P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 300

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。

子题n = 300
目标最大化 共同半径

纪录对比

共同半径 · 越大越好
纪录数值 / 区间作者 / 持有人来源
外部已知最好[0.0302195557035, 0.0302195557045]见来源署名packomania.com ↗
本站纪录暂无选手纪录——

严格定义

  • 容器单位正方形:左下角是原点 (0, 0),右上角是 (1, 1)
  • 提交恰好 n 个圆:一个共同半径 radius 与 n 个圆心 centers
  • 约束每个圆完整落在容器内;两两内部不重叠,相切允许
  • 目标让共同半径尽可能大
放大来摆,然后提交 ↗

当前展示:起步布局

1y0
0x1
已验证构造r = 0.030219555

帮助理解

哪里有优化空间

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。

前沿在哪里

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
单位正方形内的等圆装箱 n = 300 的当前构型
构型与历史

起步布局

查看构型、求解笔记与纪录历史。

挑战这个纪录 ↗提交证明 / 思路 ↓在讨论区分享证明或思路,审核采纳后可获得证明分。
ANSWER FORMAT

答案怎么写

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"。

起步布局答案

{
  "centers": [
    [
      "0.030219556",
      "0.030219556"
    ],
    [
      "0.132428233",
      "0.030219556"
    ],
    [
      "0.237111845",
      "0.030219556"
    ],
    [
      "0.341795457",
      "0.030219556"
    ],
    [
      "0.446479068",
      "0.030219556"
    ],
    [
      "0.55116268",
      "0.030219556"
    ],
    [
      "0.655846292",
      "0.030219556"
    ],
    [
      "0.760413221",
      "0.030219556"
    ],
    [
      "0.865096833",
      "0.030219556"
    ],
    [
      "0.969780444",
      "0.030219556"
    ],
    [
      "0.184770039",
      "0.060439111"
    ],
    [
      "0.289453651",
      "0.060439111"
    ],
    [
      "0.394137263",
      "0.060439111"
    ],
    [
      "0.498820874",
      "0.060439111"
    ],
    [
      "0.603504486",
      "0.060439111"
    ],
    [
      "0.812755027",
      "0.060439111"
    ],
    [
      "0.917438638",
      "0.060439111"
    ],
    [
      "0.708129756",
      "0.060539937"
    ],
    [
      "0.081323895",
      "0.062487694"
    ],
    [
      "0.237111845",
      "0.090658667"
    ],
    [
      "0.341795457",
      "0.090658667"
    ],
    [
      "0.446479068",
      "0.090658667"
    ],
    [
      "0.55116268",
      "0.090658667"
    ],
    [
      "0.865096833",
      "0.090658667"
    ],
    [
      "0.969780444",
      "0.090658667"
    ],
    [
      "0.655787951",
      "0.090759493"
    ],
    [
      "0.760471562",
      "0.090759493"
    ],
    [
      "0.1336657",
      "0.09270725"
    ],
    [
      "0.030219556",
      "0.094755832"
    ],
    [
      "0.289453651",
      "0.120878223"
    ],
    [
      "0.394137263",
      "0.120878223"
    ],
    [
      "0.498820874",
      "0.120878223"
    ],
    [
      "0.917438638",
      "0.120878223"
    ],
    [
      "0.603446145",
      "0.120979049"
    ],
    [
      "0.708129756",
      "0.120979049"
    ],
    [
      "0.812813368",
      "0.120979049"
    ],
    [
      "0.186007506",
      "0.122926805"
    ],
    [
      "0.082561362",
      "0.124975388"
    ],
    [
      "0.341795457",
      "0.151097779"
    ],
    [
      "0.446479068",
      "0.151097779"
    ],
    [
      "0.969780444",
      "0.151097779"
    ],
    [
      "0.551104339",
      "0.151198604"
    ],
    [
      "0.655787951",
      "0.151198604"
    ],
    [
      "0.760471562",
      "0.151198604"
    ],
    [
      "0.865155174",
      "0.151198604"
    ],
    [
      "0.238349312",
      "0.153146361"
    ],
    [
      "0.030219556",
      "0.155194944"
    ],
    [
      "0.134903167",
      "0.155194944"
    ],
    [
      "0.394137263",
      "0.181317334"
    ],
    [
      "0.498762533",
      "0.18141816"
    ],
    [
      "0.603446145",
      "0.18141816"
    ],
    [
      "0.708129756",
      "0.18141816"
    ],
    [
      "0.812813368",
      "0.18141816"
    ],
    [
      "0.91749698",
      "0.18141816"
    ],
    [
      "0.290691118",
      "0.183365917"
    ],
    [
      "0.082561362",
      "0.185414499"
    ],
    [
      "0.187244973",
      "0.185414499"
    ],
    [
      "0.446420727",
      "0.211637716"
    ],
    [
      "0.551104339",
      "0.211637716"
    ],
    [
      "0.655787951",
      "0.211637716"
    ],
    [
      "0.760471562",
      "0.211637716"
    ],
    [
      "0.865155174",
      "0.211637716"
    ],
    [
      "0.969780444",
      "0.211738541"
    ],
    [
      "0.343032924",
      "0.213585472"
    ],
    [
      "0.030219556",
