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。
| 纪录 | 数值 / 区间 | 作者 / 持有人 | 来源 |
|---|---|---|---|
| 外部已知最好 | [0.0348569688405, 0.0348569688415] | 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。
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
查看构型、求解笔记与纪录历史。
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"。
{
"centers": [
[
"0.034856969",
"0.034856969"
],
[
"0.155605051",
"0.034856969"
],
[
"0.276353133",
"0.034856969"
],
[
"0.397101215",
"0.034856969"
],
[
"0.517953587",
"0.034856969"
],
[
"0.638701669",
"0.034856969"
],
[
"0.759449751",
"0.034856969"
],
[
"0.880197833",
"0.034856969"
],
[
"0.964925175",
"0.063263502"
],
[
"0.457527401",
"0.069623464"
],
[
"0.09523101",
"0.069713938"
],
[
"0.215979092",
"0.069713938"
],
[
"0.336727174",
"0.069713938"
],
[
"0.578327628",
"0.069713938"
],
[
"0.69907571",
"0.069713938"
],
[
"0.819823792",
"0.069713938"
],
[
"0.90476899",
"0.100097228"
],
[
"0.034856969",
"0.104570907"
],
[
"0.155605051",
"0.104570907"
],
[
"0.276353133",
"0.104570907"
],
[
"0.397101215",
"0.104570907"
],
[
"0.517953587",
"0.104570907"
],
[
"0.638701669",
"0.104570907"
],
[
"0.759449751",
"0.104570907"
],
[
"0.844394949",
"0.134954196"
],
[
"0.965143031",
"0.134954196"
],
[
"0.457527401",
"0.139337401"
],
[
"0.09523101",
"0.139427875"
],
[
"0.215979092",
"0.139427875"
],
[
"0.336727174",
"0.139427875"
],
[
"0.578327628",
"0.139427875"
],
[
"0.69907571",
"0.139427875"
],
[
"0.784020908",
"0.169811165"
],
[
"0.90476899",
"0.169811165"
],
[
"0.034856969",
"0.174284844"
],
[
"0.155605051",
"0.174284844"
],
[
"0.276353133",
"0.174284844"
],
[
"0.397101215",
"0.174284844"
],
[
"0.517953587",
"0.174284844"
],
[
"0.638701669",
"0.174284844"
],
[
"0.723646867",
"0.204668134"
],
[
"0.844394949",
"0.204668134"
],
[
"0.965143031",
"0.204668134"
],
[
"0.457527401",
"0.209051339"
],
[
"0.09523101",
"0.209141813"
],
[
"0.215979092",
"0.209141813"
],
[
"0.336727174",
"0.209141813"
],
[
"0.578327628",
"0.209141813"
],
[
"0.663272826",
"0.239525103"
],
[
"0.784020908",
"0.239525103"
],
[
"0.90476899",
"0.239525103"
],
[
"0.034856969",
"0.243998782"
],
[
"0.155605051",
"0.243998782"
],
[
"0.276353133",
"0.243998782"
],
[
"0.397101215",
"0.243998782"
],
[
"0.517953587",
"0.243998782"
],
[
"0.602898785",
"0.274382072"
],
[
"0.723646867",
"0.274382072"
],
[
"0.844394949",
"0.274382072"
],
[
"0.965143031",
"0.274382072"
],
[
"0.457527401",
"0.278765277"
],
[
"0.09523101",
"0.278855751"
],
[
"0.215979092",
"0.278855751"
],
[
"0.336727174",
"0.278855751"
],
[
"0.542524744",
"0.309239041"
],
[
"0.663272826",
"0.309239041"
],
[
"0.784020908",
"0.309239041"
],
[
"0.90476899",
"0.309239041"
],
[
"0.034856969",
"0.31371272"
],
[
"0.155605051",
"0.31371272"
],
[
"0.276353133",
"0.31371272"
],
[
"0.397101215",
"0.31371272"
],
[
"0.602898785",
"0.344096009"
],
[
"0.723646867",
"0.344096009"
],
[
"0.844394949",
"0.344096009"
],
[
"0.965143031",
"0.344096009"
],
[
"0.457527401",
"0.348479214"
],
[
"0.09523101",
"0.348569688"
],
[
"0.215979092",
"0.348569688"
],
[
"0.336727174",
"0.348569688"
],
[
"0.521680235",
"0.37576377"
],
[
"0.663272826",
"0.378952978"
