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学习笔记——宽高比

  • 2026-01-09 16:33:45
学习笔记——宽高比
横平竖直这种线段方向的表达是大部分数学问题采用的方式，类比三比值必杀技在同一方向的投影解决问题，宽高定比就是在互相垂直的两个方向的斜线段的投影关联问题。
边对角是这个问题的主要特征，宽高比是BP:AH=1：√3，线段AB对应的投影是AH与BH，线段BK对应的投影是PB与PK，投影对应的线段之间互相垂直，各自形成的三角形是相似的，相似比是√3:1，点K是定点，BK是确定的线段，点P在圆上，转化为点圆最值。从上位思想来看，线段背靠的是三角形，考虑给出单一线段时的上位背景是必要的，本题中有∠AHB是直角，得到∠KPB是直角，再次得到直角的上位图形圆，题目的底层逻辑就显得非常自然。技巧层面概况：宽高定比一线三，斜中引入定江山。
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  1. CONNECT:[ UseTime:0.000426s ] mysql:host=127.0.0.1;port=3306;dbname=no_67808;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000717s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000248s ]
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  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000807s ]
  6. SELECT * FROM `set` [ RunTime:0.004920s ]
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  8. SELECT * FROM `article` WHERE `id` = 458294 LIMIT 1 [ RunTime:0.002257s ]
  9. UPDATE `article` SET `lasttime` = 1768189300 WHERE `id` = 458294 [ RunTime:0.016764s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000336s ]
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  14. SELECT * FROM `article` WHERE `id` < 458294 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.023626s ]
  15. SELECT * FROM `article` WHERE `id` < 458294 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.026648s ]
0.199717s