P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 287

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 = 287
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[0.0307668017345, 0.0307668017355]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 = 0.030766801

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 = 287 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": [
    [
      "0.030766802",
      "0.030766802"
    ],
    [
      "0.457084112",
      "0.030766802"
    ],
    [
      "0.56366344",
      "0.030766802"
    ],
    [
      "0.670242767",
      "0.030766802"
    ],
    [
      "0.776822095",
      "0.030766802"
    ],
    [
      "0.899865748",
      "0.030766802"
    ],
    [
      "0.137346129",
      "0.030766802"
    ],
    [
      "0.243925457",
      "0.030766802"
    ],
    [
      "0.350504785",
      "0.030766802"
    ],
    [
      "0.838343922",
      "0.031970622"
    ],
    [
      "0.968941825",
      "0.051103509"
    ],
    [
      "0.190635793",
      "0.061533603"
    ],
    [
      "0.084056466",
      "0.061533603"
    ],
    [
      "0.297215121",
      "0.061533603"
    ],
    [
      "0.723532431",
      "0.061533603"
    ],
    [
      "0.616953103",
      "0.061533603"
    ],
    [
      "0.510373776",
      "0.061533603"
    ],
    [
      "0.403794448",
      "0.061533603"
    ],
    [
      "0.80654047",
      "0.084648177"
    ],
    [
      "0.915943534",
      "0.090162838"
    ],
    [
      "0.137346129",
      "0.092300405"
    ],
    [
      "0.030766802",
      "0.092300405"
    ],
    [
      "0.243925457",
      "0.092300405"
    ],
    [
      "0.670242767",
      "0.092300405"
    ],
    [
      "0.56366344",
      "0.092300405"
    ],
    [
      "0.350504784",
      "0.092300405"
    ],
    [
      "0.457084112",
      "0.092300405"
    ],
    [
      "0.753250806",
      "0.115414978"
    ],
    [
      "0.859830133",
      "0.115414978"
    ],
    [
      "0.969233198",
      "0.12092964"
    ],
    [
      "0.190635793",
      "0.123067207"
    ],
    [
      "0.084056466",
      "0.123067207"
    ],
    [
      "0.616953103",
      "0.123067207"
    ],
    [
      "0.297215121",
      "0.123067207"
    ],
    [
      "0.510373776",
      "0.123067207"
    ],
    [
      "0.403794448",
      "0.123067207"
    ],
    [
      "0.80654047",
      "0.14618178"
    ],
    [
      "0.699961142",
      "0.14618178"
    ],
    [
      "0.915943534",
      "0.151696442"
    ],
    [
      "0.137346129",
      "0.153834009"
    ],
    [
      "0.030766802",
      "0.153834009"
    ],
    [
      "0.243925457",
      "0.153834009"
    ],
    [
      "0.350504784",
      "0.153834009"
    ],
    [
      "0.56366344",
      "0.153834009"
    ],
    [
      "0.457084112",
      "0.153834009"
    ],
    [
      "0.753250806",
      "0.176948582"
    ],
    [
      "0.859830133",
      "0.176948582"
    ],
    [
      "0.646671478",
      "0.176948582"
    ],
    [
      "0.969233198",
      "0.182463243"
    ],
    [
      "0.190635793",
      "0.18460081"
    ],
    [
      "0.084056466",
      "0.18460081"
    ],
    [
      "0.297215121",
      "0.18460081"
    ],
    [
      "0.510373776",
      "0.18460081"
    ],
    [
      "0.403794448",
      "0.184600811"
    ],
    [
      "0.80654047",
      "0.207715384"
    ],
    [
      "0.699961142",
      "0.207715384"
    ],
    [
      "0.593381814",
      "0.207715384"
    ],
    [
      "0.915943534",
      "0.213230045"
    ],
    [
      "0.137346129",
      "0.215367612"
    ],
    [
      "0.030766802",
      "0.215367612"
    ],
    [
      "0.243925457",
      "0.215367612"
    ],
    [
      "0.350504784",
      "0.215367612"
    ],
    [
      "0.457084112",
      "0.215367613"
    ],
    [
      "0.859830133",
      "0.238482185"
    ],
    [
      "0.753250806",
      "0.238482185"
    ],
    [
      "0.646671478",
      "0.238482185"
