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Peter J. Kahn
Algebra, number theory, algebraic and differential topology
For the past few years, I have been working on some algebraic problems related to the ruler and compass trisection of angles and the generalization to mm-section of angles. In particular, after showing that the cosines of mm-sectable angles are algebraic numbers in the unit interval [−1,1][−1,1], I am interested in calculating how densely these cosines are distributed among the algebraic numbers, using a concept of density based on the notion of the height of an algebraic number. If I restrict attention to a real, algebraic number field KK, I can show that the density is zero, provided mm is not a power of two. I am currently working on extending this result from KK to the field of all real algebraic numbers.
- Pseudohomology and homology (Nov. 2001), 35 pp.
- Symplectic torus bundles and group extensions (updated Jan. 2005), 20 pp.
- Automorphisms of the discrete Heisenberg group (Feb. 2005), 7 pp.
- The density of the set of trisectable angles (Dec. 2010, revised July 2011), 40 pp.
- Trisection, Pythagorean angles, and Gaussian integers (July 2011), 10 pp.
- m-Sectable angles and the density of polynomial images (April 2013), 19 pp.
- A generalization of Wantzel's theorem, mm-sectable angles, and the density of certain Chebyshev-polynomial images (Jan. 2014), 15 pp.; Journal of Pure and Applied Algebra (to appear).