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作者 deathcustom 在 PTT [ Math ] 看板的留言(推文), 共104則
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23F推: 最極限的當然在這邊看的出來明顯差距XD02/17 11:21
2F→: 恩...............誤繕,你說的對02/05 16:34
1F推: 第一種哪裡不嚴謹?嚴格遞增、極限證明上界02/02 17:48
3F推: 角C角度越大,角A角度越小,證明如下02/02 22:54
4F→: 考慮三角形ABC外接圓,角A、角B、角C分別為圓周角02/02 22:55
5F→: 根據定理,圓周角角度=所對弧角度/202/02 22:55
6F推: 並根據正弦sinA/sinB = BC/AC =定值02/02 23:08
7F→: 因此角A與角B的sin值只能同增或同減02/02 23:08
8F→: 角C增加=>角A與角B對應弧之和減少, vice versa02/02 23:09
9F推: 由上述可以推得sinA與sinB極大值出現在C 90度02/02 23:12
13F推: C改變外接圓改變,但是C的對應弧AB變大,弧BC+弧AC02/03 06:57
14F→: 就會變小,又由於sinA/sinB是定值,因此只能同增同02/03 06:58
15F→: 減,考慮弧AC+弧BC的和在角C(從90度)漸增的狀況下是02/03 06:59
16F推: 嚴格遞減,sin函數(sinA,sinB)在(0,90)是單調增函數02/03 07:02
2F→: 解x得到兩解XM跟Xm10/26 12:48
1F推: 我沒有提出這種想法,我只是觀察到這點10/25 16:47
11F→: 所以我說這個題目就是考細心跟基本觀念10/19 09:34
12F→: 那個"密度"跟那個對數都是陷阱10/19 09:34
13F→: BTW, 常用對數2:0.30103, 3:0.4771, 7:0.845110/19 09:36
14F→: e:0.4342910/19 09:37
15F→: 快速估計的時候看到6.67我的第一直覺是20/310/19 09:37
16F→: 9.8是49/510/19 09:37
3F推: 提出一個有趣的觀察:A,B,B'(7,-5),P(-18,0)共圓10/18 11:21
4F→: 圓心剛好是(-5,0)10/18 11:21
5F→: 還在想這中間有沒有甚麼可以用圓跟三角的特性的地方10/18 11:22
4F推: 十二平均律是12音程,不是12管10/04 12:15
7F推: 素養題咩XDDD10/05 10:49
12F→: 不不不,PROP. VIII是在證明全等(equal),不是相似10/04 10:13
13F→: 相似相關的"Theory of Proportion"是BOOK V10/04 10:15
14F→: 幾何原本中,相似三角形是BOOK VI, PROP. V10/04 10:25