    ],
    [
      "0.540092151",
      "0.238482185"
    ],
    [
      "0.969233198",
      "0.243996847"
    ],
    [
      "0.084056466",
      "0.246134414"
    ],
    [
      "0.190635793",
      "0.246134414"
    ],
    [
      "0.297215121",
      "0.246134414"
    ],
    [
      "0.403794448",
      "0.246134414"
    ],
    [
      "0.80654047",
      "0.269248987"
    ],
    [
      "0.699961142",
      "0.269248987"
    ],
    [
      "0.593381815",
      "0.269248987"
    ],
    [
      "0.486802487",
      "0.269248987"
    ],
    [
      "0.915943534",
      "0.274763649"
    ],
    [
      "0.137346129",
      "0.276901216"
    ],
    [
      "0.030766802",
      "0.276901216"
    ],
    [
      "0.243925457",
      "0.276901216"
    ],
    [
      "0.350504784",
      "0.276901216"
    ],
    [
      "0.859830133",
      "0.300015789"
    ],
    [
      "0.753250806",
      "0.300015789"
    ],
    [
      "0.646671478",
      "0.300015789"
    ],
    [
      "0.433512823",
      "0.300015789"
    ],
    [
      "0.540092151",
      "0.300015789"
    ],
    [
      "0.969233198",
      "0.30553045"
    ],
    [
      "0.084056466",
      "0.307668017"
    ],
    [
      "0.190635793",
      "0.307668017"
    ],
    [
      "0.297215121",
      "0.307668017"
    ],
    [
      "0.380223159",
      "0.33078259"
    ],
    [
      "0.80654047",
      "0.33078259"
    ],
    [
      "0.699961142",
      "0.330782591"
    ],
    [
      "0.486802487",
      "0.330782591"
    ],
    [
      "0.593381815",
      "0.330782591"
    ],
    [
      "0.915943535",
      "0.336297253"
    ],
    [
      "0.030766802",
      "0.338434819"
    ],
    [
      "0.137346129",
      "0.338434819"
    ],
    [
      "0.243925457",
      "0.338434819"
    ],
    [
      "0.326933496",
      "0.361549392"
    ],
    [
      "0.859830133",
      "0.361549392"
    ],
    [
      "0.753250806",
      "0.361549392"
    ],
    [
      "0.433512823",
      "0.361549392"
    ],
    [
      "0.646671479",
      "0.361549393"
    ],
    [
      "0.540092152",
      "0.361549395"
    ],
    [
      "0.969233198",
      "0.367064055"
    ],
    [
      "0.084056466",
      "0.369201621"
    ],
    [
      "0.190635793",
      "0.369201621"
    ],
    [
      "0.273643832",
      "0.392316194"
    ],
    [
      "0.380223159",
      "0.392316194"
    ],
    [
      "0.80654047",
      "0.392316194"
    ],
    [
      "0.486802487",
      "0.392316194"
    ],
    [
      "0.699961142",
      "0.392316195"
    ],
    [
      "0.593381816",
      "0.392316197"
    ],
    [
      "0.915943534",
      "0.397830857"
    ],
    [
      "0.030766802",
      "0.399968423"
    ],
    [
      "0.137346129",
      "0.399968423"
    ],
    [
      "0.220354168",
      "0.423082996"
    ],
    [
      "0.326933496",
      "0.423082996"
    ],
    [
      "0.433512823",
      "0.423082996"
    ],
    [
      "0.859830133",
      "0.423082996"
    ],
    [
      "0.753250806",
      "0.423082996"
    ],
    [
      "0.64667148",
      "0.423082999"
    ],
    [
      "0.540092158",
      "0.423083008"
    ],
    [
      "0.969233198",
      "0.428597659"
    ],
    [
      "0.084056466",
      "0.430735224"
    ],
    [
      "0.167064504",
      "0.453849797"
    ],
    [
      "0.273643832",
      "0.453849797"
    ],
    [
      "0.380223159",
      "0.453849797"
    ],
    [
      "0.486802487",
      "0.453849798"
    ],
    [
      "0.80654047",
      "0.453849799"
    ],
    [
      "0.699961144",
      "0.4538498"
    ],
    [
      "0.593381827",
      "0.453849818"
    ],
    [
      "0.915943547",
      "0.459364482"
    ],
    [
      "0.030766802",
      "0.461502026"
    ],
    [
      "0.11377484",
      "0.484616599"
    ],
    [
      "0.220354168",
      "0.484616599"
    ],
    [
      "0.326933496",
      "0.484616599"
    ],
    [
      "0.433512823",
      "0.484616599"
    ],