      "0.215634055"
    ],
    [
      "0.134903167",
      "0.215634055"
    ],
    [
      "0.239586779",
      "0.215634055"
    ],
    [
      "0.498762533",
      "0.241857271"
    ],
    [
      "0.603446145",
      "0.241857271"
    ],
    [
      "0.708129756",
      "0.241857271"
    ],
    [
      "0.812813368",
      "0.241857271"
    ],
    [
      "0.917438638",
      "0.241958097"
    ],
    [
      "0.395316388",
      "0.243905854"
    ],
    [
      "0.082561362",
      "0.245853611"
    ],
    [
      "0.187244973",
      "0.245853611"
    ],
    [
      "0.291928585",
      "0.245853611"
    ],
    [
      "0.551104339",
      "0.272076827"
    ],
    [
      "0.655787951",
      "0.272076827"
    ],
    [
      "0.760471562",
      "0.272076827"
    ],
    [
      "0.865096833",
      "0.272177653"
    ],
    [
      "0.969780444",
      "0.272177653"
    ],
    [
      "0.447658194",
      "0.27412541"
    ],
    [
      "0.030219556",
      "0.276073166"
    ],
    [
      "0.134903167",
      "0.276073166"
    ],
    [
      "0.239586779",
      "0.276073166"
    ],
    [
      "0.344212049",
      "0.276173992"
    ],
    [
      "0.603446145",
      "0.302296383"
    ],
    [
      "0.708129756",
      "0.302296383"
    ],
    [
      "0.812755027",
      "0.302397209"
    ],
    [
      "0.917438638",
      "0.302397209"
    ],
    [
      "0.5",
      "0.304344965"
    ],
    [
      "0.082561362",
      "0.306292722"
    ],
    [
      "0.187244973",
      "0.306292722"
    ],
    [
      "0.291870244",
      "0.306393548"
    ],
    [
      "0.396553855",
      "0.306393548"
    ],
    [
      "0.655787951",
      "0.332515939"
    ],
    [
      "0.760413221",
      "0.332616764"
    ],
    [
      "0.865096833",
      "0.332616764"
    ],
    [
      "0.969780444",
      "0.332616764"
    ],
    [
      "0.552341806",
      "0.334564521"
    ],
    [
      "0.030219556",
      "0.336512278"
    ],
    [
      "0.134903167",
      "0.336512278"
    ],
    [
      "0.239528438",
      "0.336613104"
    ],
    [
      "0.344212049",
      "0.336613104"
    ],
    [
      "0.448895661",
      "0.336613104"
    ],
    [
      "0.708071415",
      "0.36283632"
    ],
    [
      "0.812755027",
      "0.36283632"
    ],
    [
      "0.917438638",
      "0.36283632"
    ],
    [
      "0.604683612",
      "0.364784077"
    ],
    [
      "0.082561362",
      "0.366731833"
    ],
    [
      "0.187186632",
      "0.366832659"
    ],
    [
      "0.291870244",
      "0.366832659"
    ],
    [
      "0.396553855",
      "0.366832659"
    ],
    [
      "0.501237467",
      "0.366832659"
    ],
    [
      "0.760413221",
      "0.393055876"
    ],
    [
      "0.865096833",
      "0.393055876"
    ],
    [
      "0.969780444",
      "0.393055876"
    ],
    [
      "0.656967076",
      "0.395104458"
    ],
    [
      "0.030219556",
      "0.396951389"
    ],
    [
      "0.134844826",
      "0.397052215"
    ],
    [
      "0.239528438",
      "0.397052215"
    ],
    [
      "0.344212049",
      "0.397052215"
    ],
    [
      "0.448895661",
      "0.397052215"
    ],
    [
      "0.553579273",
      "0.397052215"
    ],
    [
      "0.812755027",
      "0.423275431"
    ],
    [
      "0.917438638",
      "0.423275431"
    ],
    [
      "0.709308882",
      "0.425324014"
    ],
    [
      "0.08250302",
      "0.427271771"
    ],
    [
      "0.187186632",
      "0.427271771"
    ],
    [
      "0.291870244",
      "0.427271771"
    ],
    [
      "0.396553855",
      "0.427271771"
    ],
    [
      "0.501237467",
      "0.427271771"
    ],
    [
      "0.605862737",
      "0.427372596"
    ],
    [
      "0.865096833",
      "0.453494987"
    ],
    [
      "0.969780444",
      "0.453494987"
    ],
    [
      "0.761650688",
      "0.45554357"
    ],
    [
      "0.134844826",
      "0.457491326"
    ],
    [
      "0.239528438",
      "0.457491326"
    ],
    [
      "0.344212049",
      "0.457491326"
    ],
    [
      "0.448895661",
      "0.457491326"
    ],
    [
      "0.030219556",
      "0.457592152"
    ],
    [
      "0.553520932",
      "0.457592152"
    ],
    [
      "0.658204543",
      "0.457592152"
    ],
    [
      "0.917438638",
