文献中也称circles in a circlepacking equal circles in a circlecci
在半径 1 的圆内放置 n 个半径相同、互不重叠的小圆，使共同半径尽可能大。
| 纪录 | 数值 / 区间 | 作者 / 持有人 | 来源 |
|---|---|---|---|
| 外部已知最好 | [0.0893107254930777188048861789945, 0.0893107254930777188048861789955] | 见来源署名 | packomania.com ↗ |
| 本站纪录 | 0.089310725 | Ἀθηνᾶ | 纪录详情 ↓ |
本站纪录尚未确认达到或超越此参考纪录。
当前展示：本站纪录
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。
查看构型、求解笔记与纪录历史。
纪录保持者还没有分享求解过程。
容器是半径 1 的圆，圆心在 (1, 1)，所以两个坐标都在 0 到 2 之间。坐标和半径用同一个单位，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 "0.2"。
{
"centers": [
[
"0.837330535",
"0.103956698"
],
[
"1.162669465",
"0.103956698"
],
[
"1.334442110",
"0.152944258"
],
[
"0.653339688",
"0.158397935"
],
[
"1.000000000",
"0.177741980"
],
[
"1.493348631",
"0.234518398"
],
[
"0.492451331",
"0.243858940"
],
[
"0.804149220",
"0.279469156"
],
[
"1.145234661",
"0.281725228"
],
[
"1.317007306",
"0.330712789"
],
[
"1.633275830",
"0.345540927"
],
[
"0.638602378",
"0.346550196"
],
[
"0.975043558",
"0.355947600"
],
[
"0.354620484",
"0.357473553"
],
[
"1.471267070",
"0.420765819"
],
[
"0.826358552",
"0.456704503"
],
[
"1.121185628",
"0.458720332"
],
[
"0.500771531",
"0.460164810"
],
[
"1.748840649",
"0.481740763"
],
[
"1.292958273",
"0.507707892"
],
[
"0.664346051",
"0.531921337"
],
[
"0.338762771",
"0.535389701"
],
[
"1.586831889",
"0.556965655"
],
[
"0.973082456",
"0.558575593"
],
[
"0.176754010",
"0.610614593"
],
[
"1.423606767",
"0.629513449"
],
[
"0.810491990",
"0.634619862"
],
[
"1.133611235",
"0.636909071"
],
[
"0.484913818",
"0.638080958"
],
[
"1.732982936",
"0.659656911"
],
[
"0.648484217",
"0.709846879"
],
[
"0.322905058",
"0.713305849"
],
[
"1.570974176",
"0.734881803"
],
[
"0.957215894",
"0.736490952"
],
[
"1.281266720",
"0.737425142"
],
[
"1.879133984",
"0.762348167"
],
[
"0.116583902",
"0.778796580"
],
[
"0.794636611",
"0.812536218"
],
[
"1.117744673",
"0.814824430"
],
[
"0.467345851",
"0.818389054"
],
[
"1.717125223",
"0.837573059"
],
[
"1.427037866",
"0.840654963"
],
[
"0.262734950",
"0.881487836"
],
[
"0.631970143",
"0.887703304"
],
[
"0.942348538",
"0.914492594"
],
[
"1.265030092",
"0.915881979"
],
[
"1.908611702",
"0.938520489"
],
[
"1.573194988",
"0.943354485"
],
[
"0.090399171",
"0.955488353"
],
[
"0.780760916",
"0.990617907"
],
[
"0.427183392",
"0.992436747"
],
[
"1.102877317",
"0.992826072"
],
[
"1.746602941",
"1.013745380"
],
[
"1.411182486",
"1.018571318"
],
[
"0.261876619",
"1.060107225"
],
[
"0.618748415",
"1.065834741"
],
[
"0.954774145",
"1.092681334"
],
[
"1.249597583",
"1.094702401"
],
[
"1.557328426",
"1.121269844"
],
[
"1.889587265",
"1.124724240"
