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Rushall, Jeff; Sima, Justin; Waechter, Riley

On constructing Greek ladders to approximate any real algebraic number. (English) Zbl 1499.97001

Int. J. Math. Educ. Sci. Technol. 53, No. 10, 2819-2830 (2022).

MSC:

97F60 Number theory (educational aspects)
97H60 Linear algebra (educational aspects)
15A18 Eigenvalues, singular values, and eigenvectors
11J68 Approximation to algebraic numbers

Keywords:

Greek ladder; Diophantine approximation; root finding; eigenvector approximation
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Full Text: DOI

References:

[1] Brand, L., The companion matrix and its properties, The American Mathematical Monthly, 71, 6, 629-634 (2018) · doi:10.1080/00029890.1964.11992294
[2] Herzinger, K.; Kunselman, C.; Pierce, I., Greek ladders via linear algebra, International Journal of Mathematical Education in Science and Technology, 49, 7, 1119-1132 (2018) · Zbl 1475.97003 · doi:10.1080/0020739X.2018.1440326
[3] Herzinger, K., & Wisner, R. (2014). Connecting greek ladders and continued fractions. Convergence.
[4] Osler, T. J.; Wright, M.; Orchard, M., Theon’s ladder for any root, International Journal of Mathematical Education in Science and Technology, 36, 4, 389-398 (2005) · doi:10.1080/00207390512331325969
[5] Ridenhour, J. R., Ladder approximations to irrational numbers, Mathematics Magazine, 59, 2, 95-105 (2018) · Zbl 0601.10024 · doi:10.1080/0025570X.1986.11977230
[6] Wisner, R. J. (2010). The classic greek ladder and newton’s method. Convergence.
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