Editing Dimensional analysis (section)

=== Mathematics ===
A simple application of dimensional analysis to mathematics is in computing the form of the [[N-sphere#Volume of the n-ball|volume of an {{math|''n''}}-ball]] (the solid ball in ''n'' dimensions), or the area of its surface, the [[n-sphere|{{math|''n''}}-sphere]]: being an {{math|''n''}}-dimensional figure, the volume scales as {{math|''x''{{sup|''n''}}}}, while the surface area, being {{math|(''n'' − 1)}}-dimensional, scales as {{math|''x''{{sup|''n''−1}}}}. Thus the volume of the {{math|''n''}}-ball in terms of the radius is {{math|''C''{{sub|''n''}}''r''{{isup|''n''}}}}, for some constant {{math|''C''{{sub|''n''}}}}. Determining the constant takes more involved mathematics, but the form can be deduced and checked by dimensional analysis alone.