      "0.483714543"
    ],
    [
      "0.813992494",
      "0.485763125"
    ],
    [
      "0.187186632",
      "0.487710882"
    ],
    [
      "0.291870244",
      "0.487710882"
    ],
    [
      "0.396553855",
      "0.487710882"
    ],
    [
      "0.082561362",
      "0.487811708"
    ],
    [
      "0.501179126",
      "0.487811708"
    ],
    [
      "0.605862737",
      "0.487811708"
    ],
    [
      "0.710546349",
      "0.487811708"
    ],
    [
      "0.969780444",
      "0.513934098"
    ],
    [
      "0.8663343",
      "0.515982681"
    ],
    [
      "0.239528438",
      "0.517930438"
    ],
    [
      "0.344212049",
      "0.517930438"
    ],
    [
      "0.030219556",
      "0.518031264"
    ],
    [
      "0.134903167",
      "0.518031264"
    ],
    [
      "0.44883732",
      "0.518031264"
    ],
    [
      "0.553520932",
      "0.518031264"
    ],
    [
      "0.658204543",
      "0.518031264"
    ],
    [
      "0.762888155",
      "0.518031264"
    ],
    [
      "0.918676105",
      "0.546202237"
    ],
    [
      "0.291870244",
      "0.548149993"
    ],
    [
      "0.082561362",
      "0.548250819"
    ],
    [
      "0.187244973",
      "0.548250819"
    ],
    [
      "0.396495514",
      "0.548250819"
    ],
    [
      "0.501179126",
      "0.548250819"
    ],
    [
      "0.605862737",
      "0.548250819"
    ],
    [
      "0.710546349",
      "0.548250819"
    ],
    [
      "0.815229961",
      "0.548250819"
    ],
    [
      "0.030219556",
      "0.578470375"
    ],
    [
      "0.134903167",
      "0.578470375"
    ],
    [
      "0.239586779",
      "0.578470375"
    ],
    [
      "0.344153708",
      "0.578470375"
    ],
    [
      "0.44883732",
      "0.578470375"
    ],
    [
      "0.553520932",
      "0.578470375"
    ],
    [
      "0.658204543",
      "0.578470375"
    ],
    [
      "0.762888155",
      "0.578470375"
    ],
    [
      "0.867571767",
      "0.578470375"
    ],
    [
      "0.969780444",
      "0.578470375"
    ],
    [
      "0.082561362",
      "0.608689931"
    ],
    [
      "0.187244973",
      "0.608689931"
    ],
    [
      "0.396495514",
      "0.608689931"
    ],
    [
      "0.501179126",
      "0.608689931"
    ],
    [
      "0.605862737",
      "0.608689931"
    ],
    [
      "0.710546349",
      "0.608689931"
    ],
    [
      "0.815229961",
      "0.608689931"
    ],
    [
      "0.291870244",
      "0.608790756"
    ],
    [
      "0.918676105",
      "0.610738513"
    ],
    [
      "0.030219556",
      "0.638909486"
    ],
    [
      "0.134903167",
      "0.638909486"
    ],
    [
      "0.44883732",
      "0.638909486"
    ],
    [
      "0.553520932",
      "0.638909486"
    ],
    [
      "0.658204543",
      "0.638909486"
    ],
    [
      "0.762888155",
      "0.638909486"
    ],
    [
      "0.239528438",
      "0.639010312"
    ],
    [
      "0.344212049",
      "0.639010312"
    ],
    [
      "0.8663343",
      "0.640958069"
    ],
    [
      "0.969780444",
      "0.643006651"
    ],
    [
      "0.082561362",
      "0.669129042"
    ],
    [
      "0.501179126",
      "0.669129042"
    ],
    [
      "0.605862737",
      "0.669129042"
    ],
    [
      "0.710546349",
      "0.669129042"
    ],
    [
      "0.187186632",
      "0.669229868"
    ],
    [
      "0.291870244",
      "0.669229868"
    ],
    [
      "0.396553855",
      "0.669229868"
    ],
    [
      "0.813992494",
      "0.671177625"
    ],
    [
      "0.917438638",
      "0.673226207"
    ],
    [
      "0.030219556",
      "0.699348598"
    ],
    [
      "0.553520932",
      "0.699348598"
    ],
    [
      "0.658204543",
      "0.699348598"
    ],
    [
      "0.134844826",
      "0.699449423"
    ],
    [
      "0.239528438",
      "0.699449423"
    ],
    [
      "0.344212049",
      "0.699449423"
    ],
    [
      "0.448895661",
      "0.699449423"
    ],
    [
      "0.761650688",
      "0.70139718"
    ],
    [
      "0.865096833",
      "0.703445763"
    ],
    [
      "0.969780444",
      "0.703445763"
    ],
    [
      "0.605862737",
      "0.729568153"
    ],
    [
      "0.08250302",
      "0.729668979"
    ],
    [
      "0.187186632",
      "0.729668979"
    ],
    [
