P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 266

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 = 266
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[0.0319969388745, 0.0319969388755]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 = 0.031996938

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 = 266 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": [
    [
      "0.081875404",
      "0.031996939"
    ],
    [
      "0.192716051",
      "0.031996939"
    ],
    [
      "0.303556699",
      "0.031996939"
    ],
    [
      "0.414397347",
      "0.031996939"
    ],
    [
      "0.525237994",
      "0.031996939"
    ],
    [
      "0.636078642",
      "0.031996939"
    ],
    [
      "0.74691929",
      "0.031996939"
    ],
    [
      "0.857759937",
      "0.031996939"
    ],
    [
      "0.968002884",
      "0.032005019"
    ],
    [
      "0.137295728",
      "0.063993878"
    ],
    [
      "0.248136375",
      "0.063993878"
    ],
    [
      "0.358977023",
      "0.063993878"
    ],
    [
      "0.46981767",
      "0.063993878"
    ],
    [
      "0.580658318",
      "0.063993878"
    ],
    [
      "0.691498966",
      "0.063993878"
    ],
    [
      "0.802339613",
      "0.063993878"
    ],
    [
      "0.912664221",
      "0.064871488"
    ],
    [
      "0.031996939",
      "0.072088773"
    ],
    [
      "0.192716051",
      "0.095990817"
    ],
    [
      "0.303556699",
      "0.095990817"
    ],
    [
      "0.414397347",
      "0.095990817"
    ],
    [
      "0.525237994",
      "0.095990817"
    ],
    [
      "0.636078642",
      "0.095990817"
    ],
    [
      "0.74691929",
      "0.095990817"
    ],
    [
      "0.857243897",
      "0.096868427"
    ],
    [
      "0.968003061",
      "0.097009148"
    ],
    [
      "0.087417263",
      "0.104085712"
    ],
    [
      "0.248136375",
      "0.127987756"
    ],
    [
      "0.358977023",
      "0.127987756"
    ],
    [
      "0.46981767",
      "0.127987756"
    ],
    [
      "0.580658318",
      "0.127987756"
    ],
    [
      "0.691498966",
      "0.127987756"
    ],
    [
      "0.801823574",
      "0.128865366"
    ],
    [
      "0.912582737",
      "0.129006087"
    ],
    [
      "0.031996939",
      "0.13608265"
    ],
    [
      "0.142837587",
      "0.13608265"
    ],
    [
      "0.303556699",
      "0.159984694"
    ],
    [
      "0.414397347",
      "0.159984694"
    ],
    [
      "0.525237994",
      "0.159984694"
    ],
    [
      "0.636078642",
      "0.159984694"
    ],
    [
      "0.74640325",
      "0.160862305"
    ],
    [
      "0.857162413",
      "0.161003026"
    ],
    [
      "0.968003061",
      "0.161003026"
    ],
    [
      "0.087417263",
      "0.168079589"
    ],
    [
      "0.19825791",
      "0.168079589"
    ],
    [
      "0.358977023",
      "0.191981633"
    ],
    [
      "0.46981767",
      "0.191981633"
    ],
    [
      "0.580658318",
      "0.191981633"
    ],
    [
      "0.690982926",
      "0.192859244"
    ],
    [
      "0.80174209",
      "0.192999965"
    ],
    [
      "0.912582737",
      "0.192999965"
    ],
    [
      "0.031996939",
      "0.200076528"
    ],
    [
      "0.142837587",
      "0.200076528"
    ],
    [
      "0.253678234",
      "0.200076528"
    ],
    [
      "0.414397347",
      "0.223978572"
    ],
    [
      "0.525237994",
      "0.223978572"
    ],
    [
      "0.635562602",
      "0.224856183"
    ],
    [
      "0.746321766",
      "0.224996904"
    ],
    [
      "0.857162413",
      "0.224996904"
    ],
    [
      "0.968003061",
      "0.224996904"
    ],
    [
      "0.087417263",
