On constructing Greek ladders to approximate any real algebraic number
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Jeff Rushall [1] ; Justin Sima [1] ; Riley Waechter [1]
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[1] Northern Arizona University
Northern Arizona University
Estados Unidos
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- 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 ...)
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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.
