The discreet charm of the square root

Authors

  • Pablo Amster Universidad de Buenos Aires. Facultad de Ciencias y Naturales. Departamento de Matemática - IMAS-CONICET
  • José Ángel Cid Universidade de Vigo. Departamento de Matemáticas

DOI:

https://doi.org/10.33044/revem.42132

Keywords:

Complex square root, Brouwer Theorem, Fundamental theorem of algebra, Winding number

Abstract

We present a version for the general readership of our article (Amster y Cid, 2022) in which we show how the complex square root allows us to prove in a very simple manner various topological results in the plane, as deep as the Brouwer Fixed Point Theorem and the Invariance of Domain Theorem, as well as the Fundamental Theorem of Algebra.

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References

Amster, P., y Cid, J. A. (2022). The full power of the half-power. Expo. Math., 40(4), 994–1013.

Benítez, F., y Carena, M. (2021). Reflexiones acerca de la definición de radicación y su relación con la construcción de nuevos conceptos. RevEM UMA, 36(1), 9–26.

Cao Labora, D. (2020). When is a continuous bijection a homeomorphism? Amer. Math. Monthly, 127(6), 547–553.

Conway, J. B. (1978). Functions of one complex variable. Second edition. New York–Berlin: Graduate Texts in Mathematics, 11, Springer–Verlag.

Ebbinghaus, H.-D., Hermes, H., Hirzebruch, F., Koecher, M., Mainzer, K., Neukirch, J., ... Remmert, R. (1991). Numbers. New York: Graduate Texts in Mathematics, 123, Springer–Verlag.

Gasull, A. (2022). Los babilonios y Newton. La Gaceta de la RSME, 25, 488.

Hasselblatt, B., y Katok, A. (2003). A first course in dynamics with a panorama of recent developments. Cambridge University Press.

Penrose, R. (2005). The road to reality. A complete guide to the laws of the universe. New York: Alfred A. Knopf, Inc.

Taussky, O. (1970). Sums of squares. Amer. Math. Monthly, 77, 805–830.

Taussky, O. (1988). From Pythagoras’ theorem via sums of squares to celestial mechanics. Math. Intelligencer, 10(1), 52–55.

Published

2023-08-03

How to Cite

Amster, P., & Cid, J. Ángel. (2023). The discreet charm of the square root. Revista De Educación Matemática, 38(2), 16–27. https://doi.org/10.33044/revem.42132

Issue

Section

Artículos de Matemática