P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 224

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 = 224
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[0.0347330618295, 0.0347330618305]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 = 0.034733061

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 = 224 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": [
    [
      "0.034733062",
      "0.034733062"
    ],
    [
      "0.155051917",
      "0.034733062"
    ],
    [
      "0.275370773",
      "0.034733062"
    ],
    [
      "0.395689639",
      "0.034733062"
    ],
    [
      "0.51609933",
      "0.034733062"
    ],
    [
      "0.639588253",
      "0.034733062"
    ],
    [
      "0.76611923",
      "0.034733062"
    ],
    [
      "0.901464872",
      "0.034733062"
    ],
    [
      "0.833792051",
      "0.05041527"
    ],
    [
      "0.965266938",
      "0.06220739"
    ],
    [
      "0.702853742",
      "0.063421392"
    ],
    [
      "0.577843792",
      "0.066563296"
    ],
    [
      "0.45589432",
      "0.069387636"
    ],
    [
      "0.335530202",
      "0.069466122"
    ],
    [
      "0.09489249",
      "0.069466124"
    ],
    [
      "0.215211345",
      "0.069466124"
    ],
    [
      "0.881209652",
      "0.101180548"
    ],
    [
      "0.759331309",
      "0.103866747"
    ],
    [
      "0.636281814",
      "0.104120451"
    ],
    [
      "0.51600845",
      "0.104199126"
    ],
    [
      "0.034733062",
      "0.104199185"
    ],
    [
      "0.155051917",
      "0.104199185"
    ],
    [
      "0.275370773",
      "0.104199185"
    ],
    [
      "0.395689629",
      "0.104199185"
    ],
    [
      "0.965266938",
      "0.131673514"
    ],
    [
      "0.821024255",
      "0.135905054"
    ],
    [
      "0.69787306",
      "0.136246153"
    ],
    [
      "0.576167878",
      "0.138932188"
    ],
    [
      "0.09489249",
      "0.138932247"
    ],
    [
      "0.215211345",
      "0.138932247"
    ],
    [
      "0.335530201",
      "0.138932247"
    ],
    [
      "0.455849056",
      "0.138932247"
    ],
    [
      "0.90510751",
      "0.166406576"
    ],
    [
      "0.759417801",
      "0.173332817"
    ],
    [
      "0.636327305",
      "0.17366525"
    ],
    [
      "0.034733062",
      "0.173665309"
    ],
    [
      "0.155051917",
      "0.173665309"
    ],
    [
      "0.275370773",
      "0.173665309"
    ],
    [
      "0.395689629",
      "0.173665309"
    ],
    [
      "0.516008484",
      "0.173665309"
    ],
    [
      "0.844901239",
      "0.201139024"
    ],
    [
      "0.965266938",
      "0.201139637"
    ],
    [
      "0.697959552",
      "0.205712223"
    ],
    [
      "0.09489249",
      "0.208398371"
    ],
    [
      "0.215211345",
      "0.208398371"
    ],
    [
      "0.335530201",
      "0.208398371"
    ],
    [
      "0.455849056",
      "0.208398371"
    ],
    [
      "0.576167912",
      "0.208398371"
    ],
    [
      "0.90510751",
      "0.235872699"
    ],
    [
      "0.783315841",
      "0.238558779"
    ],
    [
      "0.636327376",
      "0.243131373"
    ],
    [
      "0.034733062",
      "0.243131433"
    ],
    [
      "0.155051917",
      "0.243131433"
    ],
    [
      "0.275370773",
      "0.243131433"
    ],
    [
      "0.395689629",
      "0.243131433"
    ],
    [
      "0.516008484",
      "0.243131433"
    ],
    [
      "0.844948083",
      "0.270605761"
    ],
    [
      "0.965266938",
      "0.270605761"
    ],
    [