      "0.291870244",
      "0.729668979"
    ],
    [
      "0.396553855",
      "0.729668979"
    ],
    [
      "0.501237467",
      "0.729668979"
    ],
    [
      "0.709308882",
      "0.731616736"
    ],
    [
      "0.812755027",
      "0.733665318"
    ],
    [
      "0.917438638",
      "0.733665318"
    ],
    [
      "0.134844826",
      "0.759888535"
    ],
    [
      "0.239528438",
      "0.759888535"
    ],
    [
      "0.344212049",
      "0.759888535"
    ],
    [
      "0.448895661",
      "0.759888535"
    ],
    [
      "0.553579273",
      "0.759888535"
    ],
    [
      "0.030219556",
      "0.759989361"
    ],
    [
      "0.656967076",
      "0.761836292"
    ],
    [
      "0.760413221",
      "0.763884874"
    ],
    [
      "0.865096833",
      "0.763884874"
    ],
    [
      "0.969780444",
      "0.763884874"
    ],
    [
      "0.187186632",
      "0.790108091"
    ],
    [
      "0.291870244",
      "0.790108091"
    ],
    [
      "0.396553855",
      "0.790108091"
    ],
    [
      "0.501237467",
      "0.790108091"
    ],
    [
      "0.082561362",
      "0.790208916"
    ],
    [
      "0.604683612",
      "0.792156673"
    ],
    [
      "0.708071415",
      "0.79410443"
    ],
    [
      "0.812755027",
      "0.79410443"
    ],
    [
      "0.917438638",
      "0.79410443"
    ],
    [
      "0.239528438",
      "0.820327646"
    ],
    [
      "0.344212049",
      "0.820327646"
    ],
    [
      "0.448895661",
      "0.820327646"
    ],
    [
      "0.030219556",
      "0.820428472"
    ],
    [
      "0.134903167",
      "0.820428472"
    ],
    [
      "0.552341806",
      "0.822376229"
    ],
    [
      "0.760413221",
      "0.824323986"
    ],
    [
      "0.865096833",
      "0.824323986"
    ],
    [
      "0.969780444",
      "0.824323986"
    ],
    [
      "0.655787951",
      "0.824424811"
    ],
    [
      "0.291870244",
      "0.850547202"
    ],
    [
      "0.082561362",
      "0.850648028"
    ],
    [
      "0.187244973",
      "0.850648028"
    ],
    [
      "0.396760917",
      "0.850907966"
    ],
    [
      "0.5",
      "0.852595785"
    ],
    [
      "0.812755027",
      "0.854543541"
    ],
    [
      "0.917438638",
      "0.854543541"
    ],
    [
      "0.603446145",
      "0.854644367"
    ],
    [
      "0.708129756",
      "0.854644367"
    ],
    [
      "0.344212049",
      "0.880766758"
    ],
    [
      "0.030219556",
      "0.880867583"
    ],
    [
      "0.134903167",
      "0.880867583"
    ],
    [
      "0.238324012",
      "0.882956201"
    ],
    [
      "0.969780444",
      "0.884763097"
    ],
    [
      "0.863747166",
      "0.887131072"
    ],
    [
      "0.453187081",
      "0.890824527"
    ],
    [
      "0.748036306",
      "0.900035483"
    ],
    [
      "0.568907085",
      "0.904242144"
    ],
    [
      "0.291870244",
      "0.910986313"
    ],
    [
      "0.082561362",
      "0.911087139"
    ],
    [
      "0.396340831",
      "0.911352315"
    ],
    [
      "0.628685037",
      "0.913157446"
    ],
    [
      "0.185982206",
      "0.913175756"
    ],
    [
      "0.689122999",
      "0.913530236"
    ],
    [
      "0.509189553",
      "0.913553568"
    ],
    [
      "0.806675361",
      "0.914676094"
    ],
    [
      "0.917438638",
      "0.914982653"
    ],
    [
      "0.030598114",
      "0.945202237"
    ],
    [
      "0.966598915",
      "0.950334433"
    ],
    [
      "0.344690989",
      "0.95732594"
    ],
    [
      "0.591075183",
      "0.96046902"
    ],
    [
      "0.471579699",
      "0.960865143"
    ],
    [
      "0.771367263",
      "0.963729375"
    ],
    [
      "0.217643716",
      "0.964658131"
    ],
    [
      "0.096982947",
      "0.969780444"
    ],
    [
      "0.157422058",
      "0.969780444"
    ],
    [
      "0.277865374",
      "0.969780444"
    ],
    [
      "0.411801747",
      "0.969780444"
    ],
    [
      "0.531357651",
      "0.969780444"
    ],
    [
      "0.650792715",
      "0.969780444"
    ],
    [
      "0.711231826",
      "0.969780444"
    ],
    [
      "0.831502699",
      "0.969780444"
    ],
    [
      "0.891941811",
      "0.969780444"
    ]
  ],
  "radius": "0.030219555"
}
提交格式与技术细节需要编写程序或准备 JSON 答案时再查看+

