Definitions

# Polyconic projection

A polyconic projection is a conical map projection. The projection stems from "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone in a normal conic projection. Each parallel is a circular arc of true scale. The scale is also true on the central meridian of the projection. The projection was in common use by many map-making agencies of the United States from its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century.

The projection is defined by:

$x = cot\left(phi\right) sin\left(lambda sin\left(phi\right)\right),$

$y = phi + cot\left(phi\right) \left(1 - cos\left(lambda sin\left(phi\right)\right)\right),$

where $lambda$ is the longitude from the central meridian, and $phi$ is the latitude. To avoid division by zero, the formulas above are extended so that if $phi = 0$ then $x = lambda$ and $y = 0$.