Regular polygons, Morgan-Voyce polynomials, and Chebyshev polynomials

Jorma K. Merikoski
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 79–87
DOI: 10.7546/nntdm.2021.27.2.79-87
Full paper (PDF, 196 Kb)

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Authors and affiliations

Jorma K. Merikoski
Faculty of Information Technology and Communication Sciences, Tampere University
FI-33014 Tampere, Finland

Abstract

We say that a monic polynomial with integer coefficients is a polygomial if its each zero is obtained by squaring the edge or a diagonal of a regular n-gon with unit circumradius. We find connections of certain polygomials with Morgan-Voyce polynomials and further with Chebyshev polynomials of second kind.

Keywords

• Regular polygons
• Morgan-Voyce polynomials
• Chebyshev polynomials
• Vieta polynomials

2020 Mathematics Subject Classification

• 11B83
• 51M20

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