子题参数

{
  "n": 300
}

起步布局答案

{
  "centers": [
    [
      "0.030219556",
      "0.030219556"
    ],
    [
      "0.132428233",
      "0.030219556"
    ],
    [
      "0.237111845",
      "0.030219556"
    ],
    [
      "0.341795457",
      "0.030219556"
    ],
    [
      "0.446479068",
      "0.030219556"
    ],
    [
      "0.55116268",
      "0.030219556"
    ],
    [
      "0.655846292",
      "0.030219556"
    ],
    [
      "0.760413221",
      "0.030219556"
    ],
    [
      "0.865096833",
      "0.030219556"
    ],
    [
      "0.969780444",
      "0.030219556"
    ],
    [
      "0.184770039",
      "0.060439111"
    ],
    [
      "0.289453651",
      "0.060439111"
    ],
    [
      "0.394137263",
      "0.060439111"
    ],
    [
      "0.498820874",
      "0.060439111"
    ],
    [
      "0.603504486",
      "0.060439111"
    ],
    [
      "0.812755027",
      "0.060439111"
    ],
    [
      "0.917438638",
      "0.060439111"
    ],
    [
      "0.708129756",
      "0.060539937"
    ],
    [
      "0.081323895",
      "0.062487694"
    ],
    [
      "0.237111845",
      "0.090658667"
    ],
    [
      "0.341795457",
      "0.090658667"
    ],
    [
      "0.446479068",
      "0.090658667"
    ],
    [
      "0.55116268",
      "0.090658667"
    ],
    [
      "0.865096833",
      "0.090658667"
    ],
    [
      "0.969780444",
      "0.090658667"
    ],
    [
      "0.655787951",
      "0.090759493"
    ],
    [
      "0.760471562",
      "0.090759493"
    ],
    [
      "0.1336657",
      "0.09270725"
    ],
    [
      "0.030219556",
      "0.094755832"
    ],
    [
      "0.289453651",
      "0.120878223"
    ],
    [
      "0.394137263",
      "0.120878223"
    ],
    [
      "0.498820874",
      "0.120878223"
    ],
    [
      "0.917438638",
      "0.120878223"
    ],
    [
      "0.603446145",
      "0.120979049"
    ],
    [
      "0.708129756",
      "0.120979049"
    ],
    [
      "0.812813368",
      "0.120979049"
    ],
    [
      "0.186007506",
      "0.122926805"
    ],
    [
      "0.082561362",
      "0.124975388"
    ],
    [
      "0.341795457",
      "0.151097779"
    ],
    [
      "0.446479068",
      "0.151097779"
    ],
    [
      "0.969780444",
      "0.151097779"
    ],
    [
      "0.551104339",
      "0.151198604"
    ],
    [
      "0.655787951",
      "0.151198604"
    ],
    [
      "0.760471562",
      "0.151198604"
    ],
    [
      "0.865155174",
      "0.151198604"
    ],
    [
      "0.238349312",
      "0.153146361"
    ],
    [
      "0.030219556",
      "0.155194944"
    ],
    [
      "0.134903167",
      "0.155194944"
    ],
    [
      "0.394137263",
      "0.181317334"
    ],
    [
      "0.498762533",
      "0.18141816"
    ],
    [
      "0.603446145",
      "0.18141816"
    ],
    [
      "0.708129756",
      "0.18141816"
    ],
    [
      "0.812813368",
      "0.18141816"
    ],
    [
      "0.91749698",
      "0.18141816"
    ],
    [
      "0.290691118",
      "0.183365917"
    ],
    [
      "0.082561362",
      "0.185414499"
    ],
    [
      "0.187244973",
      "0.185414499"
    ],
    [
      "0.446420727",
      "0.211637716"
    ],
    [
      "0.551104339",
      "0.211637716"
    ],
    [
      "0.655787951",
      "0.211637716"
    ],
    [
      "0.760471562",
      "0.211637716"
    ],
    [
      "0.865155174",
      "0.211637716"
    ],
    [
      "0.969780444",
      "0.211738541"
    ],
    [
      "0.343032924",
      "0.213585472"
    ],
    [
      "0.030219556",
      "0.215634055"
    ],
    [
      "0.134903167",
      "0.215634055"
    ],
    [
      "0.239586779",
      "0.215634055"
    ],
    [
      "0.498762533",
      "0.241857271"
    ],
    [
      "0.603446145",
      "0.241857271"
    ],
    [
      "0.708129756",
      "0.241857271"
    ],
    [
      "0.812813368",
      "0.241857271"
    ],
    [
      "0.917438638",
      "0.241958097"
    ],
    [
      "0.395316388",
      "0.243905854"
    ],
    [
      "0.082561362",
      "0.245853611"
    ],
    [
      "0.187244973",
      "0.245853611"
    ],
    [
