I really enjoyed this video about how to trisect angles. Trisection of arbitrary angles is impossible using only a straightedge and compass; however, it is possible by carefully folding a piece of paper.
I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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2 thoughts on “Constructing an angle’s trisectors”
I remember running across an angle trisection with compass, straightedge, and two marks in Courant and Robbins’s What Is Mathematics and feeling like I’d been let in on a deep secret of the universe.
Galois Theory by Ian Stewart gives a brilliant breakdown of why this problem is impossible with straight edge and compass, as well as other famous problems such as squaring the circle.
Mean Green Math 
I remember running across an angle trisection with compass, straightedge, and two marks in Courant and Robbins’s What Is Mathematics and feeling like I’d been let in on a deep secret of the universe.
Galois Theory by Ian Stewart gives a brilliant breakdown of why this problem is impossible with straight edge and compass, as well as other famous problems such as squaring the circle.