On Tue, Dec 23, 2014 at 1:54 PM, Daniel Asimov <asimov@msri.org> wrote:
Pretending that spheres, balls, and Euclidean spaces can have real dimensions:
Very delicate hypothesis. You would have to prove that there is a continuous family of geometrical objects, to whom volume and surface make sense, etc. and according precisely to these formulae.
upsilon := 0.256946404860576780132838388690769236619+
Is it known to be irrational or transcendental? Or related to other
numbers,
like Euler gamma, whose number-theoretic properties are unknown?
Simplifying the expression for the derivative of Vmax relative to d, you get that d_Vmax is such that EulerGamma + Log[Pi] == HarmonicNumber[d_Vmax / 2] in Mathematica notation, or equivalently Log[Pi] == PolyGamma[0, d_Amax / 2] Olivier Gérard