P01 · 装箱与覆盖 · 经典问题 · 难

单位正方形内的等圆装箱 · n = 276

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 = 276
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[0.0314117661655, 0.0314117661665]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 = 0.031411765

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 = 276 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": [
    [
      "0.031411766",
      "0.031411766"
    ],
    [
      "0.140225316",
      "0.031411766"
    ],
    [
      "0.257980938",
      "0.031411766"
    ],
    [
      "0.370009263",
      "0.031411766"
    ],
    [
      "0.478927092",
      "0.031411766"
    ],
    [
      "0.696554359",
      "0.031411766"
    ],
    [
      "0.805367909",
      "0.031411766"
    ],
    [
      "0.914181459",
      "0.031411766"
    ],
    [
      "0.587740809",
      "0.031411766"
    ],
    [
      "0.199103127",
      "0.053325223"
    ],
    [
      "0.313995468",
      "0.059859104"
    ],
    [
      "0.424468295",
      "0.062733255"
    ],
    [
      "0.533333961",
      "0.062823406"
    ],
    [
      "0.642147584",
      "0.062823532"
    ],
    [
      "0.085818541",
      "0.062823532"
    ],
    [
      "0.750961134",
      "0.062823532"
    ],
    [
      "0.859774684",
      "0.062823532"
    ],
    [
      "0.968588234",
      "0.062823532"
    ],
    [
      "0.150686611",
      "0.093358175"
    ],
    [
      "0.261352429",
      "0.094144766"
    ],
    [
      "0.370113659",
      "0.094235212"
    ],
    [
      "0.478927259",
      "0.094235298"
    ],
    [
      "0.587740809",
      "0.094235298"
    ],
    [
      "0.031411766",
      "0.094235298"
    ],
    [
      "0.696554359",
      "0.094235298"
    ],
    [
      "0.805367909",
      "0.094235298"
    ],
    [
      "0.914181459",
      "0.094235298"
    ],
    [
      "0.205825426",
      "0.123556387"
    ],
    [
      "0.096279836",
      "0.124769941"
    ],
    [
      "0.315706884",
      "0.125646978"
    ],
    [
      "0.424520434",
      "0.125646978"
    ],
    [
      "0.533334034",
      "0.125647065"
    ],
    [
      "0.642147584",
      "0.125647065"
    ],
    [
      "0.750961134",
      "0.125647065"
    ],
    [
      "0.859774684",
      "0.125647065"
    ],
    [
      "0.968588234",
      "0.125647065"
    ],
    [
      "0.041873061",
      "0.156181707"
    ],
    [
      "0.150686611",
      "0.156181707"
    ],
    [
      "0.261247941",
      "0.156968211"
    ],
    [
      "0.370113659",
      "0.157058744"
    ],
    [
      "0.478927259",
      "0.157058831"
    ],
    [
      "0.587740809",
      "0.157058831"
    ],
    [
      "0.696554359",
      "0.157058831"
    ],
    [
      "0.805367909",
      "0.157058831"
    ],
    [
      "0.914181459",
      "0.157058831"
    ],
    [
      "0.205754976",
      "0.186418629"
    ],
    [
      "0.096279836",
      "0.187593473"
    ],
    [
      "0.315706884",
      "0.18847051"
    ],
    [
      "0.424520434",
      "0.18847051"
    ],
    [
      "0.533334034",
      "0.188470597"
    ],
    [
      "0.642147584",
      "0.188470597"
    ],
    [
      "0.750961134",
      "0.188470597"
    ],
    [
      "0.859774684",
      "0.188470597"
    ],
    [
      "0.968588234",
      "0.188470597"
    ],
    [
      "0.031411766",
      "0.218128115"
    ],
    [
      "0.150686611",
      "0.219005239"
    ],
    [
      "0.261247941",
      "0.219791744"
    ],
    [
      "0.370113659",
      "0.219882276"
    ],
    [
      "0.478927259",
      "0.219882363"
    ],
    [
      "0.587740809",
      "0.219882363"
    ],
    [
      "0.696554359",
      "0.219882363"
    ],
    [
      "0.805367909",
      "0.219882363"
    ],
    [
      "0.914181459",
      "0.219882363"
    ],
    [