      "0.232073467"
    ],
    [
      "0.19825791",
      "0.232073467"
    ],
    [
      "0.309098558",
      "0.232073467"
    ],
    [
      "0.46981767",
      "0.255975511"
    ],
    [
      "0.580142278",
      "0.256853121"
    ],
    [
      "0.690901442",
      "0.256993842"
    ],
    [
      "0.80174209",
      "0.256993842"
    ],
    [
      "0.912582737",
      "0.256993842"
    ],
    [
      "0.031996939",
      "0.264070406"
    ],
    [
      "0.142837587",
      "0.264070406"
    ],
    [
      "0.253678234",
      "0.264070406"
    ],
    [
      "0.364518882",
      "0.264070406"
    ],
    [
      "0.524721954",
      "0.28885006"
    ],
    [
      "0.635481118",
      "0.288990781"
    ],
    [
      "0.746321766",
      "0.288990781"
    ],
    [
      "0.857162413",
      "0.288990781"
    ],
    [
      "0.968003061",
      "0.288990781"
    ],
    [
      "0.087417263",
      "0.296067345"
    ],
    [
      "0.19825791",
      "0.296067345"
    ],
    [
      "0.309098558",
      "0.296067345"
    ],
    [
      "0.419939206",
      "0.296067345"
    ],
    [
      "0.580060794",
      "0.32098772"
    ],
    [
      "0.690901442",
      "0.32098772"
    ],
    [
      "0.80174209",
      "0.32098772"
    ],
    [
      "0.912582737",
      "0.32098772"
    ],
    [
      "0.031996939",
      "0.328064284"
    ],
    [
      "0.142837587",
      "0.328064284"
    ],
    [
      "0.253678234",
      "0.328064284"
    ],
    [
      "0.364518882",
      "0.328064284"
    ],
    [
      "0.477439181",
      "0.331972627"
    ],
    [
      "0.635481118",
      "0.352984659"
    ],
    [
      "0.746321766",
      "0.352984659"
    ],
    [
      "0.857162413",
      "0.352984659"
    ],
    [
      "0.968003061",
      "0.352984659"
    ],
    [
      "0.087417263",
      "0.360061223"
    ],
    [
      "0.19825791",
      "0.360061223"
    ],
    [
      "0.309098558",
      "0.360061223"
    ],
    [
      "0.419939206",
      "0.360061223"
    ],
    [
      "0.533202529",
      "0.364571196"
    ],
    [
      "0.690901442",
      "0.384981598"
    ],
    [
      "0.80174209",
      "0.384981598"
    ],
    [
      "0.912582737",
      "0.384981598"
    ],
    [
      "0.031996939",
      "0.392058161"
    ],
    [
      "0.142837587",
      "0.392058161"
    ],
    [
      "0.253678234",
      "0.392058161"
    ],
    [
      "0.364518882",
      "0.392058161"
    ],
    [
      "0.477439181",
      "0.395966504"
    ],
    [
      "0.588622853",
      "0.396568135"
    ],
    [
      "0.746321766",
      "0.416978537"
    ],
    [
      "0.857162413",
      "0.416978537"
    ],
    [
      "0.968003061",
      "0.416978537"
    ],
    [
      "0.087417263",
      "0.4240551"
    ],
    [
      "0.19825791",
      "0.4240551"
    ],
    [
      "0.309098558",
      "0.4240551"
    ],
    [
      "0.419939206",
      "0.4240551"
    ],
    [
      "0.533202529",
      "0.428565074"
    ],
    [
      "0.644043177",
      "0.428565074"
    ],
    [
      "0.80174209",
      "0.448975476"
    ],
    [
      "0.912582737",
      "0.448975476"
    ],
    [
      "0.031996939",
      "0.456052039"
    ],
    [
      "0.142837587",
      "0.456052039"
    ],
    [
      "0.253678234",
      "0.456052039"
    ],
    [
      "0.364518882",
      "0.456052039"
    ],
    [
      "0.477439181",
      "0.459960382"
    ],
    [
      "0.588622853",
      "0.460562013"
    ],
    [
      "0.699463501",
      "0.460562013"
    ],
    [
      "0.857162413",
      "0.480972415"
    ],
    [
      "0.968003061",
      "0.480972415"
    ],
    [
      "0.087417263",