      "0.291928585",
      "0.245853611"
    ],
    [
      "0.551104339",
      "0.272076827"
    ],
    [
      "0.655787951",
      "0.272076827"
    ],
    [
      "0.760471562",
      "0.272076827"
    ],
    [
      "0.865096833",
      "0.272177653"
    ],
    [
      "0.969780444",
      "0.272177653"
    ],
    [
      "0.447658194",
      "0.27412541"
    ],
    [
      "0.030219556",
      "0.276073166"
    ],
    [
      "0.134903167",
      "0.276073166"
    ],
    [
      "0.239586779",
      "0.276073166"
    ],
    [
      "0.344212049",
      "0.276173992"
    ],
    [
      "0.603446145",
      "0.302296383"
    ],
    [
      "0.708129756",
      "0.302296383"
    ],
    [
      "0.812755027",
      "0.302397209"
    ],
    [
      "0.917438638",
      "0.302397209"
    ],
    [
      "0.5",
      "0.304344965"
    ],
    [
      "0.082561362",
      "0.306292722"
    ],
    [
      "0.187244973",
      "0.306292722"
    ],
    [
      "0.291870244",
      "0.306393548"
    ],
    [
      "0.396553855",
      "0.306393548"
    ],
    [
      "0.655787951",
      "0.332515939"
    ],
    [
      "0.760413221",
      "0.332616764"
    ],
    [
      "0.865096833",
      "0.332616764"
    ],
    [
      "0.969780444",
      "0.332616764"
    ],
    [
      "0.552341806",
      "0.334564521"
    ],
    [
      "0.030219556",
      "0.336512278"
    ],
    [
      "0.134903167",
      "0.336512278"
    ],
    [
      "0.239528438",
      "0.336613104"
    ],
    [
      "0.344212049",
      "0.336613104"
    ],
    [
      "0.448895661",
      "0.336613104"
    ],
    [
      "0.708071415",
      "0.36283632"
    ],
    [
      "0.812755027",
      "0.36283632"
    ],
    [
      "0.917438638",
      "0.36283632"
    ],
    [
      "0.604683612",
      "0.364784077"
    ],
    [
      "0.082561362",
      "0.366731833"
    ],
    [
      "0.187186632",
      "0.366832659"
    ],
    [
      "0.291870244",
      "0.366832659"
    ],
    [
      "0.396553855",
      "0.366832659"
    ],
    [
      "0.501237467",
      "0.366832659"
    ],
    [
      "0.760413221",
      "0.393055876"
    ],
    [
      "0.865096833",
      "0.393055876"
    ],
    [
      "0.969780444",
      "0.393055876"
    ],
    [
      "0.656967076",
      "0.395104458"
    ],
    [
      "0.030219556",
      "0.396951389"
    ],
    [
      "0.134844826",
      "0.397052215"
    ],
    [
      "0.239528438",
      "0.397052215"
    ],
    [
      "0.344212049",
      "0.397052215"
    ],
    [
      "0.448895661",
      "0.397052215"
    ],
    [
      "0.553579273",
      "0.397052215"
    ],
    [
      "0.812755027",
      "0.423275431"
    ],
    [
      "0.917438638",
      "0.423275431"
    ],
    [
      "0.709308882",
      "0.425324014"
    ],
    [
      "0.08250302",
      "0.427271771"
    ],
    [
      "0.187186632",
      "0.427271771"
    ],
    [
      "0.291870244",
      "0.427271771"
    ],
    [
      "0.396553855",
      "0.427271771"
    ],
    [
      "0.501237467",
      "0.427271771"
    ],
    [
      "0.605862737",
      "0.427372596"
    ],
    [
      "0.865096833",
      "0.453494987"
    ],
    [
      "0.969780444",
      "0.453494987"
    ],
    [
      "0.761650688",
      "0.45554357"
    ],
    [
      "0.134844826",
      "0.457491326"
    ],
    [
      "0.239528438",
      "0.457491326"
    ],
    [
      "0.344212049",
      "0.457491326"
    ],
    [
      "0.448895661",
      "0.457491326"
    ],
    [
      "0.030219556",
      "0.457592152"
    ],
    [
      "0.553520932",
      "0.457592152"
    ],
    [
      "0.658204543",
      "0.457592152"
    ],
    [
      "0.917438638",
      "0.483714543"
    ],
    [
      "0.813992494",
      "0.485763125"
    ],
    [
      "0.187186632",
      "0.487710882"
    ],
    [
      "0.291870244",
      "0.487710882"
    ],
    [
      "0.396553855",
      "0.487710882"
    ],
    [
      "0.082561362",
      "0.487811708"
    ],
    [
      "0.501179126",
      "0.487811708"
    ],
    [
      "0.605862737",
      "0.487811708"
    ],
    [
