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The Mathematical Intelligencer

, Volume 40, Issue 2, pp 85–88 | Cite as

A Singular Mathematical Promenade by Étienne Ghys

ENS ÉDITIONS, LYON, 2017, VIII + 302 PP., 27.00 EUR, ISBN 978-2-84788-939-0
  • Sergei Tabachnikov
Book Reviews

Consider two graphs of real polynomials that pass through the origin. Intersect the graphs with a vertical line slightly to the left of the y-axis and then move the line to the right until it is slightly to the right of the y-axis. Follow the intersection points of the line with the graphs: you obtain a permutation of two points, either trivial or nontrivial.

It is obvious that both possibilities can be realized by choosing appropriate polynomials, for example, \(P_ 1(x)= 0\)

Notes

References

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    J. Leys, E. Ghys, A. Alvarez. Chaos: A Mathematical Adventure. Available at http://www.chaos-math.org/en, 2013.
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    J. McCarthy. How to Give a Good Colloquium. Canadian Math. Soc. Notes 31:5 (September 1999), 3–4.Google Scholar
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    J. Milnor. Singular Points of Complex Hypersurfaces. Annals of Mathematics Studies 61. Princeton University Press, University of Tokyo Press, 1968.Google Scholar
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    A. Sokal and J. Bricmont. Fashionable Nonsense. Postmodern Intellectuals’ Abuse of Science. Picador, 1998.Google Scholar
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    R. Stanley. Hipparchus, Plutarch, Schröder, and Hough. Amer. Math. Monthly 104 (1997), 344–350.MathSciNetzbMATHGoogle Scholar
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    The Online Encyclopedia of Integer Sequences https://oeis.org.
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    Images des Mathématiques http://images.math.cnrs.fr/?lang=fr.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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