      "0.205754976",
      "0.249242161"
    ],
    [
      "0.085818541",
      "0.249539882"
    ],
    [
      "0.315706884",
      "0.251294043"
    ],
    [
      "0.424520434",
      "0.251294043"
    ],
    [
      "0.533334034",
      "0.251294129"
    ],
    [
      "0.642147584",
      "0.251294129"
    ],
    [
      "0.750961134",
      "0.251294129"
    ],
    [
      "0.859774684",
      "0.251294129"
    ],
    [
      "0.968588234",
      "0.251294129"
    ],
    [
      "0.031411766",
      "0.280951648"
    ],
    [
      "0.140225316",
      "0.280951648"
    ],
    [
      "0.261247941",
      "0.282615276"
    ],
    [
      "0.370113659",
      "0.282705809"
    ],
    [
      "0.478927259",
      "0.282705895"
    ],
    [
      "0.587740809",
      "0.282705895"
    ],
    [
      "0.696554359",
      "0.282705895"
    ],
    [
      "0.805367909",
      "0.282705895"
    ],
    [
      "0.914181459",
      "0.282705895"
    ],
    [
      "0.205754976",
      "0.312065693"
    ],
    [
      "0.085818541",
      "0.312363414"
    ],
    [
      "0.315706884",
      "0.314117575"
    ],
    [
      "0.424520434",
      "0.314117575"
    ],
    [
      "0.533334034",
      "0.314117662"
    ],
    [
      "0.642147584",
      "0.314117662"
    ],
    [
      "0.750961134",
      "0.314117662"
    ],
    [
      "0.859774684",
      "0.314117662"
    ],
    [
      "0.968588234",
      "0.314117662"
    ],
    [
      "0.150988645",
      "0.342846292"
    ],
    [
      "0.031411766",
      "0.34377518"
    ],
    [
      "0.261247941",
      "0.345438808"
    ],
    [
      "0.370113659",
      "0.345529341"
    ],
    [
      "0.478927259",
      "0.345529428"
    ],
    [
      "0.587740809",
      "0.345529428"
    ],
    [
      "0.696554359",
      "0.345529428"
    ],
    [
      "0.805367909",
      "0.345529428"
    ],
    [
      "0.914181459",
      "0.345529428"
    ],
    [
      "0.09658187",
      "0.374258058"
    ],
    [
      "0.205754976",
      "0.374889226"
    ],
    [
      "0.315706884",
      "0.376941107"
    ],
    [
      "0.424520434",
      "0.376941107"
    ],
    [
      "0.533334034",
      "0.376941194"
    ],
    [
      "0.642147584",
      "0.376941194"
    ],
    [
      "0.750961134",
      "0.376941194"
    ],
    [
      "0.859774684",
      "0.376941194"
    ],
    [
      "0.968588234",
      "0.376941194"
    ],
    [
      "0.042175095",
      "0.405669824"
    ],
    [
      "0.150988645",
      "0.405669824"
    ],
    [
      "0.261247941",
      "0.408262341"
    ],
    [
      "0.370113659",
      "0.408352873"
    ],
    [
      "0.478927259",
      "0.40835296"
    ],
    [
      "0.587740809",
      "0.40835296"
    ],
    [
      "0.696554359",
      "0.40835296"
    ],
    [
      "0.805367909",
      "0.40835296"
    ],
    [
      "0.914181459",
      "0.40835296"
    ],
    [
      "0.09658187",
      "0.43708159"
    ],
    [
      "0.205754976",
      "0.437712758"
    ],
    [
      "0.315706884",
      "0.43976464"
    ],
    [
      "0.424520434",
      "0.43976464"
    ],
    [
      "0.533334034",
      "0.439764726"
    ],
    [
      "0.642147584",
      "0.439764726"
    ],
    [
      "0.750961134",
      "0.439764726"
    ],
    [
      "0.859774684",
      "0.439764726"
    ],
    [
      "0.968588234",
      "0.439764726"
    ],
    [
      "0.031411766",
      "0.467564468"
    ],
    [
      "0.150988645",
      "0.468493356"
    ],
    [
      "0.261247941",
      "0.471085873"
    ],
    [
      "0.370113659",
      "0.471176406"
    ],
    [
      "0.478927259",
      "0.471176492"
    ],
    [
      "0.587740809",
      "0.471176492"
    ],
    [
      "0.696554359",
      "0.471176492"
    ],
    [
      "0.805367909",