],
[
"0.784020908",
"0.378952978"
],
[
"0.90476899",
"0.378952978"
],
[
"0.034856969",
"0.383426657"
],
[
"0.155605051",
"0.383426657"
],
[
"0.276353133",
"0.383426657"
],
[
"0.397101215",
"0.383426657"
],
[
"0.582054276",
"0.410620738"
],
[
"0.723646867",
"0.413809947"
],
[
"0.844394949",
"0.413809947"
],
[
"0.965143031",
"0.413809947"
],
[
"0.457527401",
"0.418193152"
],
[
"0.09523101",
"0.418283626"
],
[
"0.215979092",
"0.418283626"
],
[
"0.336727174",
"0.418283626"
],
[
"0.521680235",
"0.445477707"
],
[
"0.642428317",
"0.445477707"
],
[
"0.784020908",
"0.448666916"
],
[
"0.90476899",
"0.448666916"
],
[
"0.034856969",
"0.453140595"
],
[
"0.155605051",
"0.453140595"
],
[
"0.276353133",
"0.453140595"
],
[
"0.397101215",
"0.453140595"
],
[
"0.582054276",
"0.480334676"
],
[
"0.702802358",
"0.480334676"
],
[
"0.844394949",
"0.483523885"
],
[
"0.965143031",
"0.483523885"
],
[
"0.457527401",
"0.48790709"
],
[
"0.09523101",
"0.487997564"
],
[
"0.215979092",
"0.487997564"
],
[
"0.336727174",
"0.487997564"
],
[
"0.642428317",
"0.515191645"
],
[
"0.763176399",
"0.515191645"
],
[
"0.521680235",
"0.515191645"
],
[
"0.90476899",
"0.518380854"
],
[
"0.034856969",
"0.522854533"
],
[
"0.155605051",
"0.522854533"
],
[
"0.276353133",
"0.522854533"
],
[
"0.397101215",
"0.522854533"
],
[
"0.582054276",
"0.550048614"
],
[
"0.702802358",
"0.550048614"
],
[
"0.82355044",
"0.550048614"
],
[
"0.965143031",
"0.553237822"
],
[
"0.457527401",
"0.557621027"
],
[
"0.09523101",
"0.557711501"
],
[
"0.215979092",
"0.557711501"
],
[
"0.336727174",
"0.557711501"
],
[
"0.521680235",
"0.584905583"
],
[
"0.642428317",
"0.584905583"
],
[
"0.763176399",
"0.584905583"
],
[
"0.883924482",
"0.584905583"
],
[
"0.034856969",
"0.59256847"
],
[
"0.155605051",
"0.59256847"
],
[
"0.276353133",
"0.59256847"
],
[
"0.397101215",
"0.59256847"
],
[
"0.582054276",
"0.619762551"
],
[
"0.702802358",
"0.619762551"
],
[
"0.82355044",
"0.619762551"
],
[
"0.944298523",
"0.619762551"
],
[
"0.457527401",
"0.627334965"
],
[
"0.09523101",
"0.627425439"
],
[
"0.215979092",
"0.627425439"
],
[
"0.336727174",
"0.627425439"
],
[
"0.521680235",
"0.65461952"
],
[
"0.642428317",
"0.65461952"
],
[
"0.763176399",
"0.65461952"
],
[
"0.883924482",
"0.65461952"
],
[
"0.034856969",
"0.662282408"
],
[
"0.155605051",
"0.662282408"
],
[
"0.276353133",
"0.662282408"
],
[
"0.397101215",
"0.662282408"
],
[
"0.965143031",
"0.68628728"
],
[
"0.582054276",
"0.689476489"
],
[
"0.702802358",
"0.689476489"
],
[
"0.82355044",
"0.689476489"
],
[
"0.457527401",
"0.697048903"
],
[
"0.09523101",
"0.697139377"
],
[
"0.215979092",
"0.697139377"
],
[
"0.336727174",
"0.697139377"
],
[
"0.90476899",
"0.721144249"
],
[
"0.521680235",
"0.724333458"
],
[
"0.642428317",
"0.724333458"
],
[
"0.763176399",
"0.724333458"
],
[
"0.034856969",
"0.731996346"
],
[
"0.155605051",
"0.731996346"
],
[
"0.276353133",
"0.731996346"
],
[
"0.397101215",
"0.731996346"
],
[
"0.844394949",
"0.756001218"
],
[
"0.965143031",
"0.756001218"
],
[
"0.582054276",
"0.759190427"
],
[
"0.702802358",
"0.759190427"
],
[
"0.457527401",
"0.76676284"
],
[
"0.09523101",
"0.766853315"
],
[
"0.215979092",
