1樓：樂之
作者說沒有刻度，那就先把刻度標出來～
首先直角很容易，在直角的基礎上可以畫出乙個直角三角形，另外兩角為30度 60度，那麼顯然三邊之比為1：√3：2，既然能畫出角，那就在畫直線的工具上標記上述比值中1的邊的長度，然後單位長度有了～45度很容易了
2樓：
我看到的題目已經是，這就代表了不能使用線段來輔助。單純只有30度角這個概念。
這種時候，數學證明就不行了，就輪到我們計算機工程學出馬了，哈哈哈哈，地圖四色你們也解決不了啊，還的是計算機工程學出馬。
我們有乙個數學上不承認，但是在實際生活中非常好用的2個方法：列舉和隨機
首先在任意位置得到乙個30度角，根據資料定義，乙個角有乙個頂點即為點O和兩條射線OA，OB決定。
其次，任意以同一頂點再畫乙個30度角，這個角的始邊OC到終邊OD掃過的面積要和第乙個角有重疊。
這樣你能得到乙個由第乙個角的始邊和第二個角的終邊所組成的新的角∠AOD，其角度在[30,60]範圍內。
以OD為始邊複製∠AOD，得到∠DOE
現在∠AOE是兩倍的∠AOD或∠DOE，他的範圍是[60,120]
同時，三個30度角能形成乙個直角。
接下去就是計算機工程學了：
隨機落下∠COD，能得到乙個隨機的∠AOE。每次隨機落下以後，將∠AOE和直角相比，若重合，則∠AOD為45度。
寫個隨機程式模擬下
Round:1 2∠AOD=106°
Round:2 2∠AOD=86°
Round:3 2∠AOD=114°
Round:4 2∠AOD=78°
Round:5 2∠AOD=64°
Round:6 2∠AOD=110°
Round:7 2∠AOD=90° ∠AOD hit 45° at Round 7
當然，工程學無法被科學接受，在於他不是嚴格證明，並且這其中存在乙個精度的問題，如果我採用自然數精度，跑了一百萬次，會發現最多一次只要隨機376次就能獲得結果。但是如果用0.1的擬合精度，最多一次需要隨機4469次才能獲得結果。
如下貼乙份精確到0.1的跑1萬次的結果。結果超過字數限制。23333
所以就跑了100次如下
Round:1003 2∠AOD=90° ∠AOD hit 45° at Round 1003
Round:361 2∠AOD=90° ∠AOD hit 45° at Round 361
Round:561 2∠AOD=90° ∠AOD hit 45° at Round 561
Round:197 2∠AOD=90° ∠AOD hit 45° at Round 197
Round:53 2∠AOD=90° ∠AOD hit 45° at Round 53
Round:338 2∠AOD=90° ∠AOD hit 45° at Round 338
Round:387 2∠AOD=90° ∠AOD hit 45° at Round 387
Round:10 2∠AOD=90° ∠AOD hit 45° at Round 10
Round:13 2∠AOD=90° ∠AOD hit 45° at Round 13
Round:261 2∠AOD=90° ∠AOD hit 45° at Round 261
Round:373 2∠AOD=90° ∠AOD hit 45° at Round 373
Round:313 2∠AOD=90° ∠AOD hit 45° at Round 313
Round:411 2∠AOD=90° ∠AOD hit 45° at Round 411
Round:351 2∠AOD=90° ∠AOD hit 45° at Round 351
Round:141 2∠AOD=90° ∠AOD hit 45° at Round 141
Round:168 2∠AOD=90° ∠AOD hit 45° at Round 168
Round:176 2∠AOD=90° ∠AOD hit 45° at Round 176
Round:456 2∠AOD=90° ∠AOD hit 45° at Round 456
Round:234 2∠AOD=90° ∠AOD hit 45° at Round 234
Round:182 2∠AOD=90° ∠AOD hit 45° at Round 182
Round:122 2∠AOD=90° ∠AOD hit 45° at Round 122
Round:281 2∠AOD=90° ∠AOD hit 45° at Round 281
Round:90 2∠AOD=90° ∠AOD hit 45° at Round 90
Round:305 2∠AOD=90° ∠AOD hit 45° at Round 305
Round:23 2∠AOD=90° ∠AOD hit 45° at Round 23
Round:136 2∠AOD=90° ∠AOD hit 45° at Round 136
Round:8 2∠AOD=90° ∠AOD hit 45° at Round 8
Round:316 2∠AOD=90° ∠AOD hit 45° at Round 316
Round:664 2∠AOD=90° ∠AOD hit 45° at Round 664
Round:765 2∠AOD=90° ∠AOD hit 45° at Round 765
Round:319 2∠AOD=90° ∠AOD hit 45° at Round 319
Round:187 2∠AOD=90° ∠AOD hit 45° at Round 187
Round:25 2∠AOD=90° ∠AOD hit 45° at Round 25
Round:1087 2∠AOD=90° ∠AOD hit 45° at Round 1087
Round:396 2∠AOD=90° ∠AOD hit 45° at Round 396
Round:17 2∠AOD=90° ∠AOD hit 45° at Round 17
Round:341 2∠AOD=90° ∠AOD hit 45° at Round 341
Round:522 2∠AOD=90° ∠AOD hit 45° at Round 522
Round:659 2∠AOD=90° ∠AOD hit 45° at Round 659
Round:29 2∠AOD=90° ∠AOD hit 45° at Round 29
Round:415 2∠AOD=90° ∠AOD hit 45° at Round 415
