On constructing Greek ladders to approximate any real algebraic number

• Jeff Rushall ^[1] ; Justin Sima ^[1] ; Riley Waechter ^[1]
  1. [1] Northern Arizona University

     Northern Arizona University

     Estados Unidos

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 10, 2022, págs. 2819-2830
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • form √n k for n, k ∈ N can be approximated using specific Greek ladders (Osler, T. J., Wright, M., & Orchard, M. (2005). Theon’s ladder for any root. International Journal of Mathematical Education in Science and Technology, 36(4), 389–398. https://doi.org/10.1080/00207390 512331325969). In 2018, Herzinger et al., showed that every algebraic number of degree 2 or less can be approximated using rung ratios generated by a specific Greek ladder (Herzinger, K., Kunselman, C., & Pierce, I. (2018). Greek ladders via linear algebra. International Journal of Mathematical Education in Science and Technology, 49(7), 1119–1132. https://doi.org/10.1080/0020739X.2018.1440326).

    Using techniques from linear algebra, in particular the companion matrix of a polynomial, we will prove that every real algebraic number can be approximated by a Greek ladder, as well as show how to construct such a ladder.