BIN WU

Pi_as_Dimensional_Mapping_Constant

We define a one-parameter family Π(n) of dimensionless ratios as the quotient of surface measures of consecutive unit spheres: Π(n) = Sn Sn−1 = √π Γ(n/2) Γ((n + 1)/2) , where Sn denotes the surface measure of the unit n-sphere Sn ⊂ Rn+1. In particular, Π(3) = π. The formula is cl...

Pi_as_Dimensional_Mapping_Constant

We define a one-parameter family Π(n) of dimensionless ratios as the quotient of surface measures of consecutive unit spheres: Π(n) = Sn Sn−1 = √π Γ(n/2) Γ((n + 1)/2) , where Sn denotes the surface measure of the unit n-sphere Sn ⊂ Rn+1. In particular, Π(3) = π. The formula is cl...