      "0.710546349",
      "0.487811708"
    ],
    [
      "0.969780444",
      "0.513934098"
    ],
    [
      "0.8663343",
      "0.515982681"
    ],
    [
      "0.239528438",
      "0.517930438"
    ],
    [
      "0.344212049",
      "0.517930438"
    ],
    [
      "0.030219556",
      "0.518031264"
    ],
    [
      "0.134903167",
      "0.518031264"
    ],
    [
      "0.44883732",
      "0.518031264"
    ],
    [
      "0.553520932",
      "0.518031264"
    ],
    [
      "0.658204543",
      "0.518031264"
    ],
    [
      "0.762888155",
      "0.518031264"
    ],
    [
      "0.918676105",
      "0.546202237"
    ],
    [
      "0.291870244",
      "0.548149993"
    ],
    [
      "0.082561362",
      "0.548250819"
    ],
    [
      "0.187244973",
      "0.548250819"
    ],
    [
      "0.396495514",
      "0.548250819"
    ],
    [
      "0.501179126",
      "0.548250819"
    ],
    [
      "0.605862737",
      "0.548250819"
    ],
    [
      "0.710546349",
      "0.548250819"
    ],
    [
      "0.815229961",
      "0.548250819"
    ],
    [
      "0.030219556",
      "0.578470375"
    ],
    [
      "0.134903167",
      "0.578470375"
    ],
    [
      "0.239586779",
      "0.578470375"
    ],
    [
      "0.344153708",
      "0.578470375"
    ],
    [
      "0.44883732",
      "0.578470375"
    ],
    [
      "0.553520932",
      "0.578470375"
    ],
    [
      "0.658204543",
      "0.578470375"
    ],
    [
      "0.762888155",
      "0.578470375"
    ],
    [
      "0.867571767",
      "0.578470375"
    ],
    [
      "0.969780444",
      "0.578470375"
    ],
    [
      "0.082561362",
      "0.608689931"
    ],
    [
      "0.187244973",
      "0.608689931"
    ],
    [
      "0.396495514",
      "0.608689931"
    ],
    [
      "0.501179126",
      "0.608689931"
    ],
    [
      "0.605862737",
      "0.608689931"
    ],
    [
      "0.710546349",
      "0.608689931"
    ],
    [
      "0.815229961",
      "0.608689931"
    ],
    [
      "0.291870244",
      "0.608790756"
    ],
    [
      "0.918676105",
      "0.610738513"
    ],
    [
      "0.030219556",
      "0.638909486"
    ],
    [
      "0.134903167",
      "0.638909486"
    ],
    [
      "0.44883732",
      "0.638909486"
    ],
    [
      "0.553520932",
      "0.638909486"
    ],
    [
      "0.658204543",
      "0.638909486"
    ],
    [
      "0.762888155",
      "0.638909486"
    ],
    [
      "0.239528438",
      "0.639010312"
    ],
    [
      "0.344212049",
      "0.639010312"
    ],
    [
      "0.8663343",
      "0.640958069"
    ],
    [
      "0.969780444",
      "0.643006651"
    ],
    [
      "0.082561362",
      "0.669129042"
    ],
    [
      "0.501179126",
      "0.669129042"
    ],
    [
      "0.605862737",
      "0.669129042"
    ],
    [
      "0.710546349",
      "0.669129042"
    ],
    [
      "0.187186632",
      "0.669229868"
    ],
    [
      "0.291870244",
      "0.669229868"
    ],
    [
      "0.396553855",
      "0.669229868"
    ],
    [
      "0.813992494",
      "0.671177625"
    ],
    [
      "0.917438638",
      "0.673226207"
    ],
    [
      "0.030219556",
      "0.699348598"
    ],
    [
      "0.553520932",
      "0.699348598"
    ],
    [
      "0.658204543",
      "0.699348598"
    ],
    [
      "0.134844826",
      "0.699449423"
    ],
    [
      "0.239528438",
      "0.699449423"
    ],
    [
      "0.344212049",
      "0.699449423"
    ],
    [
      "0.448895661",
      "0.699449423"
    ],
    [
      "0.761650688",
      "0.70139718"
    ],
    [
      "0.865096833",
      "0.703445763"
    ],
    [
      "0.969780444",
      "0.703445763"
    ],
    [
      "0.605862737",
      "0.729568153"
    ],
    [
      "0.08250302",
      "0.729668979"
    ],
    [
      "0.187186632",
      "0.729668979"
    ],
    [
      "0.291870244",
      "0.729668979"
    ],
    [
      "0.396553855",
      "0.729668979"
    ],
    [
      "0.501237467",
      "0.729668979"
    ],
    [
      "0.709308882",
      "0.731616736"
    ],
    [
      "0.812755027",
      "0.733665318"
    ],