    [
      "0.859830136",
      "0.4846166"
    ],
    [
      "0.753250807",
      "0.484616603"
    ],
    [
      "0.540092158",
      "0.484616612"
    ],
    [
      "0.646671494",
      "0.484616626"
    ],
    [
      "0.969233198",
      "0.490131305"
    ],
    [
      "0.060485177",
      "0.515383401"
    ],
    [
      "0.167064504",
      "0.515383401"
    ],
    [
      "0.273643832",
      "0.515383401"
    ],
    [
      "0.380223159",
      "0.515383401"
    ],
    [
      "0.486802487",
      "0.515383401"
    ],
    [
      "0.806540472",
      "0.515383402"
    ],
    [
      "0.593381828",
      "0.515383423"
    ],
    [
      "0.699961157",
      "0.515383428"
    ],
    [
      "0.915943534",
      "0.520898107"
    ],
    [
      "0.11377484",
      "0.546150203"
    ],
    [
      "0.220354168",
      "0.546150203"
    ],
    [
      "0.326933496",
      "0.546150203"
    ],
    [
      "0.433512823",
      "0.546150203"
    ],
    [
      "0.540092159",
      "0.546150216"
    ],
    [
      "0.859830124",
      "0.546150226"
    ],
    [
      "0.753250823",
      "0.546150228"
    ],
    [
      "0.646671544",
      "0.546150318"
    ],
    [
      "0.969233198",
      "0.551664909"
    ],
    [
      "0.030766802",
      "0.569264776"
    ],
    [
      "0.273643832",
      "0.576917004"
    ],
    [
      "0.167064504",
      "0.576917004"
    ],
    [
      "0.380223159",
      "0.576917004"
    ],
    [
      "0.486802487",
      "0.576917005"
    ],
    [
      "0.593381828",
      "0.576917029"
    ],
    [
      "0.806540474",
      "0.576917052"
    ],
    [
      "0.69996121",
      "0.576917118"
    ],
    [
      "0.915943997",
      "0.582432511"
    ],
    [
      "0.084056466",
      "0.600031577"
    ],
    [
      "0.220354168",
      "0.607683806"
    ],
    [
      "0.326933495",
      "0.607683806"
    ],
    [
      "0.433512823",
      "0.607683806"
    ],
    [
      "0.540092158",
      "0.60768382"
    ],
    [
      "0.859830226",
      "0.607683829"
    ],
    [
      "0.753250861",
      "0.607683941"
    ],
    [
      "0.646671935",
      "0.607684594"
    ],
    [
      "0.969233198",
      "0.613200114"
    ],
    [
      "0.030766802",
      "0.630798379"
    ],
    [
      "0.137346129",
      "0.630798379"
    ],
    [
      "0.273643832",
      "0.638450608"
    ],
    [
      "0.380223159",
      "0.638450608"
    ],
    [
      "0.486802487",
      "0.638450609"
    ],
    [
      "0.593381831",
      "0.638450632"
    ],
    [
      "0.806540576",
      "0.638450655"
    ],
    [
      "0.699961619",
      "0.638451473"
    ],
    [
      "0.915943528",
      "0.643966905"
    ],
    [
      "0.084056466",
      "0.661565181"
    ],
    [
      "0.190635793",
      "0.661565181"
    ],
    [
      "0.326933496",
      "0.66921741"
    ],
    [
      "0.433512823",
      "0.66921741"
    ],
    [
      "0.540092161",
      "0.669217424"
    ],
    [
      "0.646671924",
      "0.669218221"
    ],
    [
      "0.753251364",
      "0.66921824"
    ],
    [
      "0.859829776",
      "0.669218265"
    ],
    [
      "0.969233198",
      "0.674733718"
    ],
    [
      "0.030766802",
      "0.692331983"
    ],
    [
      "0.137346129",
      "0.692331983"
    ],
    [
      "0.243925457",
      "0.692331983"
    ],
    [
      "0.380223159",
      "0.699984212"
    ],
    [
      "0.48680249",
      "0.699984212"
    ],
    [
      "0.593381812",
      "0.699984247"
    ],
    [
      "0.699961721",
      "0.699985078"
    ],
    [
      "0.806540566",
      "0.699985853"
    ],
    [
      "0.915960687",
      "0.70553021"
    ],
    [
      "0.084056466",
      "0.723098784"
    ],
    [
      "0.190635793",
      "0.723098784"
    ],
    [
      "0.297215121",
      "0.723098784"
    ],
    [
      "0.433512826",
      "0.730751014"
    ],
    [
      "0.540092141",
      "0.730751036"
    ],
    [
