Editing Basel problem (section)

===Consequences of Euler's proof===
By the above results, we can conclude that <math>\zeta(2k)</math> is ''always'' a [[rational]] multiple of <math>\pi^{2k}</math>. In particular, since <math>\pi</math> and integer powers of it are [[Transcendental number|transcendental]], we can conclude at this point that <math>\zeta(2k)</math> is [[irrational]], and more precisely, [[Transcendental number|transcendental]] for all <math>k \geq 1</math>. By contrast, the properties of the odd-indexed [[zeta constants]], including [[Apéry's constant]] <math>\zeta(3)</math>, are almost completely unknown.