"0.766853315"
],
[
"0.336727174",
"0.766853315"
],
[
"0.784020908",
"0.790858187"
],
[
"0.90476899",
"0.790858187"
],
[
"0.521680235",
"0.794047396"
],
[
"0.642428317",
"0.794047396"
],
[
"0.034856969",
"0.801710283"
],
[
"0.155605051",
"0.801710283"
],
[
"0.276353133",
"0.801710283"
],
[
"0.397101215",
"0.801710283"
],
[
"0.723646867",
"0.825715156"
],
[
"0.844394949",
"0.825715156"
],
[
"0.965143031",
"0.825715156"
],
[
"0.582054276",
"0.828904364"
],
[
"0.457527401",
"0.836476778"
],
[
"0.09523101",
"0.836567252"
],
[
"0.215979092",
"0.836567252"
],
[
"0.336727174",
"0.836567252"
],
[
"0.663272826",
"0.860572125"
],
[
"0.784020908",
"0.860572125"
],
[
"0.90476899",
"0.860572125"
],
[
"0.521680235",
"0.863761333"
],
[
"0.034856969",
"0.871424221"
],
[
"0.163542321",
"0.885304726"
],
[
"0.602898785",
"0.895429093"
],
[
"0.723646867",
"0.895429093"
],
[
"0.844394949",
"0.895429093"
],
[
"0.965143031",
"0.895429093"
],
[
"0.376820764",
"0.895586812"
],
[
"0.304596686",
"0.898435377"
],
[
"0.235075413",
"0.903614725"
],
[
"0.446395981",
"0.905296285"
],
[
"0.09523101",
"0.90628119"
],
[
"0.542524744",
"0.930286062"
],
[
"0.663272826",
"0.930286062"
],
[
"0.784020908",
"0.930286062"
],
[
"0.90476899",
"0.930286062"
],
[
"0.341327042",
"0.957688344"
],
[
"0.038827571",
"0.964282237"
],
[
"0.132584949",
"0.965143031"
],
[
"0.202298886",
"0.965143031"
],
[
"0.272012824",
"0.965143031"
],
[
"0.410641259",
"0.965143031"
],
[
"0.482150703",
"0.965143031"
],
[
"0.602898785",
"0.965143031"
],
[
"0.723646867",
"0.965143031"
],
[
"0.844394949",
"0.965143031"
],
[
"0.965143031",
"0.965143031"
]
],
"radius": "0.034856968"
}{
"n": 222
}{
"centers": [
[
"0.034856969",
"0.034856969"
],
[
"0.155605051",
"0.034856969"
],
[
"0.276353133",
"0.034856969"
],
[
"0.397101215",
"0.034856969"
],
[
"0.517953587",
"0.034856969"
],
[
"0.638701669",
"0.034856969"
],
[
"0.759449751",
"0.034856969"
],
[
"0.880197833",
"0.034856969"
],
[
"0.964925175",
"0.063263502"
],
[
"0.457527401",
"0.069623464"
],
[
"0.09523101",
"0.069713938"
],
[
"0.215979092",
"0.069713938"
],
[
"0.336727174",
"0.069713938"
],
[
"0.578327628",
"0.069713938"
],
[
"0.69907571",
"0.069713938"
],
[
"0.819823792",
"0.069713938"
],
[
"0.90476899",
"0.100097228"
],
[
"0.034856969",
"0.104570907"
],
[
"0.155605051",
"0.104570907"
],
[
"0.276353133",
"0.104570907"
],
[
"0.397101215",
"0.104570907"
],
[
"0.517953587",
"0.104570907"
],
[
"0.638701669",
"0.104570907"
],
[
"0.759449751",
"0.104570907"
],
[
"0.844394949",
"0.134954196"
],
[
"0.965143031",
"0.134954196"
],
[
"0.457527401",
"0.139337401"
],
[
"0.09523101",
"0.139427875"
],
[
"0.215979092",
"0.139427875"
],
[
"0.336727174",
"0.139427875"
],
[
"0.578327628",
"0.139427875"
],
[
"0.69907571",
"0.139427875"
],
[
"0.784020908",
"0.169811165"
],
[
"0.90476899",
"0.169811165"
],
[
"0.034856969",
"0.174284844"
],
[
"0.155605051",
"0.174284844"
],
[
"0.276353133",
"0.174284844"
],
[
"0.397101215",
"0.174284844"
],
[
"0.517953587",
"0.174284844"
],
[
"0.638701669",
"0.174284844"
],
[
"0.723646867",
"0.204668134"
],
[
"0.844394949",
"0.204668134"
],
[
"0.965143031",
"0.204668134"
