最大的小多边形 · n = 28
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。
子题n = 28
目标最大化 面积
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
12345678910111213141516171819202122232425262728
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
0.4984468923434305
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": [
[
"1.15",
"0.75"
],
[
"1.139971165",
"0.839008374"
],
[
"1.110387547",
"0.923553496"
],
[
"1.062732593",
"0.999395921"
],
[
"0.999395921",
"1.062732593"
],
[
"0.923553496",
"1.110387547"
],
[
"0.839008374",
"1.139971165"
],
[
"0.75",
"1.15"
],
[
"0.660991626",
"1.139971165"
],
[
"0.576446504",
"1.110387547"
],
[
"0.500604079",
"1.062732593"
],
[
"0.437267407",
"0.999395921"
],
[
"0.389612453",
"0.923553496"
],
[
"0.360028835",
"0.839008374"
],
[
"0.35",
"0.75"
],
[
"0.360028835",
"0.660991626"
],
[
"0.389612453",
"0.576446504"
],
[
"0.437267407",
"0.500604079"
],
[
"0.500604079",
"0.437267407"
],
[
"0.576446504",
"0.389612453"
],
[
"0.660991626",
"0.360028835"
],
[
"0.75",
"0.35"
],
[
"0.839008374",
"0.360028835"
],
[
"0.923553496",
"0.389612453"
],
[
"0.999395921",
"0.437267407"
],
[
"1.062732593",
"0.500604079"
],
[
"1.110387547",
"0.576446504"
],
[
"1.139971165",
"0.660991626"
]
]
}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": 28
}当前第一名的答案
{
"points": [
[
"1.15",
"0.75"
],
[
"1.139971165",
"0.839008374"
],
[
"1.110387547",
"0.923553496"
],
[
"1.062732593",
"0.999395921"
],
[
"0.999395921",
"1.062732593"
],
[
"0.923553496",
"1.110387547"
],
[
"0.839008374",
"1.139971165"
],
[
"0.75",
"1.15"
],
[
"0.660991626",
"1.139971165"
],
[
"0.576446504",
"1.110387547"
],
[
"0.500604079",
"1.062732593"
],
[
"0.437267407",
"0.999395921"
],
[
"0.389612453",
"0.923553496"
],
[
"0.360028835",
"0.839008374"
],
[
"0.35",
"0.75"
],
[
"0.360028835",
"0.660991626"
],
[
"0.389612453",
"0.576446504"
],
[
"0.437267407",
"0.500604079"
],
[
"0.500604079",
"0.437267407"
],
[
"0.576446504",
"0.389612453"
],
[
"0.660991626",
"0.360028835"
],
[
"0.75",
"0.35"
],
[
"0.839008374",
"0.360028835"
],
[
"0.923553496",
"0.389612453"
],
[
"0.999395921",
"0.437267407"
],
[
"1.062732593",
"0.500604079"
],
[
"1.110387547",
"0.576446504"
],
[
"1.139971165",
"0.660991626"
]
]
}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