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 | [0.0628831450905, 0.0628831450915] | 见来源署名 | packomania.com ↗ |
| 本站纪录 | 暂无选手纪录 | — | — |
当前展示：起步布局
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。
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": [
[
"1.03601014",
"0.063575273"
],
[
"0.90771934",
"0.067508062"
],
[
"1.161075992",
"0.076830176"
],
[
"0.782962027",
"0.088362727"
],
[
"1.344716859",
"0.128588337"
],
[
"0.613192931",
"0.146437881"
],
[
"0.98007962",
"0.176220453"
],
[
"1.23066432",
"0.181590017"
],
[
"1.105145472",
"0.189475356"
],
[
"0.855220508",
"0.191298977"
],
[
"0.726605539",
"0.200795401"
],
[
"0.502381761",
"0.205919344"
],
[
"1.413968071",
"0.233571332"
],
[
"1.539733872",
"0.233922101"
],
[
"0.400533259",
"0.279703098"
],
[
"1.299915533",
"0.286573012"
],
[
"1.174396685",
"0.294458351"
],
[
"1.03737664",
"0.295683222"
],
[
"0.911720734",
"0.303659487"
],
[
"0.786201886",
"0.311544826"
],
[
"1.637453444",
"0.313093087"
],
[
"0.660332531",
"0.314019028"
],
[
"0.535107412",
"0.327353242"
],
[
"1.48768447",
"0.34841236"
],
[
"1.369511157",
"0.391449879"
],
[
"0.360325984",
"0.398869095"
],
[
"1.243985012",
"0.399218193"
],
[
"1.106829434",
"0.400532977"
],
[
"1.723691758",
"0.404636045"
],
[
"0.981310586",
"0.408418316"
],
[
"0.855790214",
"0.416304667"
],
[
"0.730271366",
"0.424190006"
],
[
"1.585404041",
"0.427583347"
],
[
"0.604752518",
"0.432075345"
],
[
"0.479176892",
"0.439998422"
],
[
"0.243885243",
"0.44639502"
],
[
"1.46798017",
"0.472625485"
],
[
"1.314331349",
"0.504464694"
],
[
"1.176417761",
"0.505292819"
],
[
"1.796895564",
"0.50690218"
],
[
"1.050898913",
"0.513178158"
],
[
"1.671642355",
"0.519126304"
],
[
"0.925380065",
"0.521063497"
],
[
"0.799859694",
"0.528949848"
],
[
"0.674340846",
"0.536835186"
],
[
"0.548821998",
"0.544720525"
],
[
"0.423246371",
"0.552643603"
],
[
"0.297699327",
"0.560066494"
],
[
"0.170974454",
"0.567702267"
],
[
"1.553547007",
"0.569424931"
],
[
"1.411100614",
"0.584794446"
],
[
"1.246006089",
"0.61005266"
],
[
"1.120487241",
"0.617937999"
],
[
"1.855746379",
"0.618049566"
],
[
"0.994968393",
"0.625823338"
],
[
"0.869449545",
"0.633708677"
],
[
"0.743929174",
"0.641595028"
],
[
"1.680010931",
"0.64461386"
],
[
"0.618410326",
"0.649480367"
],
[
"0.492891478",
"0.657365706"
],
[
"0.367315851",
"0.665288783"
],
[
"0.241768807",
"0.672711675"
],
[
"0.116788491",
"0.686750211"
],
[
"1.566632112",
"0.699041824"
],
[
"1.441113265",
"0.706927163"
],
[
"1.315594417",
"0.714812502"
],
[
"1.781180008",
"0.719326493"
],
[
"1.190075569",
"0.722697841"
],
[
"1.064556721",
"0.73058318"
],
[
"0.939037873",
"0.738468519"
],
[
"0.813519025",
"0.746353857"
],
[
"0.687998654",
"0.754240208"
],
[
"1.904074681",
"0.755426044"
],
[
"0.562479806",
"0.762125547"
],
[
"0.436960958",
"0.770010886"
],
[
"0.311385331",
"0.777933963"
],
[
"1.656831316",
"0.786855906"
],
[
"0.186355477",
"0.791524226"
],
[
"1.510701592",
