2009/11/05 by Shuxiang Goh, N. J. Wildberger, Goh, Shuxiang +1
Engineering · Mathematics · Physics and Astronomy · #14Axx #33C47 #51Fxx #Algebraic Topology (math.AT) #Classical Analysis and ODEs (math.CA) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Mechanics and Biomechanics Studies #Sports Dynamics and Biomechanics #math.AT #math.CA #msc:14Axx #msc:33C47 #msc:51Fxx
paper · pdf · doi:10.48550/arxiv.0911.1025
14 pages, 3 figures
arxiv created 2009/11/05 · openalex publication_date 2009/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spread between two lines in rational trigonometry replaces the concept of angle, allowing the complete specification of many geometrical and dynamical situations which have traditionally been viewed approximately. This paper investigates the case of powers of a rational spread rotation, and in particular, a curious periodicity in the prime power decomposition of the associated values of the spread polynomials, which are the analogs in rational trigonometry of the Chebyshev polynomials of the first kind. Rational trigonometry over finite fields plays a role, together with non-Euclidean geometries.