最大的小多边形 · n = 30
取 n 个点，两两距离都不超过 1，使它们围成的凸多边形面积尽可能大；每个点都必须是凸包的顶点。
严格定义
- 容器没有容器：唯一的全局约束是任意两点距离不超过 1；坐标写在 [0, 1.5] × [0, 1.5] 内
- 提交恰好 n 个点 points
- 约束两两距离 ≤ 1；每个点都是凸包的真顶点，落在别人连线上或内部都不算
- 目标让凸多边形面积尽可能大。内部以二倍面积精确比较
1.5y0
123456789101112131415161718192021222324252627282930
0x1.5
帮助理解
为什么偶数才难
奇数 n 的正多边形已被证明最优，没什么可争；偶数 n 时正多边形反而不是最优：Graham 的六边形比正六边形多出约 4% 的面积。所以本站只开偶数 n。
前沿在哪里
奇数 n 的正多边形由 Reinhardt (1922) 证明最优，所以只开偶数。偶数侧 n = 6, 8, 10, 12 已证明（Graham 1975 起，至 Audet 等），n ≥ 14 只有数值最好值，开放。
当前第一名
0.781673926428627079
面积
纪录保持者创始基准
解题方式人工
ANSWER FORMAT
答案怎么写
这道题没有容器，唯一的约束是任意两点距离不超过 1。坐标写在 [0, 1.5] × [0, 1.5] 的框里，这只是一个坐标系而不是额外的限制：直径不超过 1 的点集总能装进 1×1 的方格，这里四边各多留了四分之一个单位，所以放在哪里都不会被框卡住。坐标是小数，例如 "0.25"，最多九位小数。
提交 points。每个坐标写成十进制字符串，例如 "0.25"，最多九位小数。
当前第一名的答案
{
"points": [
[
"1.249518553",
"0.753842335"
],
[
"1.237170392",
"0.859679251"
],
[
"1.202871838",
"0.960003632"
],
[
"1.150098214",
"1.047659503"
],
[
"1.102618802",
"1.099136492"
],
[
"1.051652932",
"1.147164465"
],
[
"0.9645671",
"1.200873525"
],
[
"0.864615647",
"1.23624422"
],
[
"0.758917025",
"1.249724783"
],
[
"0.652683612",
"1.24051022"
],
[
"0.550800239",
"1.209003795"
],
[
"0.457898634",
"1.156634695"
],
[
"0.378194545",
"1.085778844"
],
[
"0.315303846",
"0.999650578"
],
[
"0.272079349",
"0.90215651"
],
[
"0.250481447",
"0.797715545"
],
[
"0.251492577",
"0.691039858"
],
[
"0.275121424",
"0.586802387"
],
[
"0.320891467",
"0.488717493"
],
[
"0.391736791",
"0.395825205"
],
[
"0.483865269",
"0.323989411"
],
[
"0.581454521",
"0.277171868"
],
[
"0.685433051",
"0.252428385"
],
[
"0.792091785",
"0.250275217"
],
[
"0.896758005",
"0.270753709"
],
[
"0.994709267",
"0.312931937"
],
[
"1.081505903",
"0.374896904"
],
[
"1.153211008",
"0.453837801"
],
[
"1.206571749",
"0.546173429"
],
[
"1.239167153",
"0.64771363"
]
]
}提交格式与技术细节需要编写程序或准备 JSON 答案时再查看＋
子题参数
{
"n": 30
}当前第一名的答案
{
"points": [
[
"1.249518553",
"0.753842335"
],
[
"1.237170392",
"0.859679251"
],
[
"1.202871838",
"0.960003632"
],
[
"1.150098214",
"1.047659503"
],
[
"1.102618802",
"1.099136492"
],
[
"1.051652932",
"1.147164465"
],
[
"0.9645671",
"1.200873525"
],
[
"0.864615647",
"1.23624422"
],
[
"0.758917025",
"1.249724783"
],
[
"0.652683612",
"1.24051022"
],
[
"0.550800239",
"1.209003795"
],
[
"0.457898634",
"1.156634695"
],
[
"0.378194545",
"1.085778844"
],
[
"0.315303846",
"0.999650578"
],
[
"0.272079349",
"0.90215651"
],
[
"0.250481447",
"0.797715545"
],
[
"0.251492577",
"0.691039858"
],
[
"0.275121424",
"0.586802387"
],
[
"0.320891467",
"0.488717493"
],
[
"0.391736791",
"0.395825205"
],
[
"0.483865269",
"0.323989411"
],
[
"0.581454521",
"0.277171868"
],
[
"0.685433051",
"0.252428385"
],
[
"0.792091785",
"0.250275217"
],
[
"0.896758005",
"0.270753709"
],
[
"0.994709267",
"0.312931937"
],
[
"1.081505903",
"0.374896904"
],
[
"1.153211008",
"0.453837801"
],
[
"1.206571749",
"0.546173429"
],
[
"1.239167153",
"0.64771363"
]
]
}提交 points。每个坐标写成十进制字符串，例如 "0.25"，最多九位小数。 · 验证器 v1.0.0