Peter J. Kahn

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 $m$-section of angles. In particular, after showing that the cosines of $m$-sectable angles are algebraic numbers in the unit interval $[-1,1]$, 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 $K$, I can show that the density is zero, provided $m$ is not a power of two. I am currently working on extending this result from $K$ to the field of all real algebraic numbers.