      "0.471176492"
    ],
    [
      "0.914181459",
      "0.471176492"
    ],
    [
      "0.085818541",
      "0.498976234"
    ],
    [
      "0.205754976",
      "0.50053629"
    ],
    [
      "0.424520434",
      "0.502588172"
    ],
    [
      "0.315602377",
      "0.502588207"
    ],
    [
      "0.533334034",
      "0.502588259"
    ],
    [
      "0.642147584",
      "0.502588259"
    ],
    [
      "0.750961134",
      "0.502588259"
    ],
    [
      "0.859774684",
      "0.502588259"
    ],
    [
      "0.968588234",
      "0.502588259"
    ],
    [
      "0.031411766",
      "0.530388"
    ],
    [
      "0.140225316",
      "0.530388"
    ],
    [
      "0.259006268",
      "0.533869399"
    ],
    [
      "0.370113659",
      "0.533999938"
    ],
    [
      "0.478927259",
      "0.534000025"
    ],
    [
      "0.587740809",
      "0.534000025"
    ],
    [
      "0.696554359",
      "0.534000025"
    ],
    [
      "0.805367909",
      "0.534000025"
    ],
    [
      "0.914181459",
      "0.534000025"
    ],
    [
      "0.085818541",
      "0.561799767"
    ],
    [
      "0.194991647",
      "0.562430934"
    ],
    [
      "0.315706884",
      "0.565411704"
    ],
    [
      "0.424520434",
      "0.565411704"
    ],
    [
      "0.533334034",
      "0.565411791"
    ],
    [
      "0.642147584",
      "0.565411791"
    ],
    [
      "0.750961134",
      "0.565411791"
    ],
    [
      "0.859774684",
      "0.565411791"
    ],
    [
      "0.968588234",
      "0.565411791"
    ],
    [
      "0.031411766",
      "0.593211533"
    ],
    [
      "0.140225316",
      "0.593211533"
    ],
    [
      "0.261202913",
      "0.596654516"
    ],
    [
      "0.370113659",
      "0.59682347"
    ],
    [
      "0.478927259",
      "0.596823557"
    ],
    [
      "0.587740809",
      "0.596823557"
    ],
    [
      "0.696554359",
      "0.596823557"
    ],
    [
      "0.805367909",
      "0.596823557"
    ],
    [
      "0.914181459",
      "0.596823557"
    ],
    [
      "0.204873845",
      "0.624472359"
    ],
    [
      "0.085818541",
      "0.624623299"
    ],
    [
      "0.315706884",
      "0.628235237"
    ],
    [
      "0.424520434",
      "0.628235237"
    ],
    [
      "0.533334034",
      "0.628235323"
    ],
    [
      "0.642147584",
      "0.628235323"
    ],
    [
      "0.750961134",
      "0.628235323"
    ],
    [
      "0.859774684",
      "0.628235323"
    ],
    [
      "0.968588234",
      "0.628235323"
    ],
    [
      "0.150107515",
      "0.655252957"
    ],
    [
      "0.031411766",
      "0.656035065"
    ],
    [
      "0.261202913",
      "0.659478049"
    ],
    [
      "0.370113659",
      "0.659647003"
    ],
    [
      "0.478927259",
      "0.659647089"
    ],
    [
      "0.587740809",
      "0.659647089"
    ],
    [
      "0.696554359",
      "0.659647089"
    ],
    [
      "0.805367909",
      "0.659647089"
    ],
    [
      "0.914181459",
      "0.659647089"
    ],
    [
      "0.09570074",
      "0.686664724"
    ],
    [
      "0.204873845",
      "0.687295891"
    ],
    [
      "0.424520434",
      "0.691058769"
    ],
    [
      "0.31556242",
      "0.691058847"
    ],
    [
      "0.533334034",
      "0.691058856"
    ],
    [
      "0.750961134",
      "0.691058856"
    ],
    [
      "0.859774684",
      "0.691058856"
    ],
    [
      "0.968588234",
      "0.691058856"
    ],
    [
      "0.642147584",
      "0.691058856"
    ],
    [
      "0.041293965",
      "0.71807649"
    ],
    [
      "0.150107515",
      "0.71807649"
    ],
    [
      "0.261048754",
      "0.722301392"
    ],
    [
      "0.370113659",
      "0.722470535"
    ],
    [
      "0.478927259",
      "0.722470622"
    ],
    [
      "0.587740809",
      "0.722470622"
    ],
