如果说到12月最有意思的题目,我想一定是毫无争议的。2021年12月的第37届CMO第二天,出现了一个尺规作图的魔幻题目:
On ablank piece of paper, two points with distance 1 is given.Prove that one can use (only) straightedge and compass to constructon this paper a straight line, and two points on it whose distanceissuchthat, in the process of constructing it, the total number of circlesor straight lines drawn is at most 10.
Remark:Explicit steps of the construction should be given. Label the circlesand straight lines in the order that they appear. Partial credit maybe awarded depending on the total number of circles/lines.
在一张白纸上,有两个距离为1的点。证明我们可以使用直线段和圆规在这张纸上构造一条长度为的线段,并且在构造它的过程中,圆的总数和线段的总数都不会超过10。
Remark:应该给出明确的构建步骤,并按照圆和直线段出现的顺序标记它们。我们会根据圆和线段的总数给出部分分数。
读者不妨自己先尝试构造一下这个问题的解法,下面是笔者对于最近出现的解法的整理,供大家欣赏。
Solution 1
Solution 2