      "0.646672039",
      "0.730751847"
    ],
    [
      "0.859833579",
      "0.730751869"
    ],
    [
      "0.753250923",
      "0.730752691"
    ],
    [
      "0.969233198",
      "0.736326707"
    ],
    [
      "0.030766802",
      "0.753865586"
    ],
    [
      "0.137346129",
      "0.753865586"
    ],
    [
      "0.243925457",
      "0.753865586"
    ],
    [
      "0.350504785",
      "0.753865587"
    ],
    [
      "0.486802477",
      "0.761517837"
    ],
    [
      "0.593381914",
      "0.761517851"
    ],
    [
      "0.80654437",
      "0.761519458"
    ],
    [
      "0.699961798",
      "0.761520426"
    ],
    [
      "0.915943122",
      "0.767092799"
    ],
    [
      "0.40379445",
      "0.784632388"
    ],
    [
      "0.084056466",
      "0.784632388"
    ],
    [
      "0.190635793",
      "0.784632388"
    ],
    [
      "0.297215121",
      "0.784632388"
    ],
    [
      "0.540092243",
      "0.792284639"
    ],
    [
      "0.646671115",
      "0.792285463"
    ],
    [
      "0.753254726",
      "0.792286295"
    ],
    [
      "0.859816841",
      "0.792316302"
    ],
    [
      "0.969233197",
      "0.797860312"
    ],
    [
      "0.030766802",
      "0.81539919"
    ],
    [
      "0.137346129",
      "0.81539919"
    ],
    [
      "0.243925457",
      "0.81539919"
    ],
    [
      "0.350504786",
      "0.815399191"
    ],
    [
      "0.457084138",
      "0.815399232"
    ],
    [
      "0.593381448",
      "0.823052259"
    ],
    [
      "0.699965624",
      "0.823054069"
    ],
    [
      "0.806527199",
      "0.823083148"
    ],
    [
      "0.915943124",
      "0.828626408"
    ],
    [
      "0.510373827",
      "0.846165991"
    ],
    [
      "0.40379445",
      "0.846165991"
    ],
    [
      "0.084056466",
      "0.846165991"
    ],
    [
      "0.190635793",
      "0.846165991"
    ],
    [
      "0.297215121",
      "0.846165991"
    ],
    [
      "0.646674918",
      "0.853819066"
    ],
    [
      "0.859816865",
      "0.85384996"
    ],
    [
      "0.753238145",
      "0.853851011"
    ],
    [
      "0.969233197",
      "0.859393917"
    ],
    [
      "0.030766802",
      "0.876932793"
    ],
    [
      "0.137346129",
      "0.876932793"
    ],
    [
      "0.243925458",
      "0.876932794"
    ],
    [
      "0.350504795",
      "0.876932807"
    ],
    [
      "0.457084158",
      "0.876932836"
    ],
    [
      "0.563664427",
      "0.876934381"
    ],
    [
      "0.699947682",
      "0.884616436"
    ],
    [
      "0.813402664",
      "0.90048203"
    ],
    [
      "0.616955008",
      "0.907699595"
    ],
    [
      "0.510373847",
      "0.907699595"
    ],
    [
      "0.40379447",
      "0.907699595"
    ],
    [
      "0.084056466",
      "0.907699595"
    ],
    [
      "0.190635793",
      "0.907699595"
    ],
    [
      "0.297215122",
      "0.907699595"
    ],
    [
      "0.93490683",
      "0.910463331"
    ],
    [
      "0.873466523",
      "0.913850557"
    ],
    [
      "0.753380878",
      "0.915384455"
    ],
    [
      "0.030766802",
      "0.938466397"
    ],
    [
      "0.13734613",
      "0.938466398"
    ],
    [
      "0.243925465",
      "0.938466409"
    ],
    [
      "0.350504826",
      "0.938466433"
    ],
    [
      "0.457084486",
      "0.938466923"
    ],
    [
      "0.563665221",
      "0.938467985"
    ],
    [
      "0.670279554",
      "0.938525503"
    ],
    [
      "0.969233197",
      "0.961532747"
    ],
    [
      "0.785126465",
      "0.968096924"
    ],
    [
      "0.908183281",
      "0.969233176"
    ],
    [
      "0.72360333",
      "0.96923318"
    ],
    [
      "0.846649587",
      "0.969233195"
    ],
    [
      "0.616955803",
      "0.969233198"
    ],
    [
      "0.51037464",
      "0.969233198"
    ],
    [
      "0.403794517",
      "0.969233198"
    ],
    [
      "0.084056466",
      "0.969233198"
    ],
    [