    [
      "0.696554359",
      "0.722470622"
    ],
    [
      "0.805367909",
      "0.722470622"
    ],
    [
      "0.914181459",
      "0.722470622"
    ],
    [
      "0.09570074",
      "0.749488256"
    ],
    [
      "0.204719687",
      "0.750119235"
    ],
    [
      "0.315706834",
      "0.753882215"
    ],
    [
      "0.424520434",
      "0.753882301"
    ],
    [
      "0.750961134",
      "0.753882388"
    ],
    [
      "0.859774684",
      "0.753882388"
    ],
    [
      "0.968588234",
      "0.753882388"
    ],
    [
      "0.533334034",
      "0.753882388"
    ],
    [
      "0.642147584",
      "0.753882388"
    ],
    [
      "0.031411766",
      "0.780117914"
    ],
    [
      "0.150029454",
      "0.78103484"
    ],
    [
      "0.261202696",
      "0.785124736"
    ],
    [
      "0.370113659",
      "0.785294067"
    ],
    [
      "0.478927159",
      "0.785294154"
    ],
    [
      "0.587740809",
      "0.785294154"
    ],
    [
      "0.696554359",
      "0.785294154"
    ],
    [
      "0.805367909",
      "0.785294154"
    ],
    [
      "0.914181459",
      "0.785294154"
    ],
    [
      "0.085818541",
      "0.81152968"
    ],
    [
      "0.204873628",
      "0.812942578"
    ],
    [
      "0.315706834",
      "0.816705747"
    ],
    [
      "0.424520384",
      "0.81670592"
    ],
    [
      "0.533333934",
      "0.81670592"
    ],
    [
      "0.750961134",
      "0.81670592"
    ],
    [
      "0.859774684",
      "0.81670592"
    ],
    [
      "0.968588234",
      "0.81670592"
    ],
    [
      "0.642147545",
      "0.816705988"
    ],
    [
      "0.031411766",
      "0.842941447"
    ],
    [
      "0.140318435",
      "0.843103289"
    ],
    [
      "0.261202696",
      "0.847948268"
    ],
    [
      "0.370113559",
      "0.8481176"
    ],
    [
      "0.478927159",
      "0.848117686"
    ],
    [
      "0.587740709",
      "0.848117686"
    ],
    [
      "0.696554359",
      "0.848117686"
    ],
    [
      "0.805367909",
      "0.848117686"
    ],
    [
      "0.914181459",
      "0.848117686"
    ],
    [
      "0.085818541",
      "0.874353213"
    ],
    [
      "0.194788186",
      "0.874951288"
    ],
    [
      "0.968588234",
      "0.879529453"
    ],
    [
      "0.423708557",
      "0.881035742"
    ],
    [
      "0.857987617",
      "0.882730531"
    ],
    [
      "0.308084121",
      "0.890716057"
    ],
    [
      "0.741813189",
      "0.89171341"
    ],
    [
      "0.547354309",
      "0.89623977"
    ],
    [
      "0.618951604",
      "0.902639941"
    ],
    [
      "0.031411766",
      "0.905764979"
    ],
    [
      "0.140131716",
      "0.905926544"
    ],
    [
      "0.681442466",
      "0.909096592"
    ],
    [
      "0.247427331",
      "0.909242929"
    ],
    [
      "0.486175685",
      "0.910521653"
    ],
    [
      "0.801666671",
      "0.910832095"
    ],
    [
      "0.367953249",
      "0.910903978"
    ],
    [
      "0.914181459",
      "0.910941219"
    ],
    [
      "0.088118367",
      "0.94116016"
    ],
    [
      "0.578565204",
      "0.950762025"
    ],
    [
      "0.206339718",
      "0.956767705"
    ],
    [
      "0.764007845",
      "0.961117371"
    ],
    [
      "0.330440317",
      "0.961298185"
    ],
    [
      "0.953106163",
      "0.961783622"
    ],
    [
      "0.455581641",
      "0.965392417"
    ],
    [
      "0.031598485",
      "0.968588234"
    ],
    [
      "0.144638248",
      "0.968588234"
    ],
    [
      "0.268041187",
      "0.968588234"
    ],
    [
      "0.392839446",
      "0.968588234"
    ],
    [
      "0.518323835",
      "0.968588234"
    ],
    [
      "0.638806572",
      "0.968588234"
    ],
    [
      "0.701630105",
      "0.968588234"
    ],
    [
      "0.826385584",
