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 | [0.0618461505885, 0.0618461505895] | 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": [
[
"1.001062526",
"0.061870176"
],
[
"1.124622814",
"0.070160337"
],
[
"0.860281477",
"0.072308575"
],
[
"0.739449076",
"0.098753163"
],
[
"1.233196255",
"0.129419034"
],
[
"1.356853439",
"0.132366282"
],
[
"0.607359852",
"0.147974955"
],
[
"0.93796836",
"0.168561022"
],
[
"1.061407006",
"0.176478477"
],
[
"1.467897384",
"0.186855066"
],
[
"0.498508362",
"0.207132557"
],
[
"0.709230146",
"0.218697323"
],
[
"0.832139495",
"0.23259255"
],
[
"1.277953239",
"0.244729908"
],
[
"1.156026265",
"0.265709884"
],
[
"0.600332504",
"0.277358119"
],
[
"1.602347928",
"0.280757608"
],
[
"1.036282567",
"0.297592258"
],
[
"0.424608726",
"0.306322422"
],
[
"1.482096506",
"0.309729679"
],
[
"0.915447231",
"0.324023433"
],
[
"1.361261124",
"0.336160656"
],
[
"0.794611896",
"0.350454608"
],
[
"0.313470155",
"0.360617941"
],
[
"1.24042564",
"0.362591966"
],
[
"1.692987881",
"0.367873422"
],
[
"0.67377656",
"0.376885783"
],
[
"1.119590304",
"0.389023141"
],
[
"0.551252616",
"0.395878492"
],
[
"1.567312766",
"0.399384429"
],
[
"0.998754968",
"0.415454316"
],
[
"1.444568712",
"0.427591674"
],
[
"0.43205986",
"0.429790093"
],
[
"0.877919632",
"0.441885491"
],
[
"1.323733376",
"0.454022849"
],
[
"0.235320393",
"0.456494946"
],
[
"1.771972143",
"0.466903708"
],
[
"0.757084297",
"0.468316666"
],
[
"1.202898041",
"0.480454024"
],
[
"1.650614215",
"0.490821041"
],
[
"0.636248961",
"0.494747841"
],
[
"1.082062705",
"0.506885199"
],
[
"1.529778879",
"0.517252216"
],
[
"0.515413625",
"0.521179016"
],
[
"0.961227369",
"0.533316374"
],
[
"1.407041113",
"0.545453732"
],
[
"0.394532261",
"0.547652151"
],
[
"0.840392033",
"0.559747549"
],
[
"1.286205778",
"0.571884907"
],
[
"0.273696925",
"0.574083326"
],
[
"1.732006197",
"0.583961423"
],
[
"0.719556698",
"0.586178724"
],
[
"0.152338997",
"0.598000659"
],
[
"1.165370442",
"0.598316082"
],
[
"1.853028987",
"0.609520562"
],
[
"1.611170861",
"0.610392598"
],
[
"0.598721362",
"0.612609899"
],
[
"1.044535106",
"0.624747257"
],
[
"1.49034885",
"0.636884615"
],
[
"0.477886026",
"0.639041074"
],
[
"0.92369977",
"0.651178432"
],
[
"1.369513514",
"0.66331579"
],
[
"0.357004662",
"0.665514209"
],
[
"0.802864435",
"0.677609607"
],
[
"1.248678179",
"0.689746965"
],
[
"0.233730979",
"0.691141041"
],
[
"1.694478598",
"0.701823481"
],
[
"0.682029099",
"0.704040782"
],
[
"1.127842843",
"0.71617814"
],
[
"0.107337498",
"0.716974158"
],
[
"1.896986028",
"0.725138743"
],
[
"1.573656587",
"0.728315498"
],
[
"0.561193763",
"0.730471957"
],
[
"1.007007507",
"0.742609315"
],
[
"1.452821251",
"0.754746673"
],
[
"0.440358427",
"0.756903132"
],
[
"0.886172171",
"0.76904049"
],
[
"1.331985915",
"0.781177848"
],
[
"0.317038716",
"0.782571924"
],
[
"1.777786335",
"0.793254364"
],
[
"0.765336836",
"0.795471665"
],
[
"1.21115058",
"0.807609023"
],
[
"0.196195275",
"0.809000518"
],
[
"1.656964324",
"0.819746381"
],
[
"0.6445015",
"0.82190284"
