Abstract
A quadratic irrational, 1 ζ, has the form (a + b 1/2)/c, where a, b, c are integers, b > 0, b is not the square of an integer, and c ≠ 0. Let ζ+ and ζ− be quadratic irrationals corresponding to ζ+ = (a + b 1/2)/c and ζ− (a − b 1/2)/c. A quadratic polynomial that has these roots is p(z) = (z − ζ+)(z − ζ−), or
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References
Ivan Niven, Irrational Numbers, Carus Mathematical Monographs, Mathematical Association of America, 1956.
Harold Benzinger, Scott Burns, and Julian Palmore, “Complex analytic dynamics and Newton’s method, Phys. Lett. A 119 (1987), 441–446.
Julian Palmore, “Exploring chaos: science literacy in mathematics, ” Proceedings of the Symposium on Science Learning in the Informal Setting, The Chicago Academy of Sciences, Chicago, 1988, pp. 183–200.
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© 1993 Springer-Verlag New York, Inc.
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Palmore, J. (1993). A Relation Between Newton’s Method and Successive Approximations for Quadratic Irrationals. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_25
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DOI: https://doi.org/10.1007/978-1-4612-2740-3_25
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