Bad maths and climbing: a definitive answer?

Goguelu Lemoutardier - 04 / 05 / 2023

How to be the best at climbing

The abstract is rather simple: we don't have a clue yet, just a hint.

Our talent for climbing is not homogeneously shared among us. Here is a proof.
When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ In equation \eqref{eq:sample}, we find the value of an interesting integral: \begin{equation}\label{eq:sample} \int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}. \end{equation}
Finally, note that the paper [3] has some interest.


[1] Olivier Bernardi and Mireille Bousquet-Mélou. Counting colored planar maps: Algebraicity results. Journal of Combinatorial Theory, Series B, 101(5):315--377, 2011.

[2] Olivier Bernardi and Mireille Bousquet-Mélou. Counting coloured planar maps: Differential equations. Communications in Mathematical Physics, 354:31--84, 2017.

[3] Mireille Bousquet-Mélou. Counting planar maps, coloured or uncoloured. In R. Chapman, editor, Surveys in Combinatorics 2011, London Mathematical Society Lecture Note Series, pages 1--50. Cambridge: Cambridge University Press, 2011.

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