Re: [問題] 放不平的桌子
看板puzzle (益智遊戲 - 數獨,拼圖,推理,西洋棋)作者walkwall (會走路的牆)時間14年前 (2010/05/11 18:44)推噓27(27推 0噓 57→)留言84則, 15人參與討論串2/4 (看更多)
※ 引述《walkwall (會走路的牆)》之銘言:
: 某甲 : 最近買的OO牌桌子品質真差,放在地上都無法四個腳同時著地
: 某乙 : 其實是你家的地不平吧,我買同樣一個牌子的桌子也沒這問題阿?
: 請問,如果桌子擺不平,到底是桌子本身的問題比較大,還是地面的問題比較大呢?
: 換句話說
: (A)如果桌子做的非常正,而地面有凹凹凸凸,桌子會不平嗎?
: (B)如果地面非常平,桌子的腳有點不正,桌子會不平嗎?
: 試證明之~
(解答在下頁)
(A)桌正地不平,桌子仍然可以放平
假設目前放不平
令桌椅四腳順時鐘依序為ABCD,則AC兩腳至地面的距離減去BD至地面的距離為一函數
因為放不平,故此函數目前狀態不為零
將桌面轉九十度,也就是A->B->C->D->A
因為桌正,故旋轉後上述函數的值應該與目前的值正負顛倒,絕對值相同
依中間值定理,只要地面連續,必然存在一個點可以使含數值為0
此時四腳著地,故得證
(B)桌歪地平,桌子仍然無法放平
考慮蹺翹板式桌面例子,即AC兩腳長度不變BD兩腳縮到最小
則不論如何旋轉,仍舊無法將四點均著地,故得證
結論:桌子無法放平,一定是桌子的問題 (END)
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◆ From: 140.117.169.167
※ 編輯: walkwall 來自: 140.117.169.167 (05/11 18:44)
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