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Summary: Topics for Term Projects
1. Report on the proof that it is impossible to trisect an arbitrary angle using only a compass and
unmarked straightedge. (See Project 1, Chapter I, p. 35, and the references given there.)
2. Report on the proof that it is impossible to square a circle using only a compass and unmarked
straightedge. (See Project 1, Chapter I, p. 35, and the references given there.)
3. Report on the theorem of Mohr and Mascheroni that all Euclidean constructions of points can be
made with a compass alone. (See Project 2a, Chapter I, p. 35, and the references given there.)
4. Report on the theorem of Steiner and Poncelet that all Euclidean constructions of points can be
carried out with a straightedge alone if we are rst given a single circle and its center. (See Project 2b,
Chapter I, p. 35, and the references given there.)
5. Report on Gau 's theorem that a regular polygon with n sides can be constructed with a straightedge
and compass if and only if all odd prime factors of n occur to the rst power and have the form 2 2 m
+ 1.
(See Project 4, Chapter I, p. 35, and the references given there.)
6. Report on the theorem that "Desargues's theorem" is independent of the axioms for projective planes.
(See Project 1, Chapter II, p. 68, and the references given there.)
7. Give a report on projective 3-spaces and Desargues' theorem, which includes a statement of the
axioms for a projective 3-space, and a discussion of the fact that every projective plane in a projective
3-space satis es Desargues' theorem. (See Hilbert, Foundations of Geometry, Chapter 5.)
8. Report on the current status of the question: for which numbers X does there exist a non-Desarguian
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