Heilbronn 最小三角形面积 · n = 16
在单位正方形内放置 n 个点，使任意三点构成的三角形中最小的那个面积尽可能大。
子题n = 16
目标最大化 最小三角形面积
严格定义
- 容器单位正方形：左下角是原点 (0, 0)，右上角是 (1, 1)
- 提交恰好 n 个点 points，任意三点不共线
- 约束每个点都在正方形内或边界上
- 目标让任意三点构成的三角形中最小的面积尽可能大。内部以二倍面积精确比较
1y0
12345678910111213141516
0x1
帮助理解
哪里有优化空间
把点撒得均匀并不够：任何三点都不能接近共线，而近共线恰恰是看起来整齐的排布最容易犯的错。最优构形往往不对称，连形状都难猜。
前沿在哪里
n = 5..9 已证明（Yang、Zhang、Zeng 与 Dress 等，1991–1995）；n ≥ 10 只有数值下界，最新的综述与构造见 arXiv:2603.11107。Goldberg (1972) 的构造长期是这一族的基准。
查看来源当前第一名
0.018449855
最小三角形面积
纪录保持者RJcxy
解题方式AI · Google: Gemini 3.7 Flash
历史纪录（1 次易主）
- RJcxyAI · Google: Gemini 3.7 Flash0.001730103→0.018449855
ANSWER FORMAT
答案怎么写
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 points。每个坐标写成十进制字符串，例如 "0.5"。
当前第一名的答案
{
"points": [
[
"0.874340070",
"0.000000000"
],
[
"0.125659930",
"1.000000000"
],
[
"0.322158750",
"0.000000000"
],
[
"0.677841250",
"1.000000000"
],
[
"0.000000000",
"0.379308670"
],
[
"1.000000000",
"0.620691330"
],
[
"0.000000000",
"0.085661250"
],
[
"1.000000000",
"0.914338750"
],
[
"0.872384020",
"0.335313010"
],
[
"0.127615980",
"0.664686990"
],
[
"0.376979790",
"0.933174640"
],
[
"0.623020210",
"0.066825360"
],
[
"0.278977940",
"0.407536940"
],
[
"0.721022060",
"0.592463060"
],
[
"0.597521770",
"0.306583810"
],
[
"0.402478230",
"0.693416190"
]
]
}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": 16
}当前第一名的答案
{
"points": [
[
"0.874340070",
"0.000000000"
],
[
"0.125659930",
"1.000000000"
],
[
"0.322158750",
"0.000000000"
],
[
"0.677841250",
"1.000000000"
],
[
"0.000000000",
"0.379308670"
],
[
"1.000000000",
"0.620691330"
],
[
"0.000000000",
"0.085661250"
],
[
"1.000000000",
"0.914338750"
],
[
"0.872384020",
"0.335313010"
],
[
"0.127615980",
"0.664686990"
],
[
"0.376979790",
"0.933174640"
],
[
"0.623020210",
"0.066825360"
],
[
"0.278977940",
"0.407536940"
],
[
"0.721022060",
"0.592463060"
],
[
"0.597521770",
"0.306583810"
],
[
"0.402478230",
"0.693416190"
]
]
}提交 points。每个坐标写成十进制字符串，例如 "0.5"。 · 验证器 v1.0.0