Round:268 2∠AOD=90° ∠AOD hit 45° at Round 268
Round:170 2∠AOD=90° ∠AOD hit 45° at Round 170
Round:507 2∠AOD=90° ∠AOD hit 45° at Round 507
Round:68 2∠AOD=90° ∠AOD hit 45° at Round 68
Round:293 2∠AOD=90° ∠AOD hit 45° at Round 293
Round:341 2∠AOD=90° ∠AOD hit 45° at Round 341
Round:167 2∠AOD=90° ∠AOD hit 45° at Round 167
Round:357 2∠AOD=90° ∠AOD hit 45° at Round 357
Round:1360 2∠AOD=90° ∠AOD hit 45° at Round 1360
Round:60 2∠AOD=90° ∠AOD hit 45° at Round 60
Round:515 2∠AOD=90° ∠AOD hit 45° at Round 515
Round:366 2∠AOD=90° ∠AOD hit 45° at Round 366
Round:91 2∠AOD=90° ∠AOD hit 45° at Round 91
Round:322 2∠AOD=90° ∠AOD hit 45° at Round 322
Round:81 2∠AOD=90° ∠AOD hit 45° at Round 81
Round:490 2∠AOD=90° ∠AOD hit 45° at Round 490
Round:74 2∠AOD=90° ∠AOD hit 45° at Round 74
Round:1509 2∠AOD=90° ∠AOD hit 45° at Round 1509
Round:447 2∠AOD=90° ∠AOD hit 45° at Round 447
Round:420 2∠AOD=90° ∠AOD hit 45° at Round 420
Round:6 2∠AOD=90° ∠AOD hit 45° at Round 6
Round:12 2∠AOD=90° ∠AOD hit 45° at Round 12
Round:8 2∠AOD=90° ∠AOD hit 45° at Round 8
Round:16 2∠AOD=90° ∠AOD hit 45° at Round 16
Round:449 2∠AOD=90° ∠AOD hit 45° at Round 449
Round:1524 2∠AOD=90° ∠AOD hit 45° at Round 1524
Round:408 2∠AOD=90° ∠AOD hit 45° at Round 408
Round:181 2∠AOD=90° ∠AOD hit 45° at Round 181
Round:271 2∠AOD=90° ∠AOD hit 45° at Round 271
Round:322 2∠AOD=90° ∠AOD hit 45° at Round 322
Round:271 2∠AOD=90° ∠AOD hit 45° at Round 271
Round:66 2∠AOD=90° ∠AOD hit 45° at Round 66
Round:114 2∠AOD=90° ∠AOD hit 45° at Round 114
Round:9 2∠AOD=90° ∠AOD hit 45° at Round 9
Round:211 2∠AOD=90° ∠AOD hit 45° at Round 211
Round:170 2∠AOD=90° ∠AOD hit 45° at Round 170
Round:319 2∠AOD=90° ∠AOD hit 45° at Round 319
Round:115 2∠AOD=90° ∠AOD hit 45° at Round 115
Round:322 2∠AOD=90° ∠AOD hit 45° at Round 322
Round:425 2∠AOD=90° ∠AOD hit 45° at Round 425
Round:657 2∠AOD=90° ∠AOD hit 45° at Round 657
Round:137 2∠AOD=90° ∠AOD hit 45° at Round 137
Round:415 2∠AOD=90° ∠AOD hit 45° at Round 415
Round:75 2∠AOD=90° ∠AOD hit 45° at Round 75
Round:279 2∠AOD=90° ∠AOD hit 45° at Round 279
Round:1443 2∠AOD=90° ∠AOD hit 45° at Round 1443
Round:263 2∠AOD=90° ∠AOD hit 45° at Round 263
Round:821 2∠AOD=90° ∠AOD hit 45° at Round 821
Round:184 2∠AOD=90° ∠AOD hit 45° at Round 184
Round:168 2∠AOD=90° ∠AOD hit 45° at Round 168
Round:322 2∠AOD=90° ∠AOD hit 45° at Round 322
Round:14 2∠AOD=90° ∠AOD hit 45° at Round 14
Round:68 2∠AOD=90° ∠AOD hit 45° at Round 68
Round:110 2∠AOD=90° ∠AOD hit 45° at Round 110
Round:1100 2∠AOD=90° ∠AOD hit 45° at Round 1100
Round:584 2∠AOD=90° ∠AOD hit 45° at Round 584
Round:489 2∠AOD=90° ∠AOD hit 45° at Round 489
Round:72 2∠AOD=90° ∠AOD hit 45° at Round 72
Round:82 2∠AOD=90° ∠AOD hit 45° at Round 82
Max K is:1524
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