Conformal map projection

The counterexamples are equirectangular and equal-area cylindrical projections (of normal aspects).

[1] This is also a consequence of Carl Gauss's 1827 Theorema Egregium [Remarkable Theorem].

A conformal parameterization of a disc-like domain on the sphere is deemed scale-optimal when it minimizes the ratio of maximum to minimum scale across the entire map.

Chebyshev applied this theorem to create a conformal map for the European part of the Russian Empire, which reduced scale errors to 1/50.

To make a new sheet from many maps or to change the center, the body must be re-projected.

Conformal maps containing large regions vary scales by locations, so it is difficult to compare lengths or areas.

However, some techniques require that a length of 1 degree on a meridian = 111 km = 60 nautical miles.