      "0.488048978"
    ],
    [
      "0.19825791",
      "0.488048978"
    ],
    [
      "0.309098558",
      "0.488048978"
    ],
    [
      "0.419939206",
      "0.488048978"
    ],
    [
      "0.533202529",
      "0.492558952"
    ],
    [
      "0.644043177",
      "0.492558952"
    ],
    [
      "0.754883825",
      "0.492558952"
    ],
    [
      "0.912582737",
      "0.512969353"
    ],
    [
      "0.031996939",
      "0.520045917"
    ],
    [
      "0.142837587",
      "0.520045917"
    ],
    [
      "0.253678234",
      "0.520045917"
    ],
    [
      "0.364518882",
      "0.520045917"
    ],
    [
      "0.477439181",
      "0.52395426"
    ],
    [
      "0.588622853",
      "0.524555891"
    ],
    [
      "0.699463501",
      "0.524555891"
    ],
    [
      "0.810304148",
      "0.524555891"
    ],
    [
      "0.968003061",
      "0.544966292"
    ],
    [
      "0.087417263",
      "0.552042856"
    ],
    [
      "0.19825791",
      "0.552042856"
    ],
    [
      "0.309098558",
      "0.552042856"
    ],
    [
      "0.419939206",
      "0.552042856"
    ],
    [
      "0.533202529",
      "0.556552829"
    ],
    [
      "0.644043177",
      "0.556552829"
    ],
    [
      "0.754883825",
      "0.556552829"
    ],
    [
      "0.865724472",
      "0.556552829"
    ],
    [
      "0.031996939",
      "0.584039795"
    ],
    [
      "0.142837587",
      "0.584039795"
    ],
    [
      "0.253678234",
      "0.584039795"
    ],
    [
      "0.364518882",
      "0.584039795"
    ],
    [
      "0.477439181",
      "0.587948138"
    ],
    [
      "0.588622853",
      "0.588549768"
    ],
    [
      "0.699463501",
      "0.588549768"
    ],
    [
      "0.810304148",
      "0.588549768"
    ],
    [
      "0.921144796",
      "0.588549768"
    ],
    [
      "0.087417263",
      "0.616036734"
    ],
    [
      "0.19825791",
      "0.616036734"
    ],
    [
      "0.309098558",
      "0.616036734"
    ],
    [
      "0.419939206",
      "0.616036734"
    ],
    [
      "0.533202529",
      "0.620546707"
    ],
    [
      "0.644043177",
      "0.620546707"
    ],
    [
      "0.754883825",
      "0.620546707"
    ],
    [
      "0.865724472",
      "0.620546707"
    ],
    [
      "0.968003061",
      "0.632133244"
    ],
    [
      "0.031996939",
      "0.648033672"
    ],
    [
      "0.142837587",
      "0.648033672"
    ],
    [
      "0.253678234",
      "0.648033672"
    ],
    [
      "0.364518882",
      "0.648033672"
    ],
    [
      "0.477439181",
      "0.651942015"
    ],
    [
      "0.588622853",
      "0.652543646"
    ],
    [
      "0.699463501",
      "0.652543646"
    ],
    [
      "0.810304148",
      "0.652543646"
    ],
    [
      "0.912582737",
      "0.664130183"
    ],
    [
      "0.087417263",
      "0.680030611"
    ],
    [
      "0.19825791",
      "0.680030611"
    ],
    [
      "0.309098558",
      "0.680030611"
    ],
    [
      "0.419939206",
      "0.680030611"
    ],
    [
      "0.533202529",
      "0.684540585"
    ],
    [
      "0.644043177",
      "0.684540585"
    ],
    [
      "0.754883825",
      "0.684540585"
    ],
    [
      "0.857162413",
      "0.696127122"
    ],
    [
      "0.968003061",
      "0.696127122"
    ],
    [
      "0.031996939",
      "0.71202755"
    ],
    [
      "0.142837587",
      "0.71202755"
    ],
    [
      "0.253678234",
      "0.71202755"
    ],
    [
      "0.364518882",
      "0.71202755"
    ],
    [
      "0.477439181",
      "0.715935893"
    ],
    [
      "0.699463501",
      "0.716537524"
    ],
    [
      "0.588622849",
      "0.71653753"
    ],
    [
