受以上诸位的启发,找到一个可以作图的无穷解

回答: 看似简单的一道题,其实不然万斤油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点如果充分接近A点, R点会在C点的下方,甚至会在原来矩形的外面 -15少- 给 15少 发送悄悄话 15少 的博客首页 (0 bytes) () 01/06/2024 postreply 08:44:40

是的,我忘了补充PB必须小于AB的一半 -monseigneur- 给 monseigneur 发送悄悄话 (0 bytes) () 01/06/2024 postreply 11:50:06

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