The Mathematical Intelligencer

, Volume 40, Issue 4, pp 12–13 | Cite as

From Symmetry to Monotonicity

  • Bernd KawohlEmail author
  • David Krejčiřík

Symmetry is a fascinating notion in science, primarily perhaps due to the fact that the symmetry of geometric objects evokes the aesthetic and elegant perception of every human being. More fundamentally, the symmetries of spacetime are closely related to conservation laws in physics. In this note we show how one can use a symmetry of a two-dimensional surface to prove a monotonicity property of a one-dimensional function.

A couple of years ago, Jan Ubøe gave an unconventional proof of the fact that a certain mapping  f( x) that depends on a positive parameter  a is increasing in  x if \(a>1\)



D.K. was partially supported by GACR grant No. 18-08835S and by FCT (Portugal) through project PTDC/MAT-CAL/4334/2014.


  1. [1]
    J. Ubøe, A heroic proof, Math. Intell. 37, no. 3 (2015), 72–74.Google Scholar
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    J. Ubøe, J. Andersson, K. Jörnsten, J. Lillestøl, & L. Sandal, Statistical testing of bounded rationality with applications to the newsvendor model, European J. Oper. Res. 259 (2017), 251–261.Google Scholar

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

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnCologneGermany
  2. 2.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePragueCzech Republic

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