      "0.968588234"
    ],
    [
      "0.889209117",
      "0.968588234"
    ]
  ],
  "radius": "0.031411765"
}
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": 276
}

起步布局答案

{
  "centers": [
    [
      "0.031411766",
      "0.031411766"
    ],
    [
      "0.140225316",
      "0.031411766"
    ],
    [
      "0.257980938",
      "0.031411766"
    ],
    [
      "0.370009263",
      "0.031411766"
    ],
    [
      "0.478927092",
      "0.031411766"
    ],
    [
      "0.696554359",
      "0.031411766"
    ],
    [
      "0.805367909",
      "0.031411766"
    ],
    [
      "0.914181459",
      "0.031411766"
    ],
    [
      "0.587740809",
      "0.031411766"
    ],
    [
      "0.199103127",
      "0.053325223"
    ],
    [
      "0.313995468",
      "0.059859104"
    ],
    [
      "0.424468295",
      "0.062733255"
    ],
    [
      "0.533333961",
      "0.062823406"
    ],
    [
      "0.642147584",
      "0.062823532"
    ],
    [
      "0.085818541",
      "0.062823532"
    ],
    [
      "0.750961134",
      "0.062823532"
    ],
    [
      "0.859774684",
      "0.062823532"
    ],
    [
      "0.968588234",
      "0.062823532"
    ],
    [
      "0.150686611",
      "0.093358175"
    ],
    [
      "0.261352429",
      "0.094144766"
    ],
    [
      "0.370113659",
      "0.094235212"
    ],
    [
      "0.478927259",
      "0.094235298"
    ],
    [
      "0.587740809",
      "0.094235298"
    ],
    [
      "0.031411766",
      "0.094235298"
    ],
    [
      "0.696554359",
      "0.094235298"
    ],
    [
      "0.805367909",
      "0.094235298"
    ],
    [
      "0.914181459",
      "0.094235298"
    ],
    [
      "0.205825426",
      "0.123556387"
    ],
    [
      "0.096279836",
      "0.124769941"
    ],
    [
      "0.315706884",
      "0.125646978"
    ],
    [
      "0.424520434",
      "0.125646978"
    ],
    [
      "0.533334034",
      "0.125647065"
    ],
    [
      "0.642147584",
      "0.125647065"
    ],
    [
      "0.750961134",
      "0.125647065"
    ],
    [
      "0.859774684",
      "0.125647065"
    ],
    [
      "0.968588234",
      "0.125647065"
    ],
    [
      "0.041873061",
      "0.156181707"
    ],
    [
      "0.150686611",
      "0.156181707"
    ],
    [
      "0.261247941",
      "0.156968211"
    ],
    [
      "0.370113659",
      "0.157058744"
    ],
    [
      "0.478927259",
      "0.157058831"
    ],
    [
      "0.587740809",
      "0.157058831"
    ],
    [
      "0.696554359",
      "0.157058831"
    ],
    [
      "0.805367909",
      "0.157058831"
    ],
    [
      "0.914181459",
      "0.157058831"
    ],
    [
      "0.205754976",
      "0.186418629"
    ],
    [
      "0.096279836",
      "0.187593473"
    ],
    [
      "0.315706884",
      "0.18847051"
    ],
    [
      "0.424520434",
      "0.18847051"
    ],
    [
      "0.533334034",
      "0.188470597"
    ],
    [
      "0.642147584",
      "0.188470597"
    ],
    [
      "0.750961134",
      "0.188470597"
    ],
    [
      "0.859774684",
      "0.188470597"
    ],
    [
      "0.968588234",
      "0.188470597"
    ],
    [
      "0.031411766",
      "0.218128115"
    ],
    [
      "0.150686611",
      "0.219005239"
    ],
    [
      "0.261247941",
      "0.219791744"
    ],
    [
      "0.370113659",
      "0.219882276"
    ],
    [
      "0.478927259",
      "0.219882363"
    ],
    [
      "0.587740809",
      "0.219882363"
    ],
    [
      "0.696554359",
      "0.219882363"
    ],
    [
      "0.805367909",
      "0.219882363"
    ],
    [
      "0.914181459",
      "0.219882363"
    ],
    [
      "0.205754976",
      "0.249242161"
    ],
    [
      "0.085818541",
      "0.249539882"
    ],
    [
      "0.315706884",
      "0.251294043"
    ],
    [
      "0.424520434",
