A famous problem of antiquity is to divide a given angle into three equal parts using just a compass and a straightedge. People tried very hard to solve this problem, until it was eventually proven that you can't. A compass and a straightedge just aren't enough to trisect any given angle.
Surprisingly, however, you can trisect an angle using origami. Just a few folds on a piece of paper and you're done. See this article on Wild Maths to find out how.
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