      "0.80174209",
      "0.728124061"
    ],
    [
      "0.912582737",
      "0.728124061"
    ],
    [
      "0.087417263",
      "0.744024489"
    ],
    [
      "0.19825791",
      "0.744024489"
    ],
    [
      "0.309098558",
      "0.744024489"
    ],
    [
      "0.419939206",
      "0.744024489"
    ],
    [
      "0.533202522",
      "0.748534463"
    ],
    [
      "0.644043177",
      "0.748534463"
    ],
    [
      "0.746321766",
      "0.760121"
    ],
    [
      "0.968003061",
      "0.760121"
    ],
    [
      "0.857162414",
      "0.760121"
    ],
    [
      "0.031996939",
      "0.776021428"
    ],
    [
      "0.142837587",
      "0.776021428"
    ],
    [
      "0.253678234",
      "0.776021428"
    ],
    [
      "0.364518884",
      "0.776021431"
    ],
    [
      "0.477439173",
      "0.779929771"
    ],
    [
      "0.589463417",
      "0.78208062"
    ],
    [
      "0.690901442",
      "0.792117939"
    ],
    [
      "0.80174209",
      "0.792117939"
    ],
    [
      "0.912582737",
      "0.792117939"
    ],
    [
      "0.087417263",
      "0.808018367"
    ],
    [
      "0.19825791",
      "0.808018367"
    ],
    [
      "0.309098558",
      "0.808018367"
    ],
    [
      "0.419939204",
      "0.808018381"
    ],
    [
      "0.533050242",
      "0.812528159"
    ],
    [
      "0.746321766",
      "0.824114878"
    ],
    [
      "0.968003061",
      "0.82411488"
    ],
    [
      "0.857303476",
      "0.824357971"
    ],
    [
      "0.031996939",
      "0.840015306"
    ],
    [
      "0.142837587",
      "0.840015306"
    ],
    [
      "0.253678234",
      "0.840015306"
    ],
    [
      "0.364518877",
      "0.840015314"
    ],
    [
      "0.649276209",
      "0.840724074"
    ],
    [
      "0.477286893",
      "0.843923467"
    ],
    [
      "0.585790517",
      "0.84877288"
    ],
    [
      "0.801743511",
      "0.856111816"
    ],
    [
      "0.912723799",
      "0.856354911"
    ],
    [
      "0.087417263",
      "0.872012245"
    ],
    [
      "0.309098553",
      "0.872012253"
    ],
    [
      "0.198258017",
      "0.87201243"
    ],
    [
      "0.419856769",
      "0.872154606"
    ],
    [
      "0.704696533",
      "0.872721013"
    ],
    [
      "0.532860701",
      "0.885060527"
    ],
    [
      "0.968003061",
      "0.888594942"
    ],
    [
      "0.853559379",
      "0.895269182"
    ],
    [
      "0.031996939",
      "0.904009183"
    ],
    [
      "0.142837587",
      "0.904009183"
    ],
    [
      "0.253678333",
      "0.904009383"
    ],
    [
      "0.364436445",
      "0.904151545"
    ],
    [
      "0.760117327",
      "0.904717137"
    ],
    [
      "0.473020715",
      "0.907774983"
    ],
    [
      "0.590640101",
      "0.912582737"
    ],
    [
      "0.654633979",
      "0.912582737"
    ],
    [
      "0.912442744",
      "0.920348172"
    ],
    [
      "0.087417463",
      "0.93600647"
    ],
    [
      "0.198334284",
      "0.936138072"
    ],
    [
      "0.311272457",
      "0.939771859"
    ],
    [
      "0.81017828",
      "0.944580872"
    ],
    [
      "0.431675954",
      "0.956619913"
    ],
    [
      "0.967997023",
      "0.968002574"
    ],
    [
      "0.253842363",
      "0.96800306"
    ],
    [
      "0.031996939",
      "0.968003061"
    ],
    [
      "0.142837988",
      "0.968003061"
    ],
    [
      "0.368702624",
      "0.968003061"
    ],
    [
      "0.494649285",
      "0.968003061"
    ],
    [
      "0.558643162",
      "0.968003061"
    ],
    [
      "0.62263704",
      "0.968003061"
    ],
    [
      "0.686630918",
      "0.968003061"
    ],
    [