      "0.251294043"
    ],
    [
      "0.533334034",
      "0.251294129"
    ],
    [
      "0.642147584",
      "0.251294129"
    ],
    [
      "0.750961134",
      "0.251294129"
    ],
    [
      "0.859774684",
      "0.251294129"
    ],
    [
      "0.968588234",
      "0.251294129"
    ],
    [
      "0.031411766",
      "0.280951648"
    ],
    [
      "0.140225316",
      "0.280951648"
    ],
    [
      "0.261247941",
      "0.282615276"
    ],
    [
      "0.370113659",
      "0.282705809"
    ],
    [
      "0.478927259",
      "0.282705895"
    ],
    [
      "0.587740809",
      "0.282705895"
    ],
    [
      "0.696554359",
      "0.282705895"
    ],
    [
      "0.805367909",
      "0.282705895"
    ],
    [
      "0.914181459",
      "0.282705895"
    ],
    [
      "0.205754976",
      "0.312065693"
    ],
    [
      "0.085818541",
      "0.312363414"
    ],
    [
      "0.315706884",
      "0.314117575"
    ],
    [
      "0.424520434",
      "0.314117575"
    ],
    [
      "0.533334034",
      "0.314117662"
    ],
    [
      "0.642147584",
      "0.314117662"
    ],
    [
      "0.750961134",
      "0.314117662"
    ],
    [
      "0.859774684",
      "0.314117662"
    ],
    [
      "0.968588234",
      "0.314117662"
    ],
    [
      "0.150988645",
      "0.342846292"
    ],
    [
      "0.031411766",
      "0.34377518"
    ],
    [
      "0.261247941",
      "0.345438808"
    ],
    [
      "0.370113659",
      "0.345529341"
    ],
    [
      "0.478927259",
      "0.345529428"
    ],
    [
      "0.587740809",
      "0.345529428"
    ],
    [
      "0.696554359",
      "0.345529428"
    ],
    [
      "0.805367909",
      "0.345529428"
    ],
    [
      "0.914181459",
      "0.345529428"
    ],
    [
      "0.09658187",
      "0.374258058"
    ],
    [
      "0.205754976",
      "0.374889226"
    ],
    [
      "0.315706884",
      "0.376941107"
    ],
    [
      "0.424520434",
      "0.376941107"
    ],
    [
      "0.533334034",
      "0.376941194"
    ],
    [
      "0.642147584",
      "0.376941194"
    ],
    [
      "0.750961134",
      "0.376941194"
    ],
    [
      "0.859774684",
      "0.376941194"
    ],
    [
      "0.968588234",
      "0.376941194"
    ],
    [
      "0.042175095",
      "0.405669824"
    ],
    [
      "0.150988645",
      "0.405669824"
    ],
    [
      "0.261247941",
      "0.408262341"
    ],
    [
      "0.370113659",
      "0.408352873"
    ],
    [
      "0.478927259",
      "0.40835296"
    ],
    [
      "0.587740809",
      "0.40835296"
    ],
    [
      "0.696554359",
      "0.40835296"
    ],
    [
      "0.805367909",
      "0.40835296"
    ],
    [
      "0.914181459",
      "0.40835296"
    ],
    [
      "0.09658187",
      "0.43708159"
    ],
    [
      "0.205754976",
      "0.437712758"
    ],
    [
      "0.315706884",
      "0.43976464"
    ],
    [
      "0.424520434",
      "0.43976464"
    ],
    [
      "0.533334034",
      "0.439764726"
    ],
    [
      "0.642147584",
      "0.439764726"
    ],
    [
      "0.750961134",
      "0.439764726"
    ],
    [
      "0.859774684",
      "0.439764726"
    ],
    [
      "0.968588234",
      "0.439764726"
    ],
    [
      "0.031411766",
      "0.467564468"
    ],
    [
      "0.150988645",
      "0.468493356"
    ],
    [
      "0.261247941",
      "0.471085873"
    ],
    [
      "0.370113659",
      "0.471176406"
    ],
    [
      "0.478927259",
      "0.471176492"
    ],
    [
      "0.587740809",
      "0.471176492"
    ],
    [
      "0.696554359",
      "0.471176492"
    ],
    [
      "0.805367909",
      "0.471176492"
    ],
    [
      "0.914181459",
      "0.471176492"
    ],
    [
      "0.085818541",
      "0.498976234"
    ],
    [
      "0.205754976",
      "0.50053629"