      "0.721857591",
      "0.270938185"
    ],
    [
      "0.09489249",
      "0.277864495"
    ],
    [
      "0.215211345",
      "0.277864495"
    ],
    [
      "0.335530201",
      "0.277864495"
    ],
    [
      "0.455849056",
      "0.277864495"
    ],
    [
      "0.576167912",
      "0.277864495"
    ],
    [
      "0.90510751",
      "0.305338823"
    ],
    [
      "0.78331584",
      "0.308024902"
    ],
    [
      "0.660225327",
      "0.308357367"
    ],
    [
      "0.034733062",
      "0.312597556"
    ],
    [
      "0.155051917",
      "0.312597556"
    ],
    [
      "0.275370773",
      "0.312597556"
    ],
    [
      "0.395689629",
      "0.312597556"
    ],
    [
      "0.516008484",
      "0.312597556"
    ],
    [
      "0.844948082",
      "0.340071885"
    ],
    [
      "0.965266938",
      "0.340071885"
    ],
    [
      "0.721857591",
      "0.340404308"
    ],
    [
      "0.600065871",
      "0.343090486"
    ],
    [
      "0.09489249",
      "0.347330618"
    ],
    [
      "0.215211345",
      "0.347330618"
    ],
    [
      "0.335530201",
      "0.347330618"
    ],
    [
      "0.455849056",
      "0.347330618"
    ],
    [
      "0.90510751",
      "0.374804947"
    ],
    [
      "0.783315841",
      "0.377491026"
    ],
    [
      "0.539906443",
      "0.377823548"
    ],
    [
      "0.660225298",
      "0.377823548"
    ],
    [
      "0.034733062",
      "0.38206368"
    ],
    [
      "0.155051917",
      "0.38206368"
    ],
    [
      "0.275370773",
      "0.38206368"
    ],
    [
      "0.395689629",
      "0.38206368"
    ],
    [
      "0.844948083",
      "0.409538008"
    ],
    [
      "0.965266938",
      "0.409538008"
    ],
    [
      "0.721857591",
      "0.409870432"
    ],
    [
      "0.479747015",
      "0.412556609"
    ],
    [
      "0.600065871",
      "0.412556609"
    ],
    [
      "0.09489249",
      "0.416796742"
    ],
    [
      "0.215211345",
      "0.416796742"
    ],
    [
      "0.335530201",
      "0.416796742"
    ],
    [
      "0.90510751",
      "0.44427107"
    ],
    [
      "0.783315841",
      "0.44695715"
    ],
    [
      "0.419587587",
      "0.447289671"
    ],
    [
      "0.539906443",
      "0.447289671"
    ],
    [
      "0.660225298",
      "0.447289671"
    ],
    [
      "0.034733062",
      "0.451529804"
    ],
    [
      "0.155051917",
      "0.451529804"
    ],
    [
      "0.275370773",
      "0.451529804"
    ],
    [
      "0.844948083",
      "0.479004132"
    ],
    [
      "0.965266938",
      "0.479004132"
    ],
    [
      "0.721857591",
      "0.479336556"
    ],
    [
      "0.359428159",
      "0.482022733"
    ],
    [
      "0.479747015",
      "0.482022733"
    ],
    [
      "0.600065871",
      "0.482022733"
    ],
    [
      "0.09489249",
      "0.486262866"
    ],
    [
      "0.215211345",
      "0.486262866"
    ],
    [
      "0.90510751",
      "0.513737194"
    ],
    [
      "0.783315841",
      "0.516423273"
    ],
    [
      "0.299268732",
      "0.516755795"
    ],
    [
      "0.419587587",
      "0.516755795"
    ],
    [
      "0.539906443",
      "0.516755795"
    ],
    [
      "0.660225298",
      "0.516755795"
    ],
    [
      "0.034733062",
      "0.520995927"
    ],
    [
      "0.155051917",
      "0.520995927"
    ],
    [
      "0.844948083",
      "0.548470256"
    ],
    [
      "0.965266938",
      "0.548470256"
    ],
    [
      "0.721857591",
      "0.548802679"
    ],
    [
      "0.239109304",
      "0.551488857"
    ],
