University of Michigan Math and Science Scholars
Euclid was not the first person to use a straight-edge and compass, but his use of them is certainly the most famous and long lasting. Using these two tools alone, we can create objects as simple as an equilateral triangle, and as surprising as a 17-gon (this was discovered many centuries after Euclid’s death). There are endless puzzles to be had by asking: “How can I construct [blank] with these tools?’’ and “How few moves can I do it in?”. Remarkably, what is constructible (or not) with straight-edge and compass can be answered by the study of roots of certain polynomials. This connection on its own is a beautiful result to study, but on the other hand, why choose these particular tools in the first place??? What else can be constructed (or not) with a straight-edge alone? Compass alone? A marked straight-edge? Paper folding? This course will be deeply interactive and collaborative; most of the time will be spent in small groups solving problems and puzzles with help and support from instructors. Instructors will also introduce tools, help synthesize big ideas, highlight groups’ successes and insights, and bring together pieces of more complex proofs.