],
[
"0.457527401",
"0.209051339"
],
[
"0.09523101",
"0.209141813"
],
[
"0.215979092",
"0.209141813"
],
[
"0.336727174",
"0.209141813"
],
[
"0.578327628",
"0.209141813"
],
[
"0.663272826",
"0.239525103"
],
[
"0.784020908",
"0.239525103"
],
[
"0.90476899",
"0.239525103"
],
[
"0.034856969",
"0.243998782"
],
[
"0.155605051",
"0.243998782"
],
[
"0.276353133",
"0.243998782"
],
[
"0.397101215",
"0.243998782"
],
[
"0.517953587",
"0.243998782"
],
[
"0.602898785",
"0.274382072"
],
[
"0.723646867",
"0.274382072"
],
[
"0.844394949",
"0.274382072"
],
[
"0.965143031",
"0.274382072"
],
[
"0.457527401",
"0.278765277"
],
[
"0.09523101",
"0.278855751"
],
[
"0.215979092",
"0.278855751"
],
[
"0.336727174",
"0.278855751"
],
[
"0.542524744",
"0.309239041"
],
[
"0.663272826",
"0.309239041"
],
[
"0.784020908",
"0.309239041"
],
[
"0.90476899",
"0.309239041"
],
[
"0.034856969",
"0.31371272"
],
[
"0.155605051",
"0.31371272"
],
[
"0.276353133",
"0.31371272"
],
[
"0.397101215",
"0.31371272"
],
[
"0.602898785",
"0.344096009"
],
[
"0.723646867",
"0.344096009"
],
[
"0.844394949",
"0.344096009"
],
[
"0.965143031",
"0.344096009"
],
[
"0.457527401",
"0.348479214"
],
[
"0.09523101",
"0.348569688"
],
[
"0.215979092",
"0.348569688"
],
[
"0.336727174",
"0.348569688"
],
[
"0.521680235",
"0.37576377"
],
[
"0.663272826",
"0.378952978"
],
[
"0.784020908",
"0.378952978"
],
[
"0.90476899",
"0.378952978"
],
[
"0.034856969",
"0.383426657"
],
[
"0.155605051",
"0.383426657"
],
[
"0.276353133",
"0.383426657"
],
[
"0.397101215",
"0.383426657"
],
[
"0.582054276",
"0.410620738"
],
[
"0.723646867",
"0.413809947"
],
[
"0.844394949",
"0.413809947"
],
[
"0.965143031",
"0.413809947"
],
[
"0.457527401",
"0.418193152"
],
[
"0.09523101",
"0.418283626"
],
[
"0.215979092",
"0.418283626"
],
[
"0.336727174",
"0.418283626"
],
[
"0.521680235",
"0.445477707"
],
[
"0.642428317",
"0.445477707"
],
[
"0.784020908",
"0.448666916"
],
[
"0.90476899",
"0.448666916"
],
[
"0.034856969",
"0.453140595"
],
[
"0.155605051",
"0.453140595"
],
[
"0.276353133",
"0.453140595"
],
[
"0.397101215",
"0.453140595"
],
[
"0.582054276",
"0.480334676"
],
[
"0.702802358",
"0.480334676"
],
[
"0.844394949",
"0.483523885"
],
[
"0.965143031",
"0.483523885"
],
[
"0.457527401",
"0.48790709"
],
[
"0.09523101",
"0.487997564"
],
[
"0.215979092",
"0.487997564"
],
[
"0.336727174",
"0.487997564"
],
[
"0.642428317",
"0.515191645"
],
[
"0.763176399",
"0.515191645"
],
[
"0.521680235",
"0.515191645"
],
[
"0.90476899",
"0.518380854"
],
[
"0.034856969",
"0.522854533"
],
[
"0.155605051",
"0.522854533"
],
[
"0.276353133",
"0.522854533"
],
[
"0.397101215",
"0.522854533"
],
[
"0.582054276",
"0.550048614"
],
[
"0.702802358",
"0.550048614"
],
[
"0.82355044",
"0.550048614"
],
[
"0.965143031",
"0.553237822"
],
[
"0.457527401",
"0.557621027"
],
[
"0.09523101",
"0.557711501"
],
[
"0.215979092",
"0.557711501"
],
[
"0.336727174",
"0.557711501"
],
[
"0.521680235",
"0.584905583"
],
[
"0.642428317",
"0.584905583"
],
[
"0.763176399",
"0.584905583"
],
[
"0.883924482",
"0.584905583"
],
[
"0.034856969",
"0.59256847"
],
[
"0.155605051",
"0.59256847"
],
[
"0.276353133",
"0.59256847"
],
[
