Cross-multiplication

American polyconic projection of the world

Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American Polyconic. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.

As a specific projection, the American Polyconic is conceptualized as "rolling" a cone tangent to the Earth at all parallels of latitude, instead of a single cone as 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 the time of its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century.

The projection is defined by:

$x=\cot(\varphi )\sin((\lambda -\lambda _{0})\sin(\varphi ))\,$

$y=\varphi -\varphi _{0}+\cot(\varphi )(1-\cos((\lambda -\lambda _{0})\sin(\varphi )))\,$

where $\lambda$ is the longitude of the point to be projected; $\varphi$ is the latitude of the point to be projected; $\lambda _{0}$ is the longitude of the central meridian, and $\varphi _{0}$ is the latitude chosen to be the origin at $\lambda _{0}$. To avoid division by zero, the formulas above are extended so that if $\varphi =0$ then $x=\lambda$ and $y=0$.

See also

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• List of map projections

References

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External links

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• Table of examples and properties of all common projections, from radicalcartography.net
• An interactive Java Applet to study the metric deformations of the Polyconic Projection.