A Self-Reciprocal Constant Continued Fraction Characterization of the Plastic Constant
Abstract
We show that the plastic constant ρ, the unique positive real solu-tion of ρ3 = ρ + 1, is the only real number whose reciprocal generatesa constant generalized continued fraction equal to the number itself.Specifically, the infinite continued fraction with all partial numera-tors and denominators equal to 1/ρ converges to ρ. This provides asimple self-reciprocal continued-fraction characterization of the plas-tic constant analogous to the classical constant-1 continued-fractioncharacterization of the golden ratio
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Mathematical functions and polynomials
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint