文献中也称circles in arbitrary trianglesunit circles in a minimum-area trianglecircle packing in a triangle of variable shape
在任意三角形中放置 n 个半径为 1、内部互不重叠的圆；三角形的三个顶点也是答案的一部分。让这个三角形的面积尽可能小。
普通装箱只移动圆；这里连三条边的方向都能改变。一条边转动一点，可能同时释放多个接触，也可能让整套构形失稳。
候选最优解通常由圆—圆、圆—边相切关系卡死。真正的搜索不是把圆平均铺开，而是在大量可能的接触图之间找到对的那一张。
Friedman 的公开表给出了 n≤50 的当前最好已知构形。n=1、2 已证明，n=3 仍是简单的等边三角形排布，因此本站从 n=4 开放；匹配公开构形只是到达前沿，打破它们才是新纪录。
查看来源
三角形面积
坐标单位就是圆的半径：每个圆半径固定为 1。三个顶点和所有圆心都写在 0≤x,y≤200 的坐标框内，顶点必须逆时针排列。
提交按逆时针排列的三个顶点 triangle，以及恰好 n 个圆心 centers。圆的半径固定为 1；所有数写成最多九位小数的字符串。
{
"centers": [
[
"9.683358799",
"14.772069403"
],
[
"9.087570872",
"12.862871444"
],
[
"11.046017405",
"12.457301134"
],
[
"7.732050903",
"11.392304985"
],
[
"10.536224018",
"10.523364527"
],
[
"12.474569258",
"10.030599037"
],
[
"6.732050890",
"9.660254157"
],
[
"8.732050915",
"9.660254157"
],
[
"11.716139571",
"8.179981705"
],
[
"5.732050878",
"7.928203328"
],
[
"7.732050903",
"7.928203328"
],
[
"9.732050927",
"7.928203328"
],
[
"13.702293033",
"7.945046557"
],
[
"4.732050866",
"6.196152499"
],
[
"6.732050890",
"6.196152499"
],
[
"10.732050939",
"6.196152499"
],
[
"12.732050964",
"6.196152499"
],
[
"8.732050915",
"6.196152499"
],
[
"14.732050954",
"6.195781591"
],
[
"3.732050853",
"4.464101670"
],
[
"5.732050878",
"4.464101670"
],
[
"7.732050903",
"4.464101670"
],
[
"9.732050927",
"4.464101670"
],
[
"11.732050952",
"4.464101670"
],
[
"13.754000835",
"4.451242093"
],
[
"15.753982501",
"4.459811404"
],
[
"2.732050841",
"2.732050841"
],
[
"4.732050866",
"2.732050841"
],
[
"6.732050890",
"2.732050841"
],
[
"8.732050915",
"2.732050841"
],
[
"10.732050939",
"2.732050841"
],
[
"12.732050964",
"2.732050841"
],
[
"14.754000847",
"2.719191264"
],
[
"16.768592597",
"2.736278273"
],
[
"1.732050829",
"1.000000012"
],
[
"3.732050853",
"1.000000012"
],
[
"5.732050878",
"1.000000012"
],
[
"7.732050903",
"1.000000012"
],
[
"9.732050927",
"1.000000012"
],
[
"11.732050952",
"1.000000012"
],
[
"13.732050976",
"1.000000012"
],
[
"15.775950718",
"1.000000012"
],
[
"17.783215578",
"1.012642725"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.539792944",
"0.000000000"
],
[
"9.674964344",
"16.757529806"
]
]
}{
"n": 43
}{
"centers": [
[
"9.683358799",
"14.772069403"
],
[
"9.087570872",
"12.862871444"
],
[
"11.046017405",
"12.457301134"
],
[
"7.732050903",
"11.392304985"
],
[
"10.536224018",
"10.523364527"
],
[
"12.474569258",
"10.030599037"
],
[
"6.732050890",
"9.660254157"
],
[
"8.732050915",
"9.660254157"
],
[
"11.716139571",
"8.179981705"
],
[
"5.732050878",
"7.928203328"
],
[
"7.732050903",
"7.928203328"
],
[
"9.732050927",
"7.928203328"
],
[
"13.702293033",
"7.945046557"
],
[
"4.732050866",
"6.196152499"
],
[
"6.732050890",
"6.196152499"
],
[
"10.732050939",
"6.196152499"
],
[
"12.732050964",
"6.196152499"
],
[
"8.732050915",
"6.196152499"
],
[
"14.732050954",
"6.195781591"
],
[
"3.732050853",
"4.464101670"
],
[
"5.732050878",
"4.464101670"
],
[
"7.732050903",
"4.464101670"
],
[
"9.732050927",
"4.464101670"
],
[
"11.732050952",
"4.464101670"
],
[
"13.754000835",
"4.451242093"
],
[
"15.753982501",
"4.459811404"
],
[
"2.732050841",
"2.732050841"
],
[
"4.732050866",
"2.732050841"
],
[
"6.732050890",
"2.732050841"
],
[
"8.732050915",
"2.732050841"
],
[
"10.732050939",
"2.732050841"
],
[
"12.732050964",
"2.732050841"
],
[
"14.754000847",
"2.719191264"
],
[
"16.768592597",
"2.736278273"
],
[
"1.732050829",
"1.000000012"
],
[
"3.732050853",
"1.000000012"
],
[
"5.732050878",
"1.000000012"
],
[
"7.732050903",
"1.000000012"
],
[
"9.732050927",
"1.000000012"
],
[
"11.732050952",
"1.000000012"
],
[
"13.732050976",
"1.000000012"
],
[
"15.775950718",
"1.000000012"
],
[
"17.783215578",
"1.012642725"
]
],
"triangle": [
[
"0.000000000",
"0.000000000"
],
[
"19.539792944",
"0.000000000"
],
[
"9.674964344",
"16.757529806"
]
]
}提交按逆时针排列的三个顶点 triangle，以及恰好 n 个圆心 centers。圆的半径固定为 1；所有数写成最多九位小数的字符串。 · 验证器 v1.0.0
聊思路、贴方法、问为什么卡住。发帖即公开署名，与纪录同一个名字；署名后的 #编号是账号的注册序号，冒不了名。发言资格与实绩绑定：破过一次纪录，就永久拥有发言权。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？