      "0.750624796",
      "0.968003061"
    ],
    [
      "0.869731764",
      "0.968003061"
    ]
  ],
  "radius": "0.031996938"
}
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": 266
}

起步布局答案

{
  "centers": [
    [
      "0.081875404",
      "0.031996939"
    ],
    [
      "0.192716051",
      "0.031996939"
    ],
    [
      "0.303556699",
      "0.031996939"
    ],
    [
      "0.414397347",
      "0.031996939"
    ],
    [
      "0.525237994",
      "0.031996939"
    ],
    [
      "0.636078642",
      "0.031996939"
    ],
    [
      "0.74691929",
      "0.031996939"
    ],
    [
      "0.857759937",
      "0.031996939"
    ],
    [
      "0.968002884",
      "0.032005019"
    ],
    [
      "0.137295728",
      "0.063993878"
    ],
    [
      "0.248136375",
      "0.063993878"
    ],
    [
      "0.358977023",
      "0.063993878"
    ],
    [
      "0.46981767",
      "0.063993878"
    ],
    [
      "0.580658318",
      "0.063993878"
    ],
    [
      "0.691498966",
      "0.063993878"
    ],
    [
      "0.802339613",
      "0.063993878"
    ],
    [
      "0.912664221",
      "0.064871488"
    ],
    [
      "0.031996939",
      "0.072088773"
    ],
    [
      "0.192716051",
      "0.095990817"
    ],
    [
      "0.303556699",
      "0.095990817"
    ],
    [
      "0.414397347",
      "0.095990817"
    ],
    [
      "0.525237994",
      "0.095990817"
    ],
    [
      "0.636078642",
      "0.095990817"
    ],
    [
      "0.74691929",
      "0.095990817"
    ],
    [
      "0.857243897",
      "0.096868427"
    ],
    [
      "0.968003061",
      "0.097009148"
    ],
    [
      "0.087417263",
      "0.104085712"
    ],
    [
      "0.248136375",
      "0.127987756"
    ],
    [
      "0.358977023",
      "0.127987756"
    ],
    [
      "0.46981767",
      "0.127987756"
    ],
    [
      "0.580658318",
      "0.127987756"
    ],
    [
      "0.691498966",
      "0.127987756"
    ],
    [
      "0.801823574",
      "0.128865366"
    ],
    [
      "0.912582737",
      "0.129006087"
    ],
    [
      "0.031996939",
      "0.13608265"
    ],
    [
      "0.142837587",
      "0.13608265"
    ],
    [
      "0.303556699",
      "0.159984694"
    ],
    [
      "0.414397347",
      "0.159984694"
    ],
    [
      "0.525237994",
      "0.159984694"
    ],
    [
      "0.636078642",
      "0.159984694"
    ],
    [
      "0.74640325",
      "0.160862305"
    ],
    [
      "0.857162413",
      "0.161003026"
    ],
    [
      "0.968003061",
      "0.161003026"
    ],
    [
      "0.087417263",
      "0.168079589"
    ],
    [
      "0.19825791",
      "0.168079589"
    ],
    [
      "0.358977023",
      "0.191981633"
    ],
    [
      "0.46981767",
      "0.191981633"
    ],
    [
      "0.580658318",
      "0.191981633"
    ],
    [
      "0.690982926",
      "0.192859244"
    ],
    [
      "0.80174209",
      "0.192999965"
    ],
    [
      "0.912582737",
      "0.192999965"
    ],
    [
      "0.031996939",
      "0.200076528"
    ],
    [
      "0.142837587",
      "0.200076528"
    ],
    [
      "0.253678234",
      "0.200076528"
    ],
    [
      "0.414397347",
      "0.223978572"
    ],
    [
      "0.525237994",
      "0.223978572"
    ],
    [
      "0.635562602",
      "0.224856183"
    ],
    [
      "0.746321766",
      "0.224996904"
    ],
    [
      "0.857162413",
      "0.224996904"
    ],
    [
      "0.968003061",
      "0.224996904"
    ],
    [
      "0.087417263",
      "0.232073467"
    ],
    [
      "0.19825791",
      "0.232073467"
    ],
    [
      "0.309098558",
      "0.232073467"
    ],
    [
      "0.46981767",
      "0.255975511"