      "0.190635795",
      "0.969233198"
    ],
    [
      "0.297215141",
      "0.969233198"
    ]
  ],
  "radius": "0.030766801"
}
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": 287
}

起步布局答案

{
  "centers": [
    [
      "0.030766802",
      "0.030766802"
    ],
    [
      "0.457084112",
      "0.030766802"
    ],
    [
      "0.56366344",
      "0.030766802"
    ],
    [
      "0.670242767",
      "0.030766802"
    ],
    [
      "0.776822095",
      "0.030766802"
    ],
    [
      "0.899865748",
      "0.030766802"
    ],
    [
      "0.137346129",
      "0.030766802"
    ],
    [
      "0.243925457",
      "0.030766802"
    ],
    [
      "0.350504785",
      "0.030766802"
    ],
    [
      "0.838343922",
      "0.031970622"
    ],
    [
      "0.968941825",
      "0.051103509"
    ],
    [
      "0.190635793",
      "0.061533603"
    ],
    [
      "0.084056466",
      "0.061533603"
    ],
    [
      "0.297215121",
      "0.061533603"
    ],
    [
      "0.723532431",
      "0.061533603"
    ],
    [
      "0.616953103",
      "0.061533603"
    ],
    [
      "0.510373776",
      "0.061533603"
    ],
    [
      "0.403794448",
      "0.061533603"
    ],
    [
      "0.80654047",
      "0.084648177"
    ],
    [
      "0.915943534",
      "0.090162838"
    ],
    [
      "0.137346129",
      "0.092300405"
    ],
    [
      "0.030766802",
      "0.092300405"
    ],
    [
      "0.243925457",
      "0.092300405"
    ],
    [
      "0.670242767",
      "0.092300405"
    ],
    [
      "0.56366344",
      "0.092300405"
    ],
    [
      "0.350504784",
      "0.092300405"
    ],
    [
      "0.457084112",
      "0.092300405"
    ],
    [
      "0.753250806",
      "0.115414978"
    ],
    [
      "0.859830133",
      "0.115414978"
    ],
    [
      "0.969233198",
      "0.12092964"
    ],
    [
      "0.190635793",
      "0.123067207"
    ],
    [
      "0.084056466",
      "0.123067207"
    ],
    [
      "0.616953103",
      "0.123067207"
    ],
    [
      "0.297215121",
      "0.123067207"
    ],
    [
      "0.510373776",
      "0.123067207"
    ],
    [
      "0.403794448",
      "0.123067207"
    ],
    [
      "0.80654047",
      "0.14618178"
    ],
    [
      "0.699961142",
      "0.14618178"
    ],
    [
      "0.915943534",
      "0.151696442"
    ],
    [
      "0.137346129",
      "0.153834009"
    ],
    [
      "0.030766802",
      "0.153834009"
    ],
    [
      "0.243925457",
      "0.153834009"
    ],
    [
      "0.350504784",
      "0.153834009"
    ],
    [
      "0.56366344",
      "0.153834009"
    ],
    [
      "0.457084112",
      "0.153834009"
    ],
    [
      "0.753250806",
      "0.176948582"
    ],
    [
      "0.859830133",
      "0.176948582"
    ],
    [
      "0.646671478",
      "0.176948582"
    ],
    [
      "0.969233198",
      "0.182463243"
    ],
    [
      "0.190635793",
      "0.18460081"
    ],
    [
      "0.084056466",
      "0.18460081"
    ],
    [
      "0.297215121",
      "0.18460081"
    ],
    [
      "0.510373776",
      "0.18460081"
    ],
    [
      "0.403794448",
      "0.184600811"
    ],
    [
      "0.80654047",
      "0.207715384"
    ],
    [
      "0.699961142",
      "0.207715384"
    ],
    [
      "0.593381814",
      "0.207715384"
    ],
    [
      "0.915943534",
      "0.213230045"
    ],
    [
      "0.137346129",
      "0.215367612"
    ],
    [
      "0.030766802",
      "0.215367612"
    ],
    [
      "0.243925457",
      "0.215367612"
    ],
    [
      "0.350504784",
      "0.215367612"
    ],
    [
      "0.457084112",
      "0.215367613"
    ],
    [
      "0.859830133",
      "0.238482185"
    ],
    [
      "0.753250806",
      "0.238482185"
    ],
    [
      "0.646671478",
      "0.238482185"
    ],
    [
      "0.540092151",
      "0.238482185"
    ],
    [
      "0.969233198",
      "0.243996847"
    ],
    [
      "0.084056466",
      "0.246134414"
    ],
    [