],
[
"1.090315244",
"0.834040198"
],
[
"0.075943853",
"0.837972588"
],
[
"1.536128988",
"0.846177556"
],
[
"0.523666164",
"0.848334014"
],
[
"1.888438042",
"0.848535329"
],
[
"0.969479908",
"0.860471373"
],
[
"1.415293652",
"0.872608731"
],
[
"0.402830828",
"0.874765189"
],
[
"0.848644572",
"0.886902548"
],
[
"1.294458316",
"0.899039906"
],
[
"0.281995493",
"0.901196364"
],
[
"0.727809237",
"0.913333723"
],
[
"1.748540019",
"0.914062203"
],
[
"1.173622981",
"0.925471081"
],
[
"0.161160113",
"0.927627339"
],
[
"1.619436725",
"0.937608439"
],
[
"0.606973901",
"0.939764897"
],
[
"1.052787645",
"0.951902256"
],
[
"1.937389166",
"0.962129223"
],
[
"1.498601389",
"0.964039614"
],
[
"0.486138565",
"0.966196072"
],
[
"0.931952309",
"0.978333431"
],
[
"1.377766053",
"0.990470789"
],
[
"0.365303229",
"0.992627247"
],
[
"0.061847138",
"1.001361446"
],
[
"0.811116973",
"1.004764606"
],
[
"1.825659975",
"1.015198736"
],
[
"1.256930717",
"1.016901964"
],
[
"0.244467702",
"1.019058361"
],
[
"1.702744461",
"1.029039322"
],
[
"0.690281638",
"1.03119578"
],
[
"1.136095382",
"1.043333139"
],
[
"1.581909126",
"1.055470497"
],
[
"0.569446302",
"1.057626955"
],
[
"1.015260046",
"1.069764314"
],
[
"1.46107379",
"1.081901672"
],
[
"0.448610966",
"1.08405813"
],
[
"1.934096772",
"1.085923812"
],
[
"0.89442471",
"1.096195489"
],
[
"1.340238454",
"1.108332847"
],
[
"0.32777563",
"1.110489305"
],
[
"0.773589374",
"1.122626663"
],
[
"0.07018044",
"1.124772715"
],
[
"1.219403118",
"1.134764022"
],
[
"0.206940295",
"1.13692048"
],
[
"1.822012893",
"1.138837258"
],
[
"1.665216862",
"1.14690138"
],
[
"0.652754039",
"1.149057838"
],
[
"1.098567783",
"1.161195197"
],
[
"1.544381527",
"1.173332555"
],
[
"0.531918703",
"1.175489013"
],
[
"0.977732447",
"1.187626371"
],
[
"1.423546191",
"1.19976373"
],
[
"0.411083367",
"1.201920188"
],
[
"0.856897111",
"1.214057546"
],
[
"1.910778118",
"1.2249797"
],
[
"1.302710855",
"1.226194905"
],
[
"0.284943415",
"1.233095965"
],
[
"0.12945664",
"1.233336602"
],
[
"1.748524599",
"1.238332263"
],
[
"0.736061776",
"1.240488721"
],
[
"1.18187552",
"1.25262608"
],
[
"1.627689264",
"1.264763438"
],
[
"0.61522644",
"1.266919896"
],
[
"1.061040184",
"1.279057254"
],
[
"1.506853928",
"1.291194613"
],
[
"0.494391104",
"1.293351071"
],
[
"0.940204848",
"1.305488429"
],
[
"1.386018592",
"1.317625788"
],
[
"0.373555768",
"1.319782246"
],
[
"0.819369512",
"1.331919604"
],
[
"1.873263602",
"1.342845922"
],
[
"1.265183256",
"1.344056963"
],
[
"0.132423823",
"1.356993309"
],
[
"0.698534177",
"1.358350779"
],
[
"0.256105938",
"1.358580734"
],
[
"1.751063096",
"1.361998513"
],
[
"1.144347921",
"1.370488137"
],
[
"1.590161665",
"1.382625496"
],
[
"0.577698841",
"1.384781954"
],
[
"1.023512585",
"1.396919312"
],
[
"1.469326329",
"1.409056671"
],
[
"0.456863505",
"1.411213129"
],
[
"0.902677249",
"1.423350487"
],
[
"1.348490993",
"1.435487846"
],
[
"0.781841913",
"1.449781662"
],
[
"1.227655657",
"1.46191902"
],
[
"1.682487056",
"1.464940789"
],
[
"0.187062517",
"1.468125678"
],