    [
      "0.359428159",
      "0.551488857"
    ],
    [
      "0.479747015",
      "0.551488857"
    ],
    [
      "0.600065871",
      "0.551488857"
    ],
    [
      "0.09489249",
      "0.555728989"
    ],
    [
      "0.90510751",
      "0.583203317"
    ],
    [
      "0.783315841",
      "0.585889397"
    ],
    [
      "0.178949876",
      "0.586221918"
    ],
    [
      "0.299268732",
      "0.586221918"
    ],
    [
      "0.419587587",
      "0.586221918"
    ],
    [
      "0.539906443",
      "0.586221918"
    ],
    [
      "0.660225298",
      "0.586221918"
    ],
    [
      "0.034733062",
      "0.590462051"
    ],
    [
      "0.844948083",
      "0.617936379"
    ],
    [
      "0.965266938",
      "0.617936379"
    ],
    [
      "0.721857591",
      "0.618268803"
    ],
    [
      "0.118790448",
      "0.62095498"
    ],
    [
      "0.239109304",
      "0.62095498"
    ],
    [
      "0.359428159",
      "0.62095498"
    ],
    [
      "0.479747015",
      "0.62095498"
    ],
    [
      "0.600065871",
      "0.62095498"
    ],
    [
      "0.90510751",
      "0.652669441"
    ],
    [
      "0.783315841",
      "0.655355521"
    ],
    [
      "0.178949876",
      "0.655688042"
    ],
    [
      "0.299268732",
      "0.655688042"
    ],
    [
      "0.419587587",
      "0.655688042"
    ],
    [
      "0.539906443",
      "0.655688042"
    ],
    [
      "0.660225298",
      "0.655688042"
    ],
    [
      "0.034733062",
      "0.659928175"
    ],
    [
      "0.098535153",
      "0.687402444"
    ],
    [
      "0.844948083",
      "0.687402503"
    ],
    [
      "0.965266938",
      "0.687402503"
    ],
    [
      "0.721857591",
      "0.687734927"
    ],
    [
      "0.239109304",
      "0.690421104"
    ],
    [
      "0.359428159",
      "0.690421104"
    ],
    [
      "0.479747015",
      "0.690421104"
    ],
    [
      "0.600065871",
      "0.690421104"
    ],
    [
      "0.158694581",
      "0.722135505"
    ],
    [
      "0.90510751",
      "0.722135565"
    ],
    [
      "0.783315841",
      "0.724821644"
    ],
    [
      "0.299268732",
      "0.725154166"
    ],
    [
      "0.419587587",
      "0.725154166"
    ],
    [
      "0.539906443",
      "0.725154166"
    ],
    [
      "0.660225298",
      "0.725154166"
    ],
    [
      "0.034733062",
      "0.729394298"
    ],
    [
      "0.098535153",
      "0.756868567"
    ],
    [
      "0.218854009",
      "0.756868567"
    ],
    [
      "0.844948083",
      "0.756868627"
    ],
    [
      "0.965266938",
      "0.756868627"
    ],
    [
      "0.721857591",
      "0.75720105"
    ],
    [
      "0.359428159",
      "0.759887228"
    ],
    [
      "0.479747015",
      "0.759887228"
    ],
    [
      "0.600065871",
      "0.759887228"
    ],
    [
      "0.158694581",
      "0.791601629"
    ],
    [
      "0.279013437",
      "0.791601629"
    ],
    [
      "0.90510751",
      "0.791601688"
    ],
    [
      "0.783315841",
      "0.794287768"
    ],
    [
      "0.419587587",
      "0.794620289"
    ],
    [
      "0.539906443",
      "0.794620289"
    ],
    [
      "0.660225298",
      "0.794620289"
    ],
    [
      "0.034733062",
      "0.798860422"
    ],
    [
      "0.098535153",
      "0.826334691"
    ],
    [
      "0.218854009",
      "0.826334691"
    ],
    [
      "0.339172865",
      "0.826334691"
    ],
    [
      "0.844948083",
      "0.82633475"
    ],
    [
      "0.965266938",
      "0.82633475"
    ],
    [
      "0.721857591",
