Alexander Thomas at Art and Math Seminar

From fractions to fractals and back

Abstract:

The geometry of continued fractions has been studied by numerous mathematicians, in particular through the Farey triangulation and the Ford circles. Recently in 2020, a deformation of continued fractions has been proposed by Morier-Genoud and Ovsienko in algebraic terms. In this talk, I shall present the geometry behind these deformations: the deformed Farey triangulation and a 1-dimensional circle fractal representing rational numbers. This fractal naturally suggests a new operation on rationals, which is a quadratic version of the Farey addition. An extension to complex numbers leads to partial circle packings in 2d. Joint with Perrine Jouteur and Olga Paris-Romaskevich.

More information on the meeting check at the webpage of the seminar https://www.math.ksu.edu/research/seminars/artandmathseminar.html