Abstract
The square roots of the positive integers can be placed on a well known square root spiral. In order to characterize it, polar coordinates are introduced with θ = g(r). Then we find the general solution to the functional equation
where g(1) = 0 and g(r) is monotone increasing for r > 0. The resulting curve θ = g(r) gives a continuous square root spiral
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References
Kuczma, M. Functional Equations in a single variable, Monografie Mat. 46. Polish Scientific Publishers, Warsaw, 1968.
Kuczma, M., Choczewski, B., & Ger., R. iterative Functional Equations, Cambridge Univ. Press, New York, 1990.
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© 2000 Springer Science+Business Media Dordrecht
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Heuvers, K.J., Moak, D.S., Boursaw, B. (2000). The Functional Equation of the Square Root Spiral. In: Functional Equations and Inequalities. Mathematics and Its Applications, vol 518. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4341-7_10
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DOI: https://doi.org/10.1007/978-94-011-4341-7_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5869-8
Online ISBN: 978-94-011-4341-7
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