"0.397101215",
"0.59256847"
],
[
"0.582054276",
"0.619762551"
],
[
"0.702802358",
"0.619762551"
],
[
"0.82355044",
"0.619762551"
],
[
"0.944298523",
"0.619762551"
],
[
"0.457527401",
"0.627334965"
],
[
"0.09523101",
"0.627425439"
],
[
"0.215979092",
"0.627425439"
],
[
"0.336727174",
"0.627425439"
],
[
"0.521680235",
"0.65461952"
],
[
"0.642428317",
"0.65461952"
],
[
"0.763176399",
"0.65461952"
],
[
"0.883924482",
"0.65461952"
],
[
"0.034856969",
"0.662282408"
],
[
"0.155605051",
"0.662282408"
],
[
"0.276353133",
"0.662282408"
],
[
"0.397101215",
"0.662282408"
],
[
"0.965143031",
"0.68628728"
],
[
"0.582054276",
"0.689476489"
],
[
"0.702802358",
"0.689476489"
],
[
"0.82355044",
"0.689476489"
],
[
"0.457527401",
"0.697048903"
],
[
"0.09523101",
"0.697139377"
],
[
"0.215979092",
"0.697139377"
],
[
"0.336727174",
"0.697139377"
],
[
"0.90476899",
"0.721144249"
],
[
"0.521680235",
"0.724333458"
],
[
"0.642428317",
"0.724333458"
],
[
"0.763176399",
"0.724333458"
],
[
"0.034856969",
"0.731996346"
],
[
"0.155605051",
"0.731996346"
],
[
"0.276353133",
"0.731996346"
],
[
"0.397101215",
"0.731996346"
],
[
"0.844394949",
"0.756001218"
],
[
"0.965143031",
"0.756001218"
],
[
"0.582054276",
"0.759190427"
],
[
"0.702802358",
"0.759190427"
],
[
"0.457527401",
"0.76676284"
],
[
"0.09523101",
"0.766853315"
],
[
"0.215979092",
"0.766853315"
],
[
"0.336727174",
"0.766853315"
],
[
"0.784020908",
"0.790858187"
],
[
"0.90476899",
"0.790858187"
],
[
"0.521680235",
"0.794047396"
],
[
"0.642428317",
"0.794047396"
],
[
"0.034856969",
"0.801710283"
],
[
"0.155605051",
"0.801710283"
],
[
"0.276353133",
"0.801710283"
],
[
"0.397101215",
"0.801710283"
],
[
"0.723646867",
"0.825715156"
],
[
"0.844394949",
"0.825715156"
],
[
"0.965143031",
"0.825715156"
],
[
"0.582054276",
"0.828904364"
],
[
"0.457527401",
"0.836476778"
],
[
"0.09523101",
"0.836567252"
],
[
"0.215979092",
"0.836567252"
],
[
"0.336727174",
"0.836567252"
],
[
"0.663272826",
"0.860572125"
],
[
"0.784020908",
"0.860572125"
],
[
"0.90476899",
"0.860572125"
],
[
"0.521680235",
"0.863761333"
],
[
"0.034856969",
"0.871424221"
],
[
"0.163542321",
"0.885304726"
],
[
"0.602898785",
"0.895429093"
],
[
"0.723646867",
"0.895429093"
],
[
"0.844394949",
"0.895429093"
],
[
"0.965143031",
"0.895429093"
],
[
"0.376820764",
"0.895586812"
],
[
"0.304596686",
"0.898435377"
],
[
"0.235075413",
"0.903614725"
],
[
"0.446395981",
"0.905296285"
],
[
"0.09523101",
"0.90628119"
],
[
"0.542524744",
"0.930286062"
],
[
"0.663272826",
"0.930286062"
],
[
"0.784020908",
"0.930286062"
],
[
"0.90476899",
"0.930286062"
],
[
"0.341327042",
"0.957688344"
],
[
"0.038827571",
"0.964282237"
],
[
"0.132584949",
"0.965143031"
],
[
"0.202298886",
"0.965143031"
],
[
"0.272012824",
"0.965143031"
],
[
"0.410641259",
"0.965143031"
],
[
"0.482150703",
"0.965143031"
],
[
"0.602898785",
"0.965143031"
],
[
"0.723646867",
"0.965143031"
],
[
"0.844394949",
"0.965143031"
],
[
"0.965143031",
"0.965143031"
]
],
"radius": "0.034856968"
}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
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。
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。