    ],
    [
      "0.580142278",
      "0.256853121"
    ],
    [
      "0.690901442",
      "0.256993842"
    ],
    [
      "0.80174209",
      "0.256993842"
    ],
    [
      "0.912582737",
      "0.256993842"
    ],
    [
      "0.031996939",
      "0.264070406"
    ],
    [
      "0.142837587",
      "0.264070406"
    ],
    [
      "0.253678234",
      "0.264070406"
    ],
    [
      "0.364518882",
      "0.264070406"
    ],
    [
      "0.524721954",
      "0.28885006"
    ],
    [
      "0.635481118",
      "0.288990781"
    ],
    [
      "0.746321766",
      "0.288990781"
    ],
    [
      "0.857162413",
      "0.288990781"
    ],
    [
      "0.968003061",
      "0.288990781"
    ],
    [
      "0.087417263",
      "0.296067345"
    ],
    [
      "0.19825791",
      "0.296067345"
    ],
    [
      "0.309098558",
      "0.296067345"
    ],
    [
      "0.419939206",
      "0.296067345"
    ],
    [
      "0.580060794",
      "0.32098772"
    ],
    [
      "0.690901442",
      "0.32098772"
    ],
    [
      "0.80174209",
      "0.32098772"
    ],
    [
      "0.912582737",
      "0.32098772"
    ],
    [
      "0.031996939",
      "0.328064284"
    ],
    [
      "0.142837587",
      "0.328064284"
    ],
    [
      "0.253678234",
      "0.328064284"
    ],
    [
      "0.364518882",
      "0.328064284"
    ],
    [
      "0.477439181",
      "0.331972627"
    ],
    [
      "0.635481118",
      "0.352984659"
    ],
    [
      "0.746321766",
      "0.352984659"
    ],
    [
      "0.857162413",
      "0.352984659"
    ],
    [
      "0.968003061",
      "0.352984659"
    ],
    [
      "0.087417263",
      "0.360061223"
    ],
    [
      "0.19825791",
      "0.360061223"
    ],
    [
      "0.309098558",
      "0.360061223"
    ],
    [
      "0.419939206",
      "0.360061223"
    ],
    [
      "0.533202529",
      "0.364571196"
    ],
    [
      "0.690901442",
      "0.384981598"
    ],
    [
      "0.80174209",
      "0.384981598"
    ],
    [
      "0.912582737",
      "0.384981598"
    ],
    [
      "0.031996939",
      "0.392058161"
    ],
    [
      "0.142837587",
      "0.392058161"
    ],
    [
      "0.253678234",
      "0.392058161"
    ],
    [
      "0.364518882",
      "0.392058161"
    ],
    [
      "0.477439181",
      "0.395966504"
    ],
    [
      "0.588622853",
      "0.396568135"
    ],
    [
      "0.746321766",
      "0.416978537"
    ],
    [
      "0.857162413",
      "0.416978537"
    ],
    [
      "0.968003061",
      "0.416978537"
    ],
    [
      "0.087417263",
      "0.4240551"
    ],
    [
      "0.19825791",
      "0.4240551"
    ],
    [
      "0.309098558",
      "0.4240551"
    ],
    [
      "0.419939206",
      "0.4240551"
    ],
    [
      "0.533202529",
      "0.428565074"
    ],
    [
      "0.644043177",
      "0.428565074"
    ],
    [
      "0.80174209",
      "0.448975476"
    ],
    [
      "0.912582737",
      "0.448975476"
    ],
    [
      "0.031996939",
      "0.456052039"
    ],
    [
      "0.142837587",
      "0.456052039"
    ],
    [
      "0.253678234",
      "0.456052039"
    ],
    [
      "0.364518882",
      "0.456052039"
    ],
    [
      "0.477439181",
      "0.459960382"
    ],
    [
      "0.588622853",
      "0.460562013"
    ],
    [
      "0.699463501",
      "0.460562013"
    ],
    [
      "0.857162413",
      "0.480972415"
    ],
    [
      "0.968003061",
      "0.480972415"
    ],
    [
      "0.087417263",
      "0.488048978"
    ],
    [
      "0.19825791",
      "0.488048978"
    ],
    [
      "0.309098558",
      "0.488048978"
    ],
    [
      "0.419939206",
      "0.488048978"
