Pretending that spheres, balls, and Euclidean spaces can have real dimensions: * let d_Amax := the real dimension d where the formula A(d) = 2 pi^(d/2) / Gamma(d/2) for the (d-1)-dimensional content of the unit (d-1)-sphere in R^d takes its maximum. -and- * let d_Vmax := the real dimension d where the formula V(d) = pi^(d/2) / Gamma(d/2 + 1) for the d-dimensional content of the unit d-ball in R^d takes its maximum Then d_Amax = 7.256946404860576780132838388690769236619+ and d_Vmax = 5.256946404860576780132838388690769236619+. In particular they have the same fractional part: upsilon := 0.256946404860576780132838388690769236619+ QUESTION: Is anything known about the number theoretic properties of upsilon? Is it known to be irrational or transcendental? Or related to other numbers, like Euler gamma, whose number-theoretic properties are unknown? --Dan