Polyconic projection

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A Polyconic projection of the Earth.

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.^[1]

The projection is defined by:

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

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

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