"0.811687005"
],
[
"1.385182744",
"0.819572343"
],
[
"1.259663897",
"0.827457682"
],
[
"1.134145049",
"0.835343021"
],
[
"1.812043888",
"0.84124688"
],
[
"1.008626201",
"0.84322836"
],
[
"0.074976423",
"0.849935408"
],
[
"0.883107353",
"0.851113699"
],
[
"0.757588505",
"0.858999038"
],
[
"0.632068133",
"0.866885389"
],
[
"0.506549286",
"0.874770728"
],
[
"0.381030438",
"0.882656066"
],
[
"1.930013897",
"0.884838584"
],
[
"0.256000583",
"0.896246329"
],
[
"1.705808768",
"0.908561507"
],
[
"1.58028992",
"0.916446846"
],
[
"1.454771072",
"0.924332185"
],
[
"1.329252224",
"0.932217524"
],
[
"1.203733376",
"0.940102863"
],
[
"1.078214528",
"0.947988202"
],
[
"0.952695681",
"0.95587354"
],
[
"0.827176833",
"0.963758879"
],
[
"1.817222505",
"0.966906506"
],
[
"0.701657985",
"0.971644218"
],
[
"0.063212675",
"0.975150319"
],
[
"0.576137613",
"0.979530569"
],
[
"0.450618765",
"0.987415908"
],
[
"0.325588911",
"1.001006171"
],
[
"0.200070063",
"1.00889151"
],
[
"1.937059062",
"1.010407391"
],
[
"1.649878248",
"1.021206688"
],
[
"1.5243594",
"1.029092026"
],
[
"1.398840552",
"1.036977365"
],
[
"1.273321704",
"1.044862704"
],
[
"1.147802856",
"1.052748043"
],
[
"1.022284008",
"1.060633382"
],
[
"0.89676516",
"1.068518721"
],
[
"0.771246312",
"1.07640406"
],
[
"0.645727465",
"1.084289398"
],
[
"1.840147727",
"1.09056569"
],
[
"0.520207093",
"1.092175749"
],
[
"0.106707205",
"1.09315619"
],
[
"0.395177239",
"1.105766012"
],
[
"0.268650822",
"1.114314098"
],
[
"1.719466575",
"1.125966529"
],
[
"1.593947728",
"1.133851868"
],
[
"1.46842888",
"1.141737207"
],
[
"1.342910032",
"1.149622546"
],
[
"1.217391184",
"1.157507885"
],
[
"1.091872336",
"1.165393223"
],
[
"0.966353488",
"1.173278562"
],
[
"0.84083464",
"1.181163901"
],
[
"0.715315792",
"1.18904924"
],
[
"1.917749471",
"1.189536035"
],
[
"0.589796944",
"1.196934579"
],
[
"0.46476709",
"1.210524842"
],
[
"0.088495995",
"1.217596986"
],
[
"0.339248357",
"1.218412006"
],
[
"1.797068319",
"1.224936874"
],
[
"0.213840031",
"1.227894181"
],
[
"1.666181277",
"1.239964282"
],
[
"1.538017207",
"1.246497048"
],
[
"1.41249836",
"1.254382387"
],
[
"1.286979512",
"1.262267726"
],
[
"1.161460664",
"1.270153065"
],
[
"1.035941816",
"1.278038404"
],
[
"0.910422968",
"1.285923743"
],
[
"0.78490412",
"1.293809081"
],
[
"0.659385272",
"1.30169442"
],
[
"1.880413098",
"1.319409624"
],
[
"0.502112603",
"1.33061844"
],
[
"0.125841508",
"1.337690584"
],
[
"0.37659387",
"1.338505604"
],
[
"1.753879303",
"1.343054902"
],
[
"0.251185545",
"1.34798778"
],
[
"1.607605535",
"1.35125689"
],
[
"1.482086687",
"1.359142229"
],
[
"1.356567839",
"1.367027568"
],
[
"1.231048991",
"1.374912906"
],
[
"1.105530144",
"1.382798245"
],
[
"0.980011296",
"1.390683584"
],
[
"0.854492448",
"1.398568923"
],
[
"0.7289736",
"1.406454262"
],
[
"0.598308259",
"1.411634214"
],
[
"0.446178448",
"1.443267936"
],
[
"1.823041652",
"1.448096462"
],
[
"1.686465856",
"1.449227342"
],
[
"0.178931605",
