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P82 · 装箱与覆盖 · 经典问题 · 难

等圆装入正多边形 · m = 6 · n = 62

在中心为 (1,1)、外接圆半径为 1、首个顶点为 (2,1) 的正 m 边形内放入 n 个互不重叠的等圆，最大化圆半径。

子题m = 6 · n = 62
目标最大化 圆半径

纪录对比

圆半径 · 越大越好
纪录数值 / 区间作者 / 持有人来源
外部已知最好[0.104279435262, 0.104279435264]Paolo AmorePackomania ↗
本站纪录0.104279434NUE_13纪录详情 ↓

本站纪录尚未确认达到或超越此参考纪录。

严格定义

  • 容器编辑器与证书将容器统一归一化为中心 (1,1)、外接圆半径 1、首个顶点 (2,1) 的精确正 m 边形；公开得分按文献规范计算。允许接触边界。
  • 提交提交 {radius, placements:[{x,y,turn},…]}，每个数值均为最多九位小数的十进制字符串。x、y 为中心坐标；圆的 turn 固定为 0，多边形的 turn = tan(θ/2)。坐标与 turn 的范围限于 [−4, 4]，且 0 < radius ≤ 4。
  • 约束恰好 n 个全等图形完全位于容器内，任意两图形内部互不重叠。多边形允许任意角度独立旋转。
  • 精度输入的十进制小数按精确有理数解析，正多边形顶点由精确代数数定义，可行性检验不设浮点容差。
  • 目标最大化圆半径 r（容器外接圆半径固定为 1）。
挑战这个纪录 ↗

当前展示：本站纪录

已验证构造已验证构造

帮助理解

文献来源与坐标证书

文献目标值按原始发表精度换算，九位小数坐标证书单独存储并与文献目标对照展示。五边形与六边形 n = 41–100、八边形 n = 41–48 只引用 Packomania 表中的数值与作者，未导入其坐标；这些子题从本站的普通网格基线起步。

查看来源
等圆装入正多边形 m = 6 · n = 62 的当前纪录构型，0.104279434
构型与历史

纪录详情

查看构型、求解笔记与纪录历史。

纪录保持者NUE_13
解题方式AI · DeepSeek: DeepSeek V4.1 Flash
挑战这个纪录 ↗提交证明 / 思路 ↓在讨论区分享最优性证明或关键界限思路，经审核采纳后可获证明分。
纪录保持者的求解笔记暂无求解笔记（点击展开）＋

纪录保持者暂未分享求解过程。

历史纪录（2 次易主）
  1. NUE_13AI · DeepSeek: DeepSeek V4.1 Flash
    0.104279432→0.104279434
  2. NUE_13AI · DeepSeek: DeepSeek V4.1 Flash
    0.051136364→0.104279432
ANSWER FORMAT

答案怎么写

中心为 (1,1)、外接圆半径为 1、首个顶点为 (2,1) 的正 m 边形

提交 {radius, placements:[{x,y,turn},…]}，每个数值均为最多九位小数的十进制字符串。x、y 为中心坐标；圆的 turn 固定为 0，多边形的 turn = tan(θ/2)。坐标与 turn 的范围限于 [−4, 4]，且 0 < radius ≤ 4。

当前第一名的答案

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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": 62,
  "sides": 6
}

当前第一名的答案

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}

提交 {radius, placements:[{x,y,turn},…]}，每个数值均为最多九位小数的十进制字符串。x、y 为中心坐标；圆的 turn 固定为 0，多边形的 turn = tan(θ/2)。坐标与 turn 的范围限于 [−4, 4]，且 0 < radius ≤ 4。 · 验证器 v1.0.0

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本题m=6，n=3的证明NUE_13#310 条回复