2
$\begingroup$

In the book Lie algebra, Humphreys, during classification of Dynkin diagrams, arrives at the equation over positive integers: $$\frac{1}{p} + \frac{1}{q} +\frac{1}{r}>1$$ and makes a comment in bracket

(This inequality, by the way, has a long mathematical history)

I suddenly stopped at that classification, and wondered How long back the history goes for this inequality?

  • 2
    See cases $1,2,3$ for the [generalized Fermat](https://www.staff.science.uu.nl/~beuke106/Fermatlectures.pdf) and its history. – 2017-01-23
  • 0
    Examples of places I've seen this: Solving other inequalities, Egyptian Fractions, Diophantine approximations, and and in relation to partial sums of a generalization of the Harmonic Series where we sum from $\frac 1a$ to $\frac 1b$ – 2017-01-23
  • 1
    It has to do with finite subgroups G of SO(3) (linked to regular polyhedra) with relationship $1/p + 1/q + 1/r = 1 + 2/|G|$. Have a look at lectures in (http://www.math.miami.edu/~armstrong/686sp13.html). – 2017-01-24

0 Answers 0