      "0.826667174"
    ],
    [
      "0.479747015",
      "0.829353351"
    ],
    [
      "0.600065871",
      "0.829353351"
    ],
    [
      "0.158694581",
      "0.861067753"
    ],
    [
      "0.279013437",
      "0.861067753"
    ],
    [
      "0.399332292",
      "0.861067753"
    ],
    [
      "0.90510751",
      "0.861067812"
    ],
    [
      "0.783402332",
      "0.863753838"
    ],
    [
      "0.539906443",
      "0.864086413"
    ],
    [
      "0.660249521",
      "0.864087628"
    ],
    [
      "0.034733062",
      "0.868326546"
    ],
    [
      "0.098535153",
      "0.895800815"
    ],
    [
      "0.218854009",
      "0.895800815"
    ],
    [
      "0.339172865",
      "0.895800815"
    ],
    [
      "0.45949172",
      "0.895800815"
    ],
    [
      "0.965266938",
      "0.895800874"
    ],
    [
      "0.844993574",
      "0.895879548"
    ],
    [
      "0.721944083",
      "0.896133244"
    ],
    [
      "0.600065871",
      "0.898819475"
    ],
    [
      "0.158694581",
      "0.930533876"
    ],
    [
      "0.279013437",
      "0.930533876"
    ],
    [
      "0.399332292",
      "0.930533876"
    ],
    [
      "0.519651148",
      "0.930533876"
    ],
    [
      "0.903431606",
      "0.933436687"
    ],
    [
      "0.778421703",
      "0.936578524"
    ],
    [
      "0.034733062",
      "0.937792669"
    ],
    [
      "0.647483414",
      "0.949584806"
    ],
    [
      "0.098535153",
      "0.965266938"
    ],
    [
      "0.218854009",
      "0.965266938"
    ],
    [
      "0.339172865",
      "0.965266938"
    ],
    [
      "0.45949172",
      "0.965266938"
    ],
    [
      "0.579810576",
      "0.965266938"
    ],
    [
      "0.715156253",
      "0.965266938"
    ],
    [
      "0.841687154",
      "0.965266938"
    ],
    [
      "0.965176059",
      "0.965266938"
    ]
  ],
  "radius": "0.034733061"
}
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": 224
}

起步布局答案

{
  "centers": [
    [
      "0.034733062",
      "0.034733062"
    ],
    [
      "0.155051917",
      "0.034733062"
    ],
    [
      "0.275370773",
      "0.034733062"
    ],
    [
      "0.395689639",
      "0.034733062"
    ],
    [
      "0.51609933",
      "0.034733062"
    ],
    [
      "0.639588253",
      "0.034733062"
    ],
    [
      "0.76611923",
      "0.034733062"
    ],
    [
      "0.901464872",
      "0.034733062"
    ],
    [
      "0.833792051",
      "0.05041527"
    ],
    [
      "0.965266938",
      "0.06220739"
    ],
    [
      "0.702853742",
      "0.063421392"
    ],
    [
      "0.577843792",
      "0.066563296"
    ],
    [
      "0.45589432",
      "0.069387636"
    ],
    [
      "0.335530202",
      "0.069466122"
    ],
    [
      "0.09489249",
      "0.069466124"
    ],
    [
      "0.215211345",
      "0.069466124"
    ],
    [
      "0.881209652",
      "0.101180548"
    ],
    [
      "0.759331309",
      "0.103866747"
    ],
    [
      "0.636281814",
      "0.104120451"
    ],
    [
      "0.51600845",
      "0.104199126"
    ],
    [
      "0.034733062",
      "0.104199185"
    ],
    [
      "0.155051917",
      "0.104199185"
    ],
    [
      "0.275370773",
      "0.104199185"
    ],
    [
      "0.395689629",
      "0.104199185"
    ],
    [
      "0.965266938",
      "0.131673514"
    ],
    [
      "0.821024255",
      "0.135905054"
    ],
    [
      "0.69787306",
      "0.136246153"
    ],
    [
      "0.576167878",
      "0.138932188"
    ],
    [
      "0.09489249",
      "0.138932247"