[
"0.310968544",
"1.469440465"
],
[
"1.81192963",
"1.469982168"
],
[
"0.661006578",
"1.476212837"
],
[
"1.106820322",
"1.488350195"
],
[
"1.557261409",
"1.50193101"
],
[
"0.540171242",
"1.502644012"
],
[
"0.985984986",
"1.51478137"
],
[
"1.43179873",
"1.526918729"
],
[
"0.419335906",
"1.529075187"
],
[
"0.86514965",
"1.541212545"
],
[
"1.310963394",
"1.553349903"
],
[
"0.744314314",
"1.56764372"
],
[
"1.742953363",
"1.572846354"
],
[
"1.190128058",
"1.579781078"
],
[
"0.266454921",
"1.584845502"
],
[
"0.623478979",
"1.594074895"
],
[
"1.069292723",
"1.606212253"
],
[
"1.515106467",
"1.618349611"
],
[
"0.948457387",
"1.632643428"
],
[
"1.637347105",
"1.637244364"
],
[
"0.468756961",
"1.642465419"
],
[
"1.394271174",
"1.644780983"
],
[
"0.827622051",
"1.659074603"
],
[
"1.273435795",
"1.671211961"
],
[
"0.349772806",
"1.676267137"
],
[
"0.69867493",
"1.692912389"
],
[
"1.153182405",
"1.70017586"
],
[
"0.574007521",
"1.707443146"
],
[
"1.031824477",
"1.724093193"
],
[
"1.572966121",
"1.742861003"
],
[
"0.910989141",
"1.750524368"
],
[
"1.356743381",
"1.762642982"
],
[
"0.458252582",
"1.765862823"
],
[
"0.790153806",
"1.776955543"
],
[
"1.236491959",
"1.791615053"
],
[
"1.470255477",
"1.811783488"
],
[
"1.115654806",
"1.818037918"
],
[
"0.564102472",
"1.83073822"
],
[
"0.994296878",
"1.841955251"
],
[
"0.686953232",
"1.84514225"
],
[
"1.321708219",
"1.881269804"
],
[
"1.198529974",
"1.911711851"
],
[
"0.789543817",
"1.914243316"
],
[
"0.91165062",
"1.933984492"
],
[
"1.07568886",
"1.935095632"
]
],
"radius": "0.06184615"
}{
"n": 219
}{
"centers": [
[
"1.001062526",
"0.061870176"
],
[
"1.124622814",
"0.070160337"
],
[
"0.860281477",
"0.072308575"
],
[
"0.739449076",
"0.098753163"
],
[
"1.233196255",
"0.129419034"
],
[
"1.356853439",
"0.132366282"
],
[
"0.607359852",
"0.147974955"
],
[
"0.93796836",
"0.168561022"
],
[
"1.061407006",
"0.176478477"
],
[
"1.467897384",
"0.186855066"
],
[
"0.498508362",
"0.207132557"
],
[
"0.709230146",
"0.218697323"
],
[
"0.832139495",
"0.23259255"
],
[
"1.277953239",
"0.244729908"
],
[
"1.156026265",
"0.265709884"
],
[
"0.600332504",
"0.277358119"
],
[
"1.602347928",
"0.280757608"
],
[
"1.036282567",
"0.297592258"
],
[
"0.424608726",
"0.306322422"
],
[
"1.482096506",
"0.309729679"
],
[
"0.915447231",
"0.324023433"
],
[
"1.361261124",
"0.336160656"
],
[
"0.794611896",
"0.350454608"
],
[
"0.313470155",
"0.360617941"
],
[
"1.24042564",
"0.362591966"
],
[
"1.692987881",
"0.367873422"
],
[
"0.67377656",
"0.376885783"
],
[
"1.119590304",
"0.389023141"
],
[
"0.551252616",
"0.395878492"
],
[
"1.567312766",
"0.399384429"
],
[
"0.998754968",
"0.415454316"
],
[
"1.444568712",
"0.427591674"
],
[
"0.43205986",
"0.429790093"
],
[
"0.877919632",
"0.441885491"
],
[
"1.323733376",
"0.454022849"
],
[
"0.235320393",
"0.456494946"
],
[
"1.771972143",
"0.466903708"
],
[
"0.757084297",
"0.468316666"
],
[
"1.202898041",
"0.480454024"
],
[
"1.650614215",
"0.490821041"
],
[
"0.636248961",
"0.494747841"
],
[
"1.082062705",
"0.506885199"
],
[
"1.529778879",
"0.517252216"