    ],
    [
      "0.424520434",
      "0.502588172"
    ],
    [
      "0.315602377",
      "0.502588207"
    ],
    [
      "0.533334034",
      "0.502588259"
    ],
    [
      "0.642147584",
      "0.502588259"
    ],
    [
      "0.750961134",
      "0.502588259"
    ],
    [
      "0.859774684",
      "0.502588259"
    ],
    [
      "0.968588234",
      "0.502588259"
    ],
    [
      "0.031411766",
      "0.530388"
    ],
    [
      "0.140225316",
      "0.530388"
    ],
    [
      "0.259006268",
      "0.533869399"
    ],
    [
      "0.370113659",
      "0.533999938"
    ],
    [
      "0.478927259",
      "0.534000025"
    ],
    [
      "0.587740809",
      "0.534000025"
    ],
    [
      "0.696554359",
      "0.534000025"
    ],
    [
      "0.805367909",
      "0.534000025"
    ],
    [
      "0.914181459",
      "0.534000025"
    ],
    [
      "0.085818541",
      "0.561799767"
    ],
    [
      "0.194991647",
      "0.562430934"
    ],
    [
      "0.315706884",
      "0.565411704"
    ],
    [
      "0.424520434",
      "0.565411704"
    ],
    [
      "0.533334034",
      "0.565411791"
    ],
    [
      "0.642147584",
      "0.565411791"
    ],
    [
      "0.750961134",
      "0.565411791"
    ],
    [
      "0.859774684",
      "0.565411791"
    ],
    [
      "0.968588234",
      "0.565411791"
    ],
    [
      "0.031411766",
      "0.593211533"
    ],
    [
      "0.140225316",
      "0.593211533"
    ],
    [
      "0.261202913",
      "0.596654516"
    ],
    [
      "0.370113659",
      "0.59682347"
    ],
    [
      "0.478927259",
      "0.596823557"
    ],
    [
      "0.587740809",
      "0.596823557"
    ],
    [
      "0.696554359",
      "0.596823557"
    ],
    [
      "0.805367909",
      "0.596823557"
    ],
    [
      "0.914181459",
      "0.596823557"
    ],
    [
      "0.204873845",
      "0.624472359"
    ],
    [
      "0.085818541",
      "0.624623299"
    ],
    [
      "0.315706884",
      "0.628235237"
    ],
    [
      "0.424520434",
      "0.628235237"
    ],
    [
      "0.533334034",
      "0.628235323"
    ],
    [
      "0.642147584",
      "0.628235323"
    ],
    [
      "0.750961134",
      "0.628235323"
    ],
    [
      "0.859774684",
      "0.628235323"
    ],
    [
      "0.968588234",
      "0.628235323"
    ],
    [
      "0.150107515",
      "0.655252957"
    ],
    [
      "0.031411766",
      "0.656035065"
    ],
    [
      "0.261202913",
      "0.659478049"
    ],
    [
      "0.370113659",
      "0.659647003"
    ],
    [
      "0.478927259",
      "0.659647089"
    ],
    [
      "0.587740809",
      "0.659647089"
    ],
    [
      "0.696554359",
      "0.659647089"
    ],
    [
      "0.805367909",
      "0.659647089"
    ],
    [
      "0.914181459",
      "0.659647089"
    ],
    [
      "0.09570074",
      "0.686664724"
    ],
    [
      "0.204873845",
      "0.687295891"
    ],
    [
      "0.424520434",
      "0.691058769"
    ],
    [
      "0.31556242",
      "0.691058847"
    ],
    [
      "0.533334034",
      "0.691058856"
    ],
    [
      "0.750961134",
      "0.691058856"
    ],
    [
      "0.859774684",
      "0.691058856"
    ],
    [
      "0.968588234",
      "0.691058856"
    ],
    [
      "0.642147584",
      "0.691058856"
    ],
    [
      "0.041293965",
      "0.71807649"
    ],
    [
      "0.150107515",
      "0.71807649"
    ],
    [
      "0.261048754",
      "0.722301392"
    ],
    [
      "0.370113659",
      "0.722470535"
    ],
    [
      "0.478927259",
      "0.722470622"
    ],
    [
      "0.587740809",
      "0.722470622"
    ],
    [
      "0.696554359",
      "0.722470622"
    ],
    [
      "0.805367909",
      "0.722470622"
    ],
    [
      "0.914181459",
      "0.722470622"
    ],
    [