      "0.190635793",
      "0.246134414"
    ],
    [
      "0.297215121",
      "0.246134414"
    ],
    [
      "0.403794448",
      "0.246134414"
    ],
    [
      "0.80654047",
      "0.269248987"
    ],
    [
      "0.699961142",
      "0.269248987"
    ],
    [
      "0.593381815",
      "0.269248987"
    ],
    [
      "0.486802487",
      "0.269248987"
    ],
    [
      "0.915943534",
      "0.274763649"
    ],
    [
      "0.137346129",
      "0.276901216"
    ],
    [
      "0.030766802",
      "0.276901216"
    ],
    [
      "0.243925457",
      "0.276901216"
    ],
    [
      "0.350504784",
      "0.276901216"
    ],
    [
      "0.859830133",
      "0.300015789"
    ],
    [
      "0.753250806",
      "0.300015789"
    ],
    [
      "0.646671478",
      "0.300015789"
    ],
    [
      "0.433512823",
      "0.300015789"
    ],
    [
      "0.540092151",
      "0.300015789"
    ],
    [
      "0.969233198",
      "0.30553045"
    ],
    [
      "0.084056466",
      "0.307668017"
    ],
    [
      "0.190635793",
      "0.307668017"
    ],
    [
      "0.297215121",
      "0.307668017"
    ],
    [
      "0.380223159",
      "0.33078259"
    ],
    [
      "0.80654047",
      "0.33078259"
    ],
    [
      "0.699961142",
      "0.330782591"
    ],
    [
      "0.486802487",
      "0.330782591"
    ],
    [
      "0.593381815",
      "0.330782591"
    ],
    [
      "0.915943535",
      "0.336297253"
    ],
    [
      "0.030766802",
      "0.338434819"
    ],
    [
      "0.137346129",
      "0.338434819"
    ],
    [
      "0.243925457",
      "0.338434819"
    ],
    [
      "0.326933496",
      "0.361549392"
    ],
    [
      "0.859830133",
      "0.361549392"
    ],
    [
      "0.753250806",
      "0.361549392"
    ],
    [
      "0.433512823",
      "0.361549392"
    ],
    [
      "0.646671479",
      "0.361549393"
    ],
    [
      "0.540092152",
      "0.361549395"
    ],
    [
      "0.969233198",
      "0.367064055"
    ],
    [
      "0.084056466",
      "0.369201621"
    ],
    [
      "0.190635793",
      "0.369201621"
    ],
    [
      "0.273643832",
      "0.392316194"
    ],
    [
      "0.380223159",
      "0.392316194"
    ],
    [
      "0.80654047",
      "0.392316194"
    ],
    [
      "0.486802487",
      "0.392316194"
    ],
    [
      "0.699961142",
      "0.392316195"
    ],
    [
      "0.593381816",
      "0.392316197"
    ],
    [
      "0.915943534",
      "0.397830857"
    ],
    [
      "0.030766802",
      "0.399968423"
    ],
    [
      "0.137346129",
      "0.399968423"
    ],
    [
      "0.220354168",
      "0.423082996"
    ],
    [
      "0.326933496",
      "0.423082996"
    ],
    [
      "0.433512823",
      "0.423082996"
    ],
    [
      "0.859830133",
      "0.423082996"
    ],
    [
      "0.753250806",
      "0.423082996"
    ],
    [
      "0.64667148",
      "0.423082999"
    ],
    [
      "0.540092158",
      "0.423083008"
    ],
    [
      "0.969233198",
      "0.428597659"
    ],
    [
      "0.084056466",
      "0.430735224"
    ],
    [
      "0.167064504",
      "0.453849797"
    ],
    [
      "0.273643832",
      "0.453849797"
    ],
    [
      "0.380223159",
      "0.453849797"
    ],
    [
      "0.486802487",
      "0.453849798"
    ],
    [
      "0.80654047",
      "0.453849799"
    ],
    [
      "0.699961144",
      "0.4538498"
    ],
    [
      "0.593381827",
      "0.453849818"
    ],
    [
      "0.915943547",
      "0.459364482"
    ],
    [
      "0.030766802",
      "0.461502026"
    ],
    [
      "0.11377484",
      "0.484616599"
    ],
    [
      "0.220354168",
      "0.484616599"
    ],
    [
      "0.326933496",
      "0.484616599"
    ],
    [
      "0.433512823",
      "0.484616599"
    ],
    [
      "0.859830136",
      "0.4846166"
    ],
    [
      "0.753250807",
      "0.484616603"
    ],
    [
      "0.540092158",
      "0.484616612"
    ],
    [
      "0.646671494",