    ],
    [
      "0.533202529",
      "0.492558952"
    ],
    [
      "0.644043177",
      "0.492558952"
    ],
    [
      "0.754883825",
      "0.492558952"
    ],
    [
      "0.912582737",
      "0.512969353"
    ],
    [
      "0.031996939",
      "0.520045917"
    ],
    [
      "0.142837587",
      "0.520045917"
    ],
    [
      "0.253678234",
      "0.520045917"
    ],
    [
      "0.364518882",
      "0.520045917"
    ],
    [
      "0.477439181",
      "0.52395426"
    ],
    [
      "0.588622853",
      "0.524555891"
    ],
    [
      "0.699463501",
      "0.524555891"
    ],
    [
      "0.810304148",
      "0.524555891"
    ],
    [
      "0.968003061",
      "0.544966292"
    ],
    [
      "0.087417263",
      "0.552042856"
    ],
    [
      "0.19825791",
      "0.552042856"
    ],
    [
      "0.309098558",
      "0.552042856"
    ],
    [
      "0.419939206",
      "0.552042856"
    ],
    [
      "0.533202529",
      "0.556552829"
    ],
    [
      "0.644043177",
      "0.556552829"
    ],
    [
      "0.754883825",
      "0.556552829"
    ],
    [
      "0.865724472",
      "0.556552829"
    ],
    [
      "0.031996939",
      "0.584039795"
    ],
    [
      "0.142837587",
      "0.584039795"
    ],
    [
      "0.253678234",
      "0.584039795"
    ],
    [
      "0.364518882",
      "0.584039795"
    ],
    [
      "0.477439181",
      "0.587948138"
    ],
    [
      "0.588622853",
      "0.588549768"
    ],
    [
      "0.699463501",
      "0.588549768"
    ],
    [
      "0.810304148",
      "0.588549768"
    ],
    [
      "0.921144796",
      "0.588549768"
    ],
    [
      "0.087417263",
      "0.616036734"
    ],
    [
      "0.19825791",
      "0.616036734"
    ],
    [
      "0.309098558",
      "0.616036734"
    ],
    [
      "0.419939206",
      "0.616036734"
    ],
    [
      "0.533202529",
      "0.620546707"
    ],
    [
      "0.644043177",
      "0.620546707"
    ],
    [
      "0.754883825",
      "0.620546707"
    ],
    [
      "0.865724472",
      "0.620546707"
    ],
    [
      "0.968003061",
      "0.632133244"
    ],
    [
      "0.031996939",
      "0.648033672"
    ],
    [
      "0.142837587",
      "0.648033672"
    ],
    [
      "0.253678234",
      "0.648033672"
    ],
    [
      "0.364518882",
      "0.648033672"
    ],
    [
      "0.477439181",
      "0.651942015"
    ],
    [
      "0.588622853",
      "0.652543646"
    ],
    [
      "0.699463501",
      "0.652543646"
    ],
    [
      "0.810304148",
      "0.652543646"
    ],
    [
      "0.912582737",
      "0.664130183"
    ],
    [
      "0.087417263",
      "0.680030611"
    ],
    [
      "0.19825791",
      "0.680030611"
    ],
    [
      "0.309098558",
      "0.680030611"
    ],
    [
      "0.419939206",
      "0.680030611"
    ],
    [
      "0.533202529",
      "0.684540585"
    ],
    [
      "0.644043177",
      "0.684540585"
    ],
    [
      "0.754883825",
      "0.684540585"
    ],
    [
      "0.857162413",
      "0.696127122"
    ],
    [
      "0.968003061",
      "0.696127122"
    ],
    [
      "0.031996939",
      "0.71202755"
    ],
    [
      "0.142837587",
      "0.71202755"
    ],
    [
      "0.253678234",
      "0.71202755"
    ],
    [
      "0.364518882",
      "0.71202755"
    ],
    [
      "0.477439181",
      "0.715935893"
    ],
    [
      "0.699463501",
      "0.716537524"
    ],
    [
      "0.588622849",
      "0.71653753"
    ],
    [
      "0.80174209",
      "0.728124061"
    ],
    [
      "0.912582737",
      "0.728124061"
    ],
    [
      "0.087417263",
      "0.744024489"
    ],
    [
      "0.19825791",