"1.451701993"
],
[
"0.304275642",
"1.461999189"
],
[
"1.551675015",
"1.46390207"
],
[
"1.426156167",
"1.471787409"
],
[
"1.300637319",
"1.479672748"
],
[
"1.175118471",
"1.487558087"
],
[
"1.049599623",
"1.495443426"
],
[
"0.924080775",
"1.503328764"
],
[
"0.798561928",
"1.511214103"
],
[
"0.667896587",
"1.516394055"
],
[
"0.542377739",
"1.524279394"
],
[
"1.755628205",
"1.554268901"
],
[
"0.38876092",
"1.555162473"
],
[
"1.630112938",
"1.562211032"
],
[
"1.49622556",
"1.57693012"
],
[
"0.265138503",
"1.58152092"
],
[
"1.370225647",
"1.584432589"
],
[
"1.244706799",
"1.592317928"
],
[
"1.119187951",
"1.600203267"
],
[
"0.993669103",
"1.608088606"
],
[
"0.868150255",
"1.615973945"
],
[
"0.737484914",
"1.621153897"
],
[
"0.610593224",
"1.62993832"
],
[
"0.48496021",
"1.63617393"
],
[
"0.349623782",
"1.674684203"
],
[
"1.636471932",
"1.687816457"
],
[
"1.439599987",
"1.689334261"
],
[
"1.314081139",
"1.6972196"
],
[
"1.188562291",
"1.705104939"
],
[
"1.063043443",
"1.712990278"
],
[
"0.937524595",
"1.720875616"
],
[
"0.807073242",
"1.725913738"
],
[
"0.681554394",
"1.733799077"
],
[
"0.445823072",
"1.755695661"
],
[
"1.538639409",
"1.766847825"
],
[
"0.567618165",
"1.787050326"
],
[
"1.132992804",
"1.817928659"
],
[
"1.305688017",
"1.822705516"
],
[
"1.007473956",
"1.825813998"
],
[
"0.876447582",
"1.83081541"
],
[
"1.43110538",
"1.832067396"
],
[
"0.659403677",
"1.873030437"
],
[
"0.779372393",
"1.910775197"
],
[
"1.216812956",
"1.911690815"
],
[
"1.073602859",
"1.933847816"
],
[
"0.946054542",
"1.935562872"
]
],
"radius": "0.062883144"
}{
"n": 211
}{
"centers": [
[
"1.03601014",
"0.063575273"
],
[
"0.90771934",
"0.067508062"
],
[
"1.161075992",
"0.076830176"
],
[
"0.782962027",
"0.088362727"
],
[
"1.344716859",
"0.128588337"
],
[
"0.613192931",
"0.146437881"
],
[
"0.98007962",
"0.176220453"
],
[
"1.23066432",
"0.181590017"
],
[
"1.105145472",
"0.189475356"
],
[
"0.855220508",
"0.191298977"
],
[
"0.726605539",
"0.200795401"
],
[
"0.502381761",
"0.205919344"
],
[
"1.413968071",
"0.233571332"
],
[
"1.539733872",
"0.233922101"
],
[
"0.400533259",
"0.279703098"
],
[
"1.299915533",
"0.286573012"
],
[
"1.174396685",
"0.294458351"
],
[
"1.03737664",
"0.295683222"
],
[
"0.911720734",
"0.303659487"
],
[
"0.786201886",
"0.311544826"
],
[
"1.637453444",
"0.313093087"
],
[
"0.660332531",
"0.314019028"
],
[
"0.535107412",
"0.327353242"
],
[
"1.48768447",
"0.34841236"
],
[
"1.369511157",
"0.391449879"
],
[
"0.360325984",
"0.398869095"
],
[
"1.243985012",
"0.399218193"
],
[
"1.106829434",
"0.400532977"
],
[
"1.723691758",
"0.404636045"
],
[
"0.981310586",
"0.408418316"
],
[
"0.855790214",
"0.416304667"
],
[
"0.730271366",
"0.424190006"
],
[
"1.585404041",
"0.427583347"
],
[
"0.604752518",
"0.432075345"
],
[
"0.479176892",
"0.439998422"
],
[
"0.243885243",
"0.44639502"
],
[
"1.46798017",
"0.472625485"
],
[
"1.314331349",
"0.504464694"
],
[
"1.176417761",
"0.505292819"
],
[
"1.796895564",
"0.50690218"