      "0.484616626"
    ],
    [
      "0.969233198",
      "0.490131305"
    ],
    [
      "0.060485177",
      "0.515383401"
    ],
    [
      "0.167064504",
      "0.515383401"
    ],
    [
      "0.273643832",
      "0.515383401"
    ],
    [
      "0.380223159",
      "0.515383401"
    ],
    [
      "0.486802487",
      "0.515383401"
    ],
    [
      "0.806540472",
      "0.515383402"
    ],
    [
      "0.593381828",
      "0.515383423"
    ],
    [
      "0.699961157",
      "0.515383428"
    ],
    [
      "0.915943534",
      "0.520898107"
    ],
    [
      "0.11377484",
      "0.546150203"
    ],
    [
      "0.220354168",
      "0.546150203"
    ],
    [
      "0.326933496",
      "0.546150203"
    ],
    [
      "0.433512823",
      "0.546150203"
    ],
    [
      "0.540092159",
      "0.546150216"
    ],
    [
      "0.859830124",
      "0.546150226"
    ],
    [
      "0.753250823",
      "0.546150228"
    ],
    [
      "0.646671544",
      "0.546150318"
    ],
    [
      "0.969233198",
      "0.551664909"
    ],
    [
      "0.030766802",
      "0.569264776"
    ],
    [
      "0.273643832",
      "0.576917004"
    ],
    [
      "0.167064504",
      "0.576917004"
    ],
    [
      "0.380223159",
      "0.576917004"
    ],
    [
      "0.486802487",
      "0.576917005"
    ],
    [
      "0.593381828",
      "0.576917029"
    ],
    [
      "0.806540474",
      "0.576917052"
    ],
    [
      "0.69996121",
      "0.576917118"
    ],
    [
      "0.915943997",
      "0.582432511"
    ],
    [
      "0.084056466",
      "0.600031577"
    ],
    [
      "0.220354168",
      "0.607683806"
    ],
    [
      "0.326933495",
      "0.607683806"
    ],
    [
      "0.433512823",
      "0.607683806"
    ],
    [
      "0.540092158",
      "0.60768382"
    ],
    [
      "0.859830226",
      "0.607683829"
    ],
    [
      "0.753250861",
      "0.607683941"
    ],
    [
      "0.646671935",
      "0.607684594"
    ],
    [
      "0.969233198",
      "0.613200114"
    ],
    [
      "0.030766802",
      "0.630798379"
    ],
    [
      "0.137346129",
      "0.630798379"
    ],
    [
      "0.273643832",
      "0.638450608"
    ],
    [
      "0.380223159",
      "0.638450608"
    ],
    [
      "0.486802487",
      "0.638450609"
    ],
    [
      "0.593381831",
      "0.638450632"
    ],
    [
      "0.806540576",
      "0.638450655"
    ],
    [
      "0.699961619",
      "0.638451473"
    ],
    [
      "0.915943528",
      "0.643966905"
    ],
    [
      "0.084056466",
      "0.661565181"
    ],
    [
      "0.190635793",
      "0.661565181"
    ],
    [
      "0.326933496",
      "0.66921741"
    ],
    [
      "0.433512823",
      "0.66921741"
    ],
    [
      "0.540092161",
      "0.669217424"
    ],
    [
      "0.646671924",
      "0.669218221"
    ],
    [
      "0.753251364",
      "0.66921824"
    ],
    [
      "0.859829776",
      "0.669218265"
    ],
    [
      "0.969233198",
      "0.674733718"
    ],
    [
      "0.030766802",
      "0.692331983"
    ],
    [
      "0.137346129",
      "0.692331983"
    ],
    [
      "0.243925457",
      "0.692331983"
    ],
    [
      "0.380223159",
      "0.699984212"
    ],
    [
      "0.48680249",
      "0.699984212"
    ],
    [
      "0.593381812",
      "0.699984247"
    ],
    [
      "0.699961721",
      "0.699985078"
    ],
    [
      "0.806540566",
      "0.699985853"
    ],
    [
      "0.915960687",
      "0.70553021"
    ],
    [
      "0.084056466",
      "0.723098784"
    ],
    [
      "0.190635793",
      "0.723098784"
    ],
    [
      "0.297215121",
      "0.723098784"
    ],
    [
      "0.433512826",
      "0.730751014"
    ],
    [
      "0.540092141",
      "0.730751036"
    ],
    [
      "0.646672039",
      "0.730751847"
    ],
    [
      "0.859833579",
      "0.730751869"
    ],
    [
      "0.753250923",
      "0.730752691"
    ],
    [
      "0.969233198",
