A more complex calculation is needed to find the diameter of the dish "measured along its surface". This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: formula_7 (or the equivalent: formula_8 and formula_9 where formula_10 formula_11 and formula_6 are defined as above. The diameter of the dish, measured along the surface, is then given by: formula_13 where formula_14 means the natural logarithm of formula_15, i.e. its logarithm to base "e".