2024/03/14 by Michael Assis, Assis, Michael
Engineering · #Advanced Materials and Mechanics #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2403.09277
openalex publication_date 2024/03/14 · openalex created_date 2024/03/16 · openalex updated_date 2026/07/28
It is well known that the set of origami constructible numbers is larger than the classical straight-edge and compass constructible numbers. However, the Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the transcendental number π can only be approximated using a finite number of straight line folds. Using these methods we give a convergent sequence for folding π as well as other methods to approximate π. Folding along curved creases, however, allows for the construction of transcendental numbers. We here give a method to construct π exactly by folding along a parabola, and we discuss generalizations for folding other transcendental numbers such as Γ(1/4).