# Gall stereographic projection

Gall stereographic projection of the world. 15° graticule.

The Gall stereographic projection, presented by James Gall in 1855, is cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.

## Formulae

The projection is conventionally defined as:[1]

$x = R\lambda/\sqrt 2$

$y = R (1+\sqrt 2/2)\tan \frac{\varphi}{2}$

where λ is the longitude from the central meridian in degrees, φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. It is a perspective projection if the point of projection is allowed to vary with longitude: the point of projection being on the equator on the opposite side of the earth from the point being mapped and with the projective surface being a cylinder secant to the sphere at 45°N and 45°S.[2] Gall called the projection "stereographic" because the spacing of the parallels is the same as the spacing of the parallels along the central meridian of the equatorial stereographic projection.

## Braun stereographic projection

This later (1867) cylindrical projection by Carl Braun is similar, differing only in the asymmetric scaling horizontally and vertically. This yields a projection tangent to the sphere.[3] Its formula is:

$x = R\lambda$

$y = 2 R \tan \frac{\varphi}{2}$