American polyconic projection

In the cartography of the United States, the American polyconic projection is a map projection used for maps of the United States and its regions beginning early in the 19th century.

The American polyconic projection was probably invented by Swiss-American cartographer Ferdinand Rudolph Hassler around 1825.

It was commonly used by many map-making agencies of the United States from the time of its proposal until the middle of the 20th century.

[1] It is not used much these days, having been replaced by conformal projections in the State Plane Coordinate System.

The American polyconic projection can be thought of as "rolling" a cone tangent to the Earth at all parallels of latitude.

By using this continuously varying cone, each parallel becomes a circular arc having true scale, contrasting with a conic projection, which can only have one or two parallels at true scale.

where: To avoid division by zero, the formulas above are extended so that if φ = 0, then x = λ − λ0 and y = −φ0.