    ],
    [
      "0.215211345",
      "0.138932247"
    ],
    [
      "0.335530201",
      "0.138932247"
    ],
    [
      "0.455849056",
      "0.138932247"
    ],
    [
      "0.90510751",
      "0.166406576"
    ],
    [
      "0.759417801",
      "0.173332817"
    ],
    [
      "0.636327305",
      "0.17366525"
    ],
    [
      "0.034733062",
      "0.173665309"
    ],
    [
      "0.155051917",
      "0.173665309"
    ],
    [
      "0.275370773",
      "0.173665309"
    ],
    [
      "0.395689629",
      "0.173665309"
    ],
    [
      "0.516008484",
      "0.173665309"
    ],
    [
      "0.844901239",
      "0.201139024"
    ],
    [
      "0.965266938",
      "0.201139637"
    ],
    [
      "0.697959552",
      "0.205712223"
    ],
    [
      "0.09489249",
      "0.208398371"
    ],
    [
      "0.215211345",
      "0.208398371"
    ],
    [
      "0.335530201",
      "0.208398371"
    ],
    [
      "0.455849056",
      "0.208398371"
    ],
    [
      "0.576167912",
      "0.208398371"
    ],
    [
      "0.90510751",
      "0.235872699"
    ],
    [
      "0.783315841",
      "0.238558779"
    ],
    [
      "0.636327376",
      "0.243131373"
    ],
    [
      "0.034733062",
      "0.243131433"
    ],
    [
      "0.155051917",
      "0.243131433"
    ],
    [
      "0.275370773",
      "0.243131433"
    ],
    [
      "0.395689629",
      "0.243131433"
    ],
    [
      "0.516008484",
      "0.243131433"
    ],
    [
      "0.844948083",
      "0.270605761"
    ],
    [
      "0.965266938",
      "0.270605761"
    ],
    [
      "0.721857591",
      "0.270938185"
    ],
    [
      "0.09489249",
      "0.277864495"
    ],
    [
      "0.215211345",
      "0.277864495"
    ],
    [
      "0.335530201",
      "0.277864495"
    ],
    [
      "0.455849056",
      "0.277864495"
    ],
    [
      "0.576167912",
      "0.277864495"
    ],
    [
      "0.90510751",
      "0.305338823"
    ],
    [
      "0.78331584",
      "0.308024902"
    ],
    [
      "0.660225327",
      "0.308357367"
    ],
    [
      "0.034733062",
      "0.312597556"
    ],
    [
      "0.155051917",
      "0.312597556"
    ],
    [
      "0.275370773",
      "0.312597556"
    ],
    [
      "0.395689629",
      "0.312597556"
    ],
    [
      "0.516008484",
      "0.312597556"
    ],
    [
      "0.844948082",
      "0.340071885"
    ],
    [
      "0.965266938",
      "0.340071885"
    ],
    [
      "0.721857591",
      "0.340404308"
    ],
    [
      "0.600065871",
      "0.343090486"
    ],
    [
      "0.09489249",
      "0.347330618"
    ],
    [
      "0.215211345",
      "0.347330618"
    ],
    [
      "0.335530201",
      "0.347330618"
    ],
    [
      "0.455849056",
      "0.347330618"
    ],
    [
      "0.90510751",
      "0.374804947"
    ],
    [
      "0.783315841",
      "0.377491026"
    ],
    [
      "0.539906443",
      "0.377823548"
    ],
    [
      "0.660225298",
      "0.377823548"
    ],
    [
      "0.034733062",
      "0.38206368"
    ],
    [
      "0.155051917",
      "0.38206368"
    ],
    [
      "0.275370773",
      "0.38206368"
    ],
    [
      "0.395689629",
      "0.38206368"
    ],
    [
      "0.844948083",
      "0.409538008"
    ],
    [
      "0.965266938",
      "0.409538008"
    ],
    [
      "0.721857591",
      "0.409870432"
    ],
    [
      "0.479747015",
      "0.412556609"
    ],
    [
      "0.600065871",
      "0.412556609"
    ],
    [
      "0.09489249",
      "0.416796742"
    ],
    [
      "0.215211345",
