Brooks coil

A Brooks coils has the shortest length of wire for a given inductance.

The radius, height and width of a brooks coil are all the same yielding a square section coil shown here.

$$L\cong 0.025391c{N}^{2}\phantom{\rule{0.5em}{0ex}}\mu {\rm H}$$

Where c is the width and height of the coil in cm and N is the number of turns.