],
[
"0.515413625",
"0.521179016"
],
[
"0.961227369",
"0.533316374"
],
[
"1.407041113",
"0.545453732"
],
[
"0.394532261",
"0.547652151"
],
[
"0.840392033",
"0.559747549"
],
[
"1.286205778",
"0.571884907"
],
[
"0.273696925",
"0.574083326"
],
[
"1.732006197",
"0.583961423"
],
[
"0.719556698",
"0.586178724"
],
[
"0.152338997",
"0.598000659"
],
[
"1.165370442",
"0.598316082"
],
[
"1.853028987",
"0.609520562"
],
[
"1.611170861",
"0.610392598"
],
[
"0.598721362",
"0.612609899"
],
[
"1.044535106",
"0.624747257"
],
[
"1.49034885",
"0.636884615"
],
[
"0.477886026",
"0.639041074"
],
[
"0.92369977",
"0.651178432"
],
[
"1.369513514",
"0.66331579"
],
[
"0.357004662",
"0.665514209"
],
[
"0.802864435",
"0.677609607"
],
[
"1.248678179",
"0.689746965"
],
[
"0.233730979",
"0.691141041"
],
[
"1.694478598",
"0.701823481"
],
[
"0.682029099",
"0.704040782"
],
[
"1.127842843",
"0.71617814"
],
[
"0.107337498",
"0.716974158"
],
[
"1.896986028",
"0.725138743"
],
[
"1.573656587",
"0.728315498"
],
[
"0.561193763",
"0.730471957"
],
[
"1.007007507",
"0.742609315"
],
[
"1.452821251",
"0.754746673"
],
[
"0.440358427",
"0.756903132"
],
[
"0.886172171",
"0.76904049"
],
[
"1.331985915",
"0.781177848"
],
[
"0.317038716",
"0.782571924"
],
[
"1.777786335",
"0.793254364"
],
[
"0.765336836",
"0.795471665"
],
[
"1.21115058",
"0.807609023"
],
[
"0.196195275",
"0.809000518"
],
[
"1.656964324",
"0.819746381"
],
[
"0.6445015",
"0.82190284"
],
[
"1.090315244",
"0.834040198"
],
[
"0.075943853",
"0.837972588"
],
[
"1.536128988",
"0.846177556"
],
[
"0.523666164",
"0.848334014"
],
[
"1.888438042",
"0.848535329"
],
[
"0.969479908",
"0.860471373"
],
[
"1.415293652",
"0.872608731"
],
[
"0.402830828",
"0.874765189"
],
[
"0.848644572",
"0.886902548"
],
[
"1.294458316",
"0.899039906"
],
[
"0.281995493",
"0.901196364"
],
[
"0.727809237",
"0.913333723"
],
[
"1.748540019",
"0.914062203"
],
[
"1.173622981",
"0.925471081"
],
[
"0.161160113",
"0.927627339"
],
[
"1.619436725",
"0.937608439"
],
[
"0.606973901",
"0.939764897"
],
[
"1.052787645",
"0.951902256"
],
[
"1.937389166",
"0.962129223"
],
[
"1.498601389",
"0.964039614"
],
[
"0.486138565",
"0.966196072"
],
[
"0.931952309",
"0.978333431"
],
[
"1.377766053",
"0.990470789"
],
[
"0.365303229",
"0.992627247"
],
[
"0.061847138",
"1.001361446"
],
[
"0.811116973",
"1.004764606"
],
[
"1.825659975",
"1.015198736"
],
[
"1.256930717",
"1.016901964"
],
[
"0.244467702",
"1.019058361"
],
[
"1.702744461",
"1.029039322"
],
[
"0.690281638",
"1.03119578"
],
[
"1.136095382",
"1.043333139"
],
[
"1.581909126",
"1.055470497"
],
[
"0.569446302",
"1.057626955"
],
[
"1.015260046",
"1.069764314"
],
[
"1.46107379",
"1.081901672"
],
[
"0.448610966",
"1.08405813"
],
[
"1.934096772",
"1.085923812"
],
[
"0.89442471",
"1.096195489"
],
[
"1.340238454",
"1.108332847"
],
[
"0.32777563",
"1.110489305"
],
[
"0.773589374",
"1.122626663"
],
[
"0.07018044",
"1.124772715"
],
[
"1.219403118",
"1.134764022"
],
[
"0.206940295",
"1.13692048"
],
[
"1.822012893",
"1.138837258"
],
[
"1.665216862",
"1.14690138"
],