      "0.09570074",
      "0.749488256"
    ],
    [
      "0.204719687",
      "0.750119235"
    ],
    [
      "0.315706834",
      "0.753882215"
    ],
    [
      "0.424520434",
      "0.753882301"
    ],
    [
      "0.750961134",
      "0.753882388"
    ],
    [
      "0.859774684",
      "0.753882388"
    ],
    [
      "0.968588234",
      "0.753882388"
    ],
    [
      "0.533334034",
      "0.753882388"
    ],
    [
      "0.642147584",
      "0.753882388"
    ],
    [
      "0.031411766",
      "0.780117914"
    ],
    [
      "0.150029454",
      "0.78103484"
    ],
    [
      "0.261202696",
      "0.785124736"
    ],
    [
      "0.370113659",
      "0.785294067"
    ],
    [
      "0.478927159",
      "0.785294154"
    ],
    [
      "0.587740809",
      "0.785294154"
    ],
    [
      "0.696554359",
      "0.785294154"
    ],
    [
      "0.805367909",
      "0.785294154"
    ],
    [
      "0.914181459",
      "0.785294154"
    ],
    [
      "0.085818541",
      "0.81152968"
    ],
    [
      "0.204873628",
      "0.812942578"
    ],
    [
      "0.315706834",
      "0.816705747"
    ],
    [
      "0.424520384",
      "0.81670592"
    ],
    [
      "0.533333934",
      "0.81670592"
    ],
    [
      "0.750961134",
      "0.81670592"
    ],
    [
      "0.859774684",
      "0.81670592"
    ],
    [
      "0.968588234",
      "0.81670592"
    ],
    [
      "0.642147545",
      "0.816705988"
    ],
    [
      "0.031411766",
      "0.842941447"
    ],
    [
      "0.140318435",
      "0.843103289"
    ],
    [
      "0.261202696",
      "0.847948268"
    ],
    [
      "0.370113559",
      "0.8481176"
    ],
    [
      "0.478927159",
      "0.848117686"
    ],
    [
      "0.587740709",
      "0.848117686"
    ],
    [
      "0.696554359",
      "0.848117686"
    ],
    [
      "0.805367909",
      "0.848117686"
    ],
    [
      "0.914181459",
      "0.848117686"
    ],
    [
      "0.085818541",
      "0.874353213"
    ],
    [
      "0.194788186",
      "0.874951288"
    ],
    [
      "0.968588234",
      "0.879529453"
    ],
    [
      "0.423708557",
      "0.881035742"
    ],
    [
      "0.857987617",
      "0.882730531"
    ],
    [
      "0.308084121",
      "0.890716057"
    ],
    [
      "0.741813189",
      "0.89171341"
    ],
    [
      "0.547354309",
      "0.89623977"
    ],
    [
      "0.618951604",
      "0.902639941"
    ],
    [
      "0.031411766",
      "0.905764979"
    ],
    [
      "0.140131716",
      "0.905926544"
    ],
    [
      "0.681442466",
      "0.909096592"
    ],
    [
      "0.247427331",
      "0.909242929"
    ],
    [
      "0.486175685",
      "0.910521653"
    ],
    [
      "0.801666671",
      "0.910832095"
    ],
    [
      "0.367953249",
      "0.910903978"
    ],
    [
      "0.914181459",
      "0.910941219"
    ],
    [
      "0.088118367",
      "0.94116016"
    ],
    [
      "0.578565204",
      "0.950762025"
    ],
    [
      "0.206339718",
      "0.956767705"
    ],
    [
      "0.764007845",
      "0.961117371"
    ],
    [
      "0.330440317",
      "0.961298185"
    ],
    [
      "0.953106163",
      "0.961783622"
    ],
    [
      "0.455581641",
      "0.965392417"
    ],
    [
      "0.031598485",
      "0.968588234"
    ],
    [
      "0.144638248",
      "0.968588234"
    ],
    [
      "0.268041187",
      "0.968588234"
    ],
    [
      "0.392839446",
      "0.968588234"
    ],
    [
      "0.518323835",
      "0.968588234"
    ],
    [
      "0.638806572",
      "0.968588234"
    ],
    [
      "0.701630105",
      "0.968588234"
    ],
    [
      "0.826385584",
      "0.968588234"
    ],
    [
      "0.889209117",
      "0.968588234"
    ]
  ],
  "radius": "0.031411765"
}

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。