    [
      "0.917438638",
      "0.733665318"
    ],
    [
      "0.134844826",
      "0.759888535"
    ],
    [
      "0.239528438",
      "0.759888535"
    ],
    [
      "0.344212049",
      "0.759888535"
    ],
    [
      "0.448895661",
      "0.759888535"
    ],
    [
      "0.553579273",
      "0.759888535"
    ],
    [
      "0.030219556",
      "0.759989361"
    ],
    [
      "0.656967076",
      "0.761836292"
    ],
    [
      "0.760413221",
      "0.763884874"
    ],
    [
      "0.865096833",
      "0.763884874"
    ],
    [
      "0.969780444",
      "0.763884874"
    ],
    [
      "0.187186632",
      "0.790108091"
    ],
    [
      "0.291870244",
      "0.790108091"
    ],
    [
      "0.396553855",
      "0.790108091"
    ],
    [
      "0.501237467",
      "0.790108091"
    ],
    [
      "0.082561362",
      "0.790208916"
    ],
    [
      "0.604683612",
      "0.792156673"
    ],
    [
      "0.708071415",
      "0.79410443"
    ],
    [
      "0.812755027",
      "0.79410443"
    ],
    [
      "0.917438638",
      "0.79410443"
    ],
    [
      "0.239528438",
      "0.820327646"
    ],
    [
      "0.344212049",
      "0.820327646"
    ],
    [
      "0.448895661",
      "0.820327646"
    ],
    [
      "0.030219556",
      "0.820428472"
    ],
    [
      "0.134903167",
      "0.820428472"
    ],
    [
      "0.552341806",
      "0.822376229"
    ],
    [
      "0.760413221",
      "0.824323986"
    ],
    [
      "0.865096833",
      "0.824323986"
    ],
    [
      "0.969780444",
      "0.824323986"
    ],
    [
      "0.655787951",
      "0.824424811"
    ],
    [
      "0.291870244",
      "0.850547202"
    ],
    [
      "0.082561362",
      "0.850648028"
    ],
    [
      "0.187244973",
      "0.850648028"
    ],
    [
      "0.396760917",
      "0.850907966"
    ],
    [
      "0.5",
      "0.852595785"
    ],
    [
      "0.812755027",
      "0.854543541"
    ],
    [
      "0.917438638",
      "0.854543541"
    ],
    [
      "0.603446145",
      "0.854644367"
    ],
    [
      "0.708129756",
      "0.854644367"
    ],
    [
      "0.344212049",
      "0.880766758"
    ],
    [
      "0.030219556",
      "0.880867583"
    ],
    [
      "0.134903167",
      "0.880867583"
    ],
    [
      "0.238324012",
      "0.882956201"
    ],
    [
      "0.969780444",
      "0.884763097"
    ],
    [
      "0.863747166",
      "0.887131072"
    ],
    [
      "0.453187081",
      "0.890824527"
    ],
    [
      "0.748036306",
      "0.900035483"
    ],
    [
      "0.568907085",
      "0.904242144"
    ],
    [
      "0.291870244",
      "0.910986313"
    ],
    [
      "0.082561362",
      "0.911087139"
    ],
    [
      "0.396340831",
      "0.911352315"
    ],
    [
      "0.628685037",
      "0.913157446"
    ],
    [
      "0.185982206",
      "0.913175756"
    ],
    [
      "0.689122999",
      "0.913530236"
    ],
    [
      "0.509189553",
      "0.913553568"
    ],
    [
      "0.806675361",
      "0.914676094"
    ],
    [
      "0.917438638",
      "0.914982653"
    ],
    [
      "0.030598114",
      "0.945202237"
    ],
    [
      "0.966598915",
      "0.950334433"
    ],
    [
      "0.344690989",
      "0.95732594"
    ],
    [
      "0.591075183",
      "0.96046902"
    ],
    [
      "0.471579699",
      "0.960865143"
    ],
    [
      "0.771367263",
      "0.963729375"
    ],
    [
      "0.217643716",
      "0.964658131"
    ],
    [
      "0.096982947",
      "0.969780444"
    ],
    [
      "0.157422058",
      "0.969780444"
    ],
    [
      "0.277865374",
      "0.969780444"
    ],
    [
      "0.411801747",
      "0.969780444"
    ],
    [
      "0.531357651",
      "0.969780444"
    ],
    [
      "0.650792715",
      "0.969780444"
    ],
    [
      "0.711231826",
      "0.969780444"
    ],
    [
      "0.831502699",
      "0.969780444"
    ],
    [
      "0.891941811",
      "0.969780444"
    ]
  ],
  "radius": "0.030219555"
}

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

DISCUSSION

讨论区

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。