      "0.736326707"
    ],
    [
      "0.030766802",
      "0.753865586"
    ],
    [
      "0.137346129",
      "0.753865586"
    ],
    [
      "0.243925457",
      "0.753865586"
    ],
    [
      "0.350504785",
      "0.753865587"
    ],
    [
      "0.486802477",
      "0.761517837"
    ],
    [
      "0.593381914",
      "0.761517851"
    ],
    [
      "0.80654437",
      "0.761519458"
    ],
    [
      "0.699961798",
      "0.761520426"
    ],
    [
      "0.915943122",
      "0.767092799"
    ],
    [
      "0.40379445",
      "0.784632388"
    ],
    [
      "0.084056466",
      "0.784632388"
    ],
    [
      "0.190635793",
      "0.784632388"
    ],
    [
      "0.297215121",
      "0.784632388"
    ],
    [
      "0.540092243",
      "0.792284639"
    ],
    [
      "0.646671115",
      "0.792285463"
    ],
    [
      "0.753254726",
      "0.792286295"
    ],
    [
      "0.859816841",
      "0.792316302"
    ],
    [
      "0.969233197",
      "0.797860312"
    ],
    [
      "0.030766802",
      "0.81539919"
    ],
    [
      "0.137346129",
      "0.81539919"
    ],
    [
      "0.243925457",
      "0.81539919"
    ],
    [
      "0.350504786",
      "0.815399191"
    ],
    [
      "0.457084138",
      "0.815399232"
    ],
    [
      "0.593381448",
      "0.823052259"
    ],
    [
      "0.699965624",
      "0.823054069"
    ],
    [
      "0.806527199",
      "0.823083148"
    ],
    [
      "0.915943124",
      "0.828626408"
    ],
    [
      "0.510373827",
      "0.846165991"
    ],
    [
      "0.40379445",
      "0.846165991"
    ],
    [
      "0.084056466",
      "0.846165991"
    ],
    [
      "0.190635793",
      "0.846165991"
    ],
    [
      "0.297215121",
      "0.846165991"
    ],
    [
      "0.646674918",
      "0.853819066"
    ],
    [
      "0.859816865",
      "0.85384996"
    ],
    [
      "0.753238145",
      "0.853851011"
    ],
    [
      "0.969233197",
      "0.859393917"
    ],
    [
      "0.030766802",
      "0.876932793"
    ],
    [
      "0.137346129",
      "0.876932793"
    ],
    [
      "0.243925458",
      "0.876932794"
    ],
    [
      "0.350504795",
      "0.876932807"
    ],
    [
      "0.457084158",
      "0.876932836"
    ],
    [
      "0.563664427",
      "0.876934381"
    ],
    [
      "0.699947682",
      "0.884616436"
    ],
    [
      "0.813402664",
      "0.90048203"
    ],
    [
      "0.616955008",
      "0.907699595"
    ],
    [
      "0.510373847",
      "0.907699595"
    ],
    [
      "0.40379447",
      "0.907699595"
    ],
    [
      "0.084056466",
      "0.907699595"
    ],
    [
      "0.190635793",
      "0.907699595"
    ],
    [
      "0.297215122",
      "0.907699595"
    ],
    [
      "0.93490683",
      "0.910463331"
    ],
    [
      "0.873466523",
      "0.913850557"
    ],
    [
      "0.753380878",
      "0.915384455"
    ],
    [
      "0.030766802",
      "0.938466397"
    ],
    [
      "0.13734613",
      "0.938466398"
    ],
    [
      "0.243925465",
      "0.938466409"
    ],
    [
      "0.350504826",
      "0.938466433"
    ],
    [
      "0.457084486",
      "0.938466923"
    ],
    [
      "0.563665221",
      "0.938467985"
    ],
    [
      "0.670279554",
      "0.938525503"
    ],
    [
      "0.969233197",
      "0.961532747"
    ],
    [
      "0.785126465",
      "0.968096924"
    ],
    [
      "0.908183281",
      "0.969233176"
    ],
    [
      "0.72360333",
      "0.96923318"
    ],
    [
      "0.846649587",
      "0.969233195"
    ],
    [
      "0.616955803",
      "0.969233198"
    ],
    [
      "0.51037464",
      "0.969233198"
    ],
    [
      "0.403794517",
      "0.969233198"
    ],
    [
      "0.084056466",
      "0.969233198"
    ],
    [
      "0.190635795",
      "0.969233198"
    ],
    [
      "0.297215141",
      "0.969233198"
    ]
  ],
  "radius": "0.030766801"
}

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。