受以上諸位的啟發,找到一個可以作圖的無窮解

回答: 看似簡單的一道題,其實不然萬斤油2024-01-03 09:29:33

ABC is the missing corner. On AB, randomly choose a point P. The goal is to subsequently identify point R on AC, such that rectangle APSR's area is equal to that of ABC. It is feasible. For example, draw line PC, then draw BQ in parallel to PC. It can be proven that area(ABC)=area(APQ). Find the middle point of AQ, mark it as R. So area(APSR)=area(ABC).

Now, imagine ABC is reshaped into APSR. This is possible because they are of equal area. This transforms the paper into two rectangles: the lower left small one, and the big right one. Connect the center of these two rectangles O1 O2. Cut along O1O2.

所有跟帖: 

P點如果充分接近A點, R點會在C點的下方,甚至會在原來矩形的外麵 -15少- 給 15少 發送悄悄話 15少 的博客首頁 (0 bytes) () 01/06/2024 postreply 08:44:40

是的,我忘了補充PB必須小於AB的一半 -monseigneur- 給 monseigneur 發送悄悄話 (0 bytes) () 01/06/2024 postreply 11:50:06

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