],
[
"0.099207154",
"1.133892507"
],
[
"0.470645243",
"1.165690002"
],
[
"0.793186523",
"1.168806647"
],
[
"1.721923405",
"1.190653671"
],
[
"1.101494411",
"1.194557663"
],
[
"1.395743522",
"1.197400926"
],
[
"0.305338470",
"1.233360480"
],
[
"0.631174022",
"1.244023481"
],
[
"0.940333297",
"1.271581803"
],
[
"1.247640351",
"1.297256188"
],
[
"1.570210532",
"1.300386015"
],
[
"0.142669005",
"1.307145762"
],
[
"1.857330995",
"1.307145762"
],
[
"0.454807789",
"1.343614568"
],
[
"0.778325523",
"1.346808819"
],
[
"1.086763137",
"1.374871553"
],
[
"1.408169130",
"1.375589666"
],
[
"0.287903666",
"1.411129010"
],
[
"1.712096334",
"1.411129010"
],
[
"0.616313022",
"1.422025653"
],
[
"0.924477918",
"1.449498159"
],
[
"1.549426869",
"1.484914292"
],
[
"1.279858335",
"1.499855360"
],
[
"0.762458962",
"1.524724178"
],
[
"0.473927375",
"1.529877173"
],
[
"1.109047381",
"1.552097497"
],
[
"0.305338470",
"1.588897541"
],
[
"1.694661530",
"1.588897541"
],
[
"1.421116074",
"1.609179986"
],
[
"0.944112006",
"1.627037240"
],
[
"0.614794681",
"1.639704424"
],
[
"1.265997981",
"1.697746345"
],
[
"0.782103246",
"1.702262132"
],
[
"1.566350735",
"1.713163235"
],
[
"0.450054520",
"1.713373241"
],
[
"1.090263053",
"1.729728496"
],
[
"0.928254293",
"1.804953388"
],
[
"1.416252197",
"1.809993249"
],
[
"0.598936968",
"1.817620571"
],
[
"1.250140268",
"1.875662493"
],
[
"0.766245533",
"1.880178280"
],
[
"1.074405340",
"1.907644644"
]
],
"radius": "0.089310725"
}{
"n": 102
}{
"centers": [
[
"0.837330535",
"0.103956698"
],
[
"1.162669465",
"0.103956698"
],
[
"1.334442110",
"0.152944258"
],
[
"0.653339688",
"0.158397935"
],
[
"1.000000000",
"0.177741980"
],
[
"1.493348631",
"0.234518398"
],
[
"0.492451331",
"0.243858940"
],
[
"0.804149220",
"0.279469156"
],
[
"1.145234661",
"0.281725228"
],
[
"1.317007306",
"0.330712789"
],
[
"1.633275830",
"0.345540927"
],
[
"0.638602378",
"0.346550196"
],
[
"0.975043558",
"0.355947600"
],
[
"0.354620484",
"0.357473553"
],
[
"1.471267070",
"0.420765819"
],
[
"0.826358552",
"0.456704503"
],
[
"1.121185628",
"0.458720332"
],
[
"0.500771531",
"0.460164810"
],
[
"1.748840649",
"0.481740763"
],
[
"1.292958273",
"0.507707892"
],
[
"0.664346051",
"0.531921337"
],
[
"0.338762771",
"0.535389701"
],
[
"1.586831889",
"0.556965655"
],
[
"0.973082456",
"0.558575593"
],
[
"0.176754010",
"0.610614593"
],
[
"1.423606767",
"0.629513449"
],
[
"0.810491990",
"0.634619862"
],
[
"1.133611235",
"0.636909071"
],
[
"0.484913818",
"0.638080958"
],
[
"1.732982936",
"0.659656911"
],
[
"0.648484217",
"0.709846879"
],
[
"0.322905058",
"0.713305849"
],
[