      "0.744024489"
    ],
    [
      "0.309098558",
      "0.744024489"
    ],
    [
      "0.419939206",
      "0.744024489"
    ],
    [
      "0.533202522",
      "0.748534463"
    ],
    [
      "0.644043177",
      "0.748534463"
    ],
    [
      "0.746321766",
      "0.760121"
    ],
    [
      "0.968003061",
      "0.760121"
    ],
    [
      "0.857162414",
      "0.760121"
    ],
    [
      "0.031996939",
      "0.776021428"
    ],
    [
      "0.142837587",
      "0.776021428"
    ],
    [
      "0.253678234",
      "0.776021428"
    ],
    [
      "0.364518884",
      "0.776021431"
    ],
    [
      "0.477439173",
      "0.779929771"
    ],
    [
      "0.589463417",
      "0.78208062"
    ],
    [
      "0.690901442",
      "0.792117939"
    ],
    [
      "0.80174209",
      "0.792117939"
    ],
    [
      "0.912582737",
      "0.792117939"
    ],
    [
      "0.087417263",
      "0.808018367"
    ],
    [
      "0.19825791",
      "0.808018367"
    ],
    [
      "0.309098558",
      "0.808018367"
    ],
    [
      "0.419939204",
      "0.808018381"
    ],
    [
      "0.533050242",
      "0.812528159"
    ],
    [
      "0.746321766",
      "0.824114878"
    ],
    [
      "0.968003061",
      "0.82411488"
    ],
    [
      "0.857303476",
      "0.824357971"
    ],
    [
      "0.031996939",
      "0.840015306"
    ],
    [
      "0.142837587",
      "0.840015306"
    ],
    [
      "0.253678234",
      "0.840015306"
    ],
    [
      "0.364518877",
      "0.840015314"
    ],
    [
      "0.649276209",
      "0.840724074"
    ],
    [
      "0.477286893",
      "0.843923467"
    ],
    [
      "0.585790517",
      "0.84877288"
    ],
    [
      "0.801743511",
      "0.856111816"
    ],
    [
      "0.912723799",
      "0.856354911"
    ],
    [
      "0.087417263",
      "0.872012245"
    ],
    [
      "0.309098553",
      "0.872012253"
    ],
    [
      "0.198258017",
      "0.87201243"
    ],
    [
      "0.419856769",
      "0.872154606"
    ],
    [
      "0.704696533",
      "0.872721013"
    ],
    [
      "0.532860701",
      "0.885060527"
    ],
    [
      "0.968003061",
      "0.888594942"
    ],
    [
      "0.853559379",
      "0.895269182"
    ],
    [
      "0.031996939",
      "0.904009183"
    ],
    [
      "0.142837587",
      "0.904009183"
    ],
    [
      "0.253678333",
      "0.904009383"
    ],
    [
      "0.364436445",
      "0.904151545"
    ],
    [
      "0.760117327",
      "0.904717137"
    ],
    [
      "0.473020715",
      "0.907774983"
    ],
    [
      "0.590640101",
      "0.912582737"
    ],
    [
      "0.654633979",
      "0.912582737"
    ],
    [
      "0.912442744",
      "0.920348172"
    ],
    [
      "0.087417463",
      "0.93600647"
    ],
    [
      "0.198334284",
      "0.936138072"
    ],
    [
      "0.311272457",
      "0.939771859"
    ],
    [
      "0.81017828",
      "0.944580872"
    ],
    [
      "0.431675954",
      "0.956619913"
    ],
    [
      "0.967997023",
      "0.968002574"
    ],
    [
      "0.253842363",
      "0.96800306"
    ],
    [
      "0.031996939",
      "0.968003061"
    ],
    [
      "0.142837988",
      "0.968003061"
    ],
    [
      "0.368702624",
      "0.968003061"
    ],
    [
      "0.494649285",
      "0.968003061"
    ],
    [
      "0.558643162",
      "0.968003061"
    ],
    [
      "0.62263704",
      "0.968003061"
    ],
    [
      "0.686630918",
      "0.968003061"
    ],
    [
      "0.750624796",
      "0.968003061"
    ],
    [
      "0.869731764",
      "0.968003061"
    ]
  ],
  "radius": "0.031996938"
}

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。