],
[
"1.050898913",
"0.513178158"
],
[
"1.671642355",
"0.519126304"
],
[
"0.925380065",
"0.521063497"
],
[
"0.799859694",
"0.528949848"
],
[
"0.674340846",
"0.536835186"
],
[
"0.548821998",
"0.544720525"
],
[
"0.423246371",
"0.552643603"
],
[
"0.297699327",
"0.560066494"
],
[
"0.170974454",
"0.567702267"
],
[
"1.553547007",
"0.569424931"
],
[
"1.411100614",
"0.584794446"
],
[
"1.246006089",
"0.61005266"
],
[
"1.120487241",
"0.617937999"
],
[
"1.855746379",
"0.618049566"
],
[
"0.994968393",
"0.625823338"
],
[
"0.869449545",
"0.633708677"
],
[
"0.743929174",
"0.641595028"
],
[
"1.680010931",
"0.64461386"
],
[
"0.618410326",
"0.649480367"
],
[
"0.492891478",
"0.657365706"
],
[
"0.367315851",
"0.665288783"
],
[
"0.241768807",
"0.672711675"
],
[
"0.116788491",
"0.686750211"
],
[
"1.566632112",
"0.699041824"
],
[
"1.441113265",
"0.706927163"
],
[
"1.315594417",
"0.714812502"
],
[
"1.781180008",
"0.719326493"
],
[
"1.190075569",
"0.722697841"
],
[
"1.064556721",
"0.73058318"
],
[
"0.939037873",
"0.738468519"
],
[
"0.813519025",
"0.746353857"
],
[
"0.687998654",
"0.754240208"
],
[
"1.904074681",
"0.755426044"
],
[
"0.562479806",
"0.762125547"
],
[
"0.436960958",
"0.770010886"
],
[
"0.311385331",
"0.777933963"
],
[
"1.656831316",
"0.786855906"
],
[
"0.186355477",
"0.791524226"
],
[
"1.510701592",
"0.811687005"
],
[
"1.385182744",
"0.819572343"
],
[
"1.259663897",
"0.827457682"
],
[
"1.134145049",
"0.835343021"
],
[
"1.812043888",
"0.84124688"
],
[
"1.008626201",
"0.84322836"
],
[
"0.074976423",
"0.849935408"
],
[
"0.883107353",
"0.851113699"
],
[
"0.757588505",
"0.858999038"
],
[
"0.632068133",
"0.866885389"
],
[
"0.506549286",
"0.874770728"
],
[
"0.381030438",
"0.882656066"
],
[
"1.930013897",
"0.884838584"
],
[
"0.256000583",
"0.896246329"
],
[
"1.705808768",
"0.908561507"
],
[
"1.58028992",
"0.916446846"
],
[
"1.454771072",
"0.924332185"
],
[
"1.329252224",
"0.932217524"
],
[
"1.203733376",
"0.940102863"
],
[
"1.078214528",
"0.947988202"
],
[
"0.952695681",
"0.95587354"
],
[
"0.827176833",
"0.963758879"
],
[
"1.817222505",
"0.966906506"
],
[
"0.701657985",
"0.971644218"
],
[
"0.063212675",
"0.975150319"
],
[
"0.576137613",
"0.979530569"
],
[
"0.450618765",
"0.987415908"
],
[
"0.325588911",
"1.001006171"
],
[
"0.200070063",
"1.00889151"
],
[
"1.937059062",
"1.010407391"
],
[
"1.649878248",
"1.021206688"
],
[
"1.5243594",
"1.029092026"
],
[
"1.398840552",
"1.036977365"
],
[
"1.273321704",
"1.044862704"
],
[
"1.147802856",
"1.052748043"
],
[
"1.022284008",
"1.060633382"
],
[
"0.89676516",
"1.068518721"
],
[
"0.771246312",
"1.07640406"
],
[
"0.645727465",
"1.084289398"
],
[
"1.840147727",
"1.09056569"
],
[
"0.520207093",
"1.092175749"
],
[
"0.106707205",
"1.09315619"
],
[
"0.395177239",
"1.105766012"
],
[
"0.268650822",
"1.114314098"
],
[
"1.719466575",
"1.125966529"
],
[
"1.593947728",
"1.133851868"
],
[
"1.46842888",
"1.141737207"
],
[
"1.342910032",
"1.149622546"
],
[
"1.217391184",