"1.570974176",
"0.734881803"
],
[
"0.957215894",
"0.736490952"
],
[
"1.281266720",
"0.737425142"
],
[
"1.879133984",
"0.762348167"
],
[
"0.116583902",
"0.778796580"
],
[
"0.794636611",
"0.812536218"
],
[
"1.117744673",
"0.814824430"
],
[
"0.467345851",
"0.818389054"
],
[
"1.717125223",
"0.837573059"
],
[
"1.427037866",
"0.840654963"
],
[
"0.262734950",
"0.881487836"
],
[
"0.631970143",
"0.887703304"
],
[
"0.942348538",
"0.914492594"
],
[
"1.265030092",
"0.915881979"
],
[
"1.908611702",
"0.938520489"
],
[
"1.573194988",
"0.943354485"
],
[
"0.090399171",
"0.955488353"
],
[
"0.780760916",
"0.990617907"
],
[
"0.427183392",
"0.992436747"
],
[
"1.102877317",
"0.992826072"
],
[
"1.746602941",
"1.013745380"
],
[
"1.411182486",
"1.018571318"
],
[
"0.261876619",
"1.060107225"
],
[
"0.618748415",
"1.065834741"
],
[
"0.954774145",
"1.092681334"
],
[
"1.249597583",
"1.094702401"
],
[
"1.557328426",
"1.121269844"
],
[
"1.889587265",
"1.124724240"
],
[
"0.099207154",
"1.133892507"
],
[
"0.470645243",
"1.165690002"
],
[
"0.793186523",
"1.168806647"
],
[
"1.721923405",
"1.190653671"
],
[
"1.101494411",
"1.194557663"
],
[
"1.395743522",
"1.197400926"
],
[
"0.305338470",
"1.233360480"
],
[
"0.631174022",
"1.244023481"
],
[
"0.940333297",
"1.271581803"
],
[
"1.247640351",
"1.297256188"
],
[
"1.570210532",
"1.300386015"
],
[
"0.142669005",
"1.307145762"
],
[
"1.857330995",
"1.307145762"
],
[
"0.454807789",
"1.343614568"
],
[
"0.778325523",
"1.346808819"
],
[
"1.086763137",
"1.374871553"
],
[
"1.408169130",
"1.375589666"
],
[
"0.287903666",
"1.411129010"
],
[
"1.712096334",
"1.411129010"
],
[
"0.616313022",
"1.422025653"
],
[
"0.924477918",
"1.449498159"
],
[
"1.549426869",
"1.484914292"
],
[
"1.279858335",
"1.499855360"
],
[
"0.762458962",
"1.524724178"
],
[
"0.473927375",
"1.529877173"
],
[
"1.109047381",
"1.552097497"
],
[
"0.305338470",
"1.588897541"
],
[
"1.694661530",
"1.588897541"
],
[
"1.421116074",
"1.609179986"
],
[
"0.944112006",
"1.627037240"
],
[
"0.614794681",
"1.639704424"
],
[
"1.265997981",
"1.697746345"
],
[
"0.782103246",
"1.702262132"
],
[
"1.566350735",
"1.713163235"
],
[
"0.450054520",
"1.713373241"
],
[
"1.090263053",
"1.729728496"
],
[
"0.928254293",
"1.804953388"
],
[
"1.416252197",
"1.809993249"
],
[
"0.598936968",
"1.817620571"
],
[
"1.250140268",
"1.875662493"
],
[
"0.766245533",
"1.880178280"
],
[
"1.074405340",
"1.907644644"
]
],
"radius": "0.089310725"
}提交 radius 与 centers。每个数写成十进制字符串，例如 "0.2"。 · 验证器 v1.0.0
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。
还没有帖子。第一个聊聊这道题的思路？
按选手与子题分组，默认展示最新一篇。历史笔记及回复完整保留，点击笔记可查看和回复。笔记随纪录提交发布。