[
"0.652754039",
"1.149057838"
],
[
"1.098567783",
"1.161195197"
],
[
"1.544381527",
"1.173332555"
],
[
"0.531918703",
"1.175489013"
],
[
"0.977732447",
"1.187626371"
],
[
"1.423546191",
"1.19976373"
],
[
"0.411083367",
"1.201920188"
],
[
"0.856897111",
"1.214057546"
],
[
"1.910778118",
"1.2249797"
],
[
"1.302710855",
"1.226194905"
],
[
"0.284943415",
"1.233095965"
],
[
"0.12945664",
"1.233336602"
],
[
"1.748524599",
"1.238332263"
],
[
"0.736061776",
"1.240488721"
],
[
"1.18187552",
"1.25262608"
],
[
"1.627689264",
"1.264763438"
],
[
"0.61522644",
"1.266919896"
],
[
"1.061040184",
"1.279057254"
],
[
"1.506853928",
"1.291194613"
],
[
"0.494391104",
"1.293351071"
],
[
"0.940204848",
"1.305488429"
],
[
"1.386018592",
"1.317625788"
],
[
"0.373555768",
"1.319782246"
],
[
"0.819369512",
"1.331919604"
],
[
"1.873263602",
"1.342845922"
],
[
"1.265183256",
"1.344056963"
],
[
"0.132423823",
"1.356993309"
],
[
"0.698534177",
"1.358350779"
],
[
"0.256105938",
"1.358580734"
],
[
"1.751063096",
"1.361998513"
],
[
"1.144347921",
"1.370488137"
],
[
"1.590161665",
"1.382625496"
],
[
"0.577698841",
"1.384781954"
],
[
"1.023512585",
"1.396919312"
],
[
"1.469326329",
"1.409056671"
],
[
"0.456863505",
"1.411213129"
],
[
"0.902677249",
"1.423350487"
],
[
"1.348490993",
"1.435487846"
],
[
"0.781841913",
"1.449781662"
],
[
"1.227655657",
"1.46191902"
],
[
"1.682487056",
"1.464940789"
],
[
"0.187062517",
"1.468125678"
],
[
"0.310968544",
"1.469440465"
],
[
"1.81192963",
"1.469982168"
],
[
"0.661006578",
"1.476212837"
],
[
"1.106820322",
"1.488350195"
],
[
"1.557261409",
"1.50193101"
],
[
"0.540171242",
"1.502644012"
],
[
"0.985984986",
"1.51478137"
],
[
"1.43179873",
"1.526918729"
],
[
"0.419335906",
"1.529075187"
],
[
"0.86514965",
"1.541212545"
],
[
"1.310963394",
"1.553349903"
],
[
"0.744314314",
"1.56764372"
],
[
"1.742953363",
"1.572846354"
],
[
"1.190128058",
"1.579781078"
],
[
"0.266454921",
"1.584845502"
],
[
"0.623478979",
"1.594074895"
],
[
"1.069292723",
"1.606212253"
],
[
"1.515106467",
"1.618349611"
],
[
"0.948457387",
"1.632643428"
],
[
"1.637347105",
"1.637244364"
],
[
"0.468756961",
"1.642465419"
],
[
"1.394271174",
"1.644780983"
],
[
"0.827622051",
"1.659074603"
],
[
"1.273435795",
"1.671211961"
],
[
"0.349772806",
"1.676267137"
],
[
"0.69867493",
"1.692912389"
],
[
"1.153182405",
"1.70017586"
],
[
"0.574007521",
"1.707443146"
],
[
"1.031824477",
"1.724093193"
],
[
"1.572966121",
"1.742861003"
],
[
"0.910989141",
"1.750524368"
],
[
"1.356743381",
"1.762642982"
],
[
"0.458252582",
"1.765862823"
],
[
"0.790153806",
"1.776955543"
],
[
"1.236491959",
"1.791615053"
],
[
"1.470255477",
"1.811783488"
],
[
"1.115654806",
"1.818037918"
],
[
"0.564102472",
"1.83073822"
],
[
"0.994296878",
"1.841955251"
],
[
"0.686953232",
"1.84514225"
],
[
"1.321708219",
"1.881269804"
],
[
"1.198529974",
"1.911711851"
],
[
"0.789543817",
"1.914243316"
],
[
"0.91165062",
"1.933984492"
],
[
"1.07568886",
"1.935095632"
]
],
"radius": "0.06184615"
}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。