      "0.416796742"
    ],
    [
      "0.335530201",
      "0.416796742"
    ],
    [
      "0.90510751",
      "0.44427107"
    ],
    [
      "0.783315841",
      "0.44695715"
    ],
    [
      "0.419587587",
      "0.447289671"
    ],
    [
      "0.539906443",
      "0.447289671"
    ],
    [
      "0.660225298",
      "0.447289671"
    ],
    [
      "0.034733062",
      "0.451529804"
    ],
    [
      "0.155051917",
      "0.451529804"
    ],
    [
      "0.275370773",
      "0.451529804"
    ],
    [
      "0.844948083",
      "0.479004132"
    ],
    [
      "0.965266938",
      "0.479004132"
    ],
    [
      "0.721857591",
      "0.479336556"
    ],
    [
      "0.359428159",
      "0.482022733"
    ],
    [
      "0.479747015",
      "0.482022733"
    ],
    [
      "0.600065871",
      "0.482022733"
    ],
    [
      "0.09489249",
      "0.486262866"
    ],
    [
      "0.215211345",
      "0.486262866"
    ],
    [
      "0.90510751",
      "0.513737194"
    ],
    [
      "0.783315841",
      "0.516423273"
    ],
    [
      "0.299268732",
      "0.516755795"
    ],
    [
      "0.419587587",
      "0.516755795"
    ],
    [
      "0.539906443",
      "0.516755795"
    ],
    [
      "0.660225298",
      "0.516755795"
    ],
    [
      "0.034733062",
      "0.520995927"
    ],
    [
      "0.155051917",
      "0.520995927"
    ],
    [
      "0.844948083",
      "0.548470256"
    ],
    [
      "0.965266938",
      "0.548470256"
    ],
    [
      "0.721857591",
      "0.548802679"
    ],
    [
      "0.239109304",
      "0.551488857"
    ],
    [
      "0.359428159",
      "0.551488857"
    ],
    [
      "0.479747015",
      "0.551488857"
    ],
    [
      "0.600065871",
      "0.551488857"
    ],
    [
      "0.09489249",
      "0.555728989"
    ],
    [
      "0.90510751",
      "0.583203317"
    ],
    [
      "0.783315841",
      "0.585889397"
    ],
    [
      "0.178949876",
      "0.586221918"
    ],
    [
      "0.299268732",
      "0.586221918"
    ],
    [
      "0.419587587",
      "0.586221918"
    ],
    [
      "0.539906443",
      "0.586221918"
    ],
    [
      "0.660225298",
      "0.586221918"
    ],
    [
      "0.034733062",
      "0.590462051"
    ],
    [
      "0.844948083",
      "0.617936379"
    ],
    [
      "0.965266938",
      "0.617936379"
    ],
    [
      "0.721857591",
      "0.618268803"
    ],
    [
      "0.118790448",
      "0.62095498"
    ],
    [
      "0.239109304",
      "0.62095498"
    ],
    [
      "0.359428159",
      "0.62095498"
    ],
    [
      "0.479747015",
      "0.62095498"
    ],
    [
      "0.600065871",
      "0.62095498"
    ],
    [
      "0.90510751",
      "0.652669441"
    ],
    [
      "0.783315841",
      "0.655355521"
    ],
    [
      "0.178949876",
      "0.655688042"
    ],
    [
      "0.299268732",
      "0.655688042"
    ],
    [
      "0.419587587",
      "0.655688042"
    ],
    [
      "0.539906443",
      "0.655688042"
    ],
    [
      "0.660225298",
      "0.655688042"
    ],
    [
      "0.034733062",
      "0.659928175"
    ],
    [
      "0.098535153",
      "0.687402444"
    ],
    [
      "0.844948083",
      "0.687402503"
    ],
    [
      "0.965266938",
      "0.687402503"
    ],
    [
      "0.721857591",
      "0.687734927"
    ],
    [
      "0.239109304",
      "0.690421104"
    ],
    [
      "0.359428159",
      "0.690421104"
    ],
    [
      "0.479747015",
      "0.690421104"
    ],
    [
      "0.600065871",
      "0.690421104"
    ],
    [