"1.157507885"
],
[
"1.091872336",
"1.165393223"
],
[
"0.966353488",
"1.173278562"
],
[
"0.84083464",
"1.181163901"
],
[
"0.715315792",
"1.18904924"
],
[
"1.917749471",
"1.189536035"
],
[
"0.589796944",
"1.196934579"
],
[
"0.46476709",
"1.210524842"
],
[
"0.088495995",
"1.217596986"
],
[
"0.339248357",
"1.218412006"
],
[
"1.797068319",
"1.224936874"
],
[
"0.213840031",
"1.227894181"
],
[
"1.666181277",
"1.239964282"
],
[
"1.538017207",
"1.246497048"
],
[
"1.41249836",
"1.254382387"
],
[
"1.286979512",
"1.262267726"
],
[
"1.161460664",
"1.270153065"
],
[
"1.035941816",
"1.278038404"
],
[
"0.910422968",
"1.285923743"
],
[
"0.78490412",
"1.293809081"
],
[
"0.659385272",
"1.30169442"
],
[
"1.880413098",
"1.319409624"
],
[
"0.502112603",
"1.33061844"
],
[
"0.125841508",
"1.337690584"
],
[
"0.37659387",
"1.338505604"
],
[
"1.753879303",
"1.343054902"
],
[
"0.251185545",
"1.34798778"
],
[
"1.607605535",
"1.35125689"
],
[
"1.482086687",
"1.359142229"
],
[
"1.356567839",
"1.367027568"
],
[
"1.231048991",
"1.374912906"
],
[
"1.105530144",
"1.382798245"
],
[
"0.980011296",
"1.390683584"
],
[
"0.854492448",
"1.398568923"
],
[
"0.7289736",
"1.406454262"
],
[
"0.598308259",
"1.411634214"
],
[
"0.446178448",
"1.443267936"
],
[
"1.823041652",
"1.448096462"
],
[
"1.686465856",
"1.449227342"
],
[
"0.178931605",
"1.451701993"
],
[
"0.304275642",
"1.461999189"
],
[
"1.551675015",
"1.46390207"
],
[
"1.426156167",
"1.471787409"
],
[
"1.300637319",
"1.479672748"
],
[
"1.175118471",
"1.487558087"
],
[
"1.049599623",
"1.495443426"
],
[
"0.924080775",
"1.503328764"
],
[
"0.798561928",
"1.511214103"
],
[
"0.667896587",
"1.516394055"
],
[
"0.542377739",
"1.524279394"
],
[
"1.755628205",
"1.554268901"
],
[
"0.38876092",
"1.555162473"
],
[
"1.630112938",
"1.562211032"
],
[
"1.49622556",
"1.57693012"
],
[
"0.265138503",
"1.58152092"
],
[
"1.370225647",
"1.584432589"
],
[
"1.244706799",
"1.592317928"
],
[
"1.119187951",
"1.600203267"
],
[
"0.993669103",
"1.608088606"
],
[
"0.868150255",
"1.615973945"
],
[
"0.737484914",
"1.621153897"
],
[
"0.610593224",
"1.62993832"
],
[
"0.48496021",
"1.63617393"
],
[
"0.349623782",
"1.674684203"
],
[
"1.636471932",
"1.687816457"
],
[
"1.439599987",
"1.689334261"
],
[
"1.314081139",
"1.6972196"
],
[
"1.188562291",
"1.705104939"
],
[
"1.063043443",
"1.712990278"
],
[
"0.937524595",
"1.720875616"
],
[
"0.807073242",
"1.725913738"
],
[
"0.681554394",
"1.733799077"
],
[
"0.445823072",
"1.755695661"
],
[
"1.538639409",
"1.766847825"
],
[
"0.567618165",
"1.787050326"
],
[
"1.132992804",
"1.817928659"
],
[
"1.305688017",
"1.822705516"
],
[
"1.007473956",
"1.825813998"
],
[
"0.876447582",
"1.83081541"
],
[
"1.43110538",
"1.832067396"
],
[
"0.659403677",
"1.873030437"
],
[
"0.779372393",
"1.910775197"
],
[
"1.216812956",
"1.911690815"
],
[
"1.073602859",
"1.933847816"
],
[
"0.946054542",
"1.935562872"
]
],
"radius": "0.062883144"
}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。