Peter J. Kahn

Professor Emeritus

Research Focus

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.