Table 1 Representative approximate values of the surface areas of the sphere

n

$\frac{\mathbf{1}}{{\mathit{a}}^{\mathbf{2}}}{\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{n}}{\mathbf{\sum }}_{\mathit{j}\mathbf{=}\mathbf{1}}^{\mathit{k}}\mathbf{(}\overrightarrow{{\mathit{n}}_{\mathit{j},\mathit{k}}}\mathbf{\cdot }\overrightarrow{{\mathbf{\Delta }}^{\mathbf{2}}{\mathit{\sigma }}_{\mathit{j},\mathit{k}}}\mathbf{+}\overrightarrow{{\mathit{n}}_{\mathit{k},\mathit{j}}}\mathbf{\cdot }\overrightarrow{{\mathbf{\Delta }}^{\mathbf{2}}{\mathit{\sigma }}_{\mathit{k},\mathit{j}}}\mathbf{)}$

$\frac{\mathbf{1}}{{\mathit{a}}^{\mathbf{2}}}{\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{n}}\overrightarrow{{\mathit{n}}_{\mathit{k},\mathit{k}}}\mathbf{\cdot }\overrightarrow{{\mathbf{\Delta }}^{\mathbf{2}}{\mathit{\sigma }}_{\mathit{k},\mathit{k}}}$

$\frac{\mathbf{1}}{{\mathit{a}}^{\mathbf{2}}}{\mathit{S}}_{{\mathit{n}}^{\mathbf{2}}}$