"0.296168565",
"0.588096442"
],
[
"0.429251316",
"0.588096442"
],
[
"0.562334067",
"0.588096442"
],
[
"0.695416818",
"0.588096442"
],
[
"0.828499568",
"0.588096442"
],
[
"0.961582319",
"0.588096442"
],
[
"0.038417681",
"0.59992767"
],
[
"0.22962719",
"0.626514123"
],
[
"0.495792692",
"0.626514123"
],
[
"0.628875442",
"0.626514123"
],
[
"0.761958193",
"0.626514123"
],
[
"0.895040944",
"0.626514123"
],
[
"0.362679606",
"0.626566616"
],
[
"0.104959056",
"0.638345351"
],
[
"0.429251261",
"0.664931804"
],
[
"0.562334067",
"0.664931804"
],
[
"0.695416818",
"0.664931804"
],
[
"0.828499568",
"0.664931804"
],
[
"0.961582319",
"0.664931804"
],
[
"0.296138231",
"0.664984297"
],
[
"0.038417681",
"0.676763031"
],
[
"0.171500432",
"0.676763031"
],
[
"0.495792636",
"0.703349485"
],
[
"0.761958193",
"0.703349485"
],
[
"0.895040944",
"0.703349485"
],
[
"0.362679606",
"0.703401978"
],
[
"0.627774573",
"0.705196094"
],
[
"0.104959056",
"0.715180712"
],
[
"0.238190738",
"0.715439832"
],
[
"0.695348471",
"0.741767136"
],
[
"0.429251261",
"0.741767166"
],
[
"0.828499568",
"0.741767166"
],
[
"0.961582319",
"0.741767166"
],
[
"0.561233171",
"0.743613729"
],
[
"0.038417681",
"0.753598393"
],
[
"0.171500432",
"0.753598393"
],
[
"0.304732114",
"0.753857513"
],
[
"0.761889847",
"0.780184817"
],
[
"0.895036508",
"0.78019253"
],
[
"0.627774573",
"0.782031456"
],
[
"0.493662389",
"0.783816765"
],
[
"0.116049286",
"0.811224915"
],
[
"0.347932507",
"0.817398042"
],
[
"0.424760375",
"0.818471174"
],
[
"0.695348471",
"0.818602498"
],
[
"0.828431222",
"0.818602498"
],
[
"0.961582319",
"0.818602528"
],
[
"0.561233171",
"0.820449091"
],
[
"0.270666806",
"0.824106155"
],
[
"0.193217962",
"0.827300644"
],
[
"0.038417681",
"0.830433755"
],
[
"0.616987985",
"0.879764923"
],
[
"0.772195417",
"0.879764923"
],
[
"0.464292694",
"0.884356442"
],
[
"0.385417081",
"0.884469493"
],
[
"0.856589051",
"0.890092423"
],
[
"0.933424413",
"0.890092423"
],
[
"0.308921566",
"0.891688141"
],
[
"0.232109164",
"0.893566376"
],
[
"0.155275755",
"0.894114278"
],
[
"0.540465554",
"0.89442462"
],
[
"0.693697833",
"0.895420127"
],
[
"0.078463735",
"0.896008037"
],
[
"0.808755938",
"0.950222833"
],
[
"0.4249494",
"0.950354761"
],
[
"0.272141964",
"0.95914875"
],
[
"0.038417681",
"0.961582319"
],
[
"0.118509788",
"0.961582319"
],
[
"0.19534515",
"0.961582319"
],
[
"0.348938777",
"0.961582319"
],
[
"0.500960023",
"0.961582319"
],
[
"0.577795385",
"0.961582319"
],
[
"0.654630747",
"0.961582319"
],
[
"0.73276492",
"0.961582319"
],
[
"0.884746957",
"0.961582319"
],
[
"0.961582319",
"0.961582319"
]
],
"radius": "0.03841768"
}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。