      "0.158694581",
      "0.722135505"
    ],
    [
      "0.90510751",
      "0.722135565"
    ],
    [
      "0.783315841",
      "0.724821644"
    ],
    [
      "0.299268732",
      "0.725154166"
    ],
    [
      "0.419587587",
      "0.725154166"
    ],
    [
      "0.539906443",
      "0.725154166"
    ],
    [
      "0.660225298",
      "0.725154166"
    ],
    [
      "0.034733062",
      "0.729394298"
    ],
    [
      "0.098535153",
      "0.756868567"
    ],
    [
      "0.218854009",
      "0.756868567"
    ],
    [
      "0.844948083",
      "0.756868627"
    ],
    [
      "0.965266938",
      "0.756868627"
    ],
    [
      "0.721857591",
      "0.75720105"
    ],
    [
      "0.359428159",
      "0.759887228"
    ],
    [
      "0.479747015",
      "0.759887228"
    ],
    [
      "0.600065871",
      "0.759887228"
    ],
    [
      "0.158694581",
      "0.791601629"
    ],
    [
      "0.279013437",
      "0.791601629"
    ],
    [
      "0.90510751",
      "0.791601688"
    ],
    [
      "0.783315841",
      "0.794287768"
    ],
    [
      "0.419587587",
      "0.794620289"
    ],
    [
      "0.539906443",
      "0.794620289"
    ],
    [
      "0.660225298",
      "0.794620289"
    ],
    [
      "0.034733062",
      "0.798860422"
    ],
    [
      "0.098535153",
      "0.826334691"
    ],
    [
      "0.218854009",
      "0.826334691"
    ],
    [
      "0.339172865",
      "0.826334691"
    ],
    [
      "0.844948083",
      "0.82633475"
    ],
    [
      "0.965266938",
      "0.82633475"
    ],
    [
      "0.721857591",
      "0.826667174"
    ],
    [
      "0.479747015",
      "0.829353351"
    ],
    [
      "0.600065871",
      "0.829353351"
    ],
    [
      "0.158694581",
      "0.861067753"
    ],
    [
      "0.279013437",
      "0.861067753"
    ],
    [
      "0.399332292",
      "0.861067753"
    ],
    [
      "0.90510751",
      "0.861067812"
    ],
    [
      "0.783402332",
      "0.863753838"
    ],
    [
      "0.539906443",
      "0.864086413"
    ],
    [
      "0.660249521",
      "0.864087628"
    ],
    [
      "0.034733062",
      "0.868326546"
    ],
    [
      "0.098535153",
      "0.895800815"
    ],
    [
      "0.218854009",
      "0.895800815"
    ],
    [
      "0.339172865",
      "0.895800815"
    ],
    [
      "0.45949172",
      "0.895800815"
    ],
    [
      "0.965266938",
      "0.895800874"
    ],
    [
      "0.844993574",
      "0.895879548"
    ],
    [
      "0.721944083",
      "0.896133244"
    ],
    [
      "0.600065871",
      "0.898819475"
    ],
    [
      "0.158694581",
      "0.930533876"
    ],
    [
      "0.279013437",
      "0.930533876"
    ],
    [
      "0.399332292",
      "0.930533876"
    ],
    [
      "0.519651148",
      "0.930533876"
    ],
    [
      "0.903431606",
      "0.933436687"
    ],
    [
      "0.778421703",
      "0.936578524"
    ],
    [
      "0.034733062",
      "0.937792669"
    ],
    [
      "0.647483414",
      "0.949584806"
    ],
    [
      "0.098535153",
      "0.965266938"
    ],
    [
      "0.218854009",
      "0.965266938"
    ],
    [
      "0.339172865",
      "0.965266938"
    ],
    [
      "0.45949172",
      "0.965266938"
    ],
    [
      "0.579810576",
      "0.965266938"
    ],
    [
      "0.715156253",
      "0.965266938"
    ],
    [
      "0.841687154",
      "0.965266938"
    ],
    [
      "0.965176059",
      "0.965266938"
    ]
  ],
  "radius": "0.034733061"
}

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。