# Berghaus star

## Description

The Berghaus star projection uses the azimuthal equidistant projection for the central hemisphere. The other half of the world is split into five triangular pieces, forming a star around the circular center. Usually centered at the North Pole, it can minimize breaks in land masses. The American Association of Geographers (AAG) incorporated a version of the Berghaus star projection into its logo in 1911.

The projection was developed by Hermann Berghaus in 1879. Equations for an ellipsoid of revolution were developed at Esri. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 10.0 and later.

## Projection properties

The subsections below describe the Berghaus star projection properties.

### Graticule

The straightness of the latitude and longitude lines depends on the projection's center. If the center is at the North or South Pole, meridians are straight but broken at the equator, while parallels are presented as circular arcs. If the latitude of origin is at the Equator, the equator and the central meridian are straight lines. If the latitude of origin is elsewhere, only the central meridian is shown as a straight line. For all cases except a polar case, latitude lines are complex curves. Both poles project as points regardless of the map center. The graticule is radially symmetric about the center in polar aspect.

### Distortion

Projection is neither conformal nor equal-area. Shapes, areas, and angles are all generally distorted. The projection preserves both distance and direction from the central point though a hemisphere. Scale is true only along straight lines radiating from the center of the map for a hemisphere and along the lines between the center and the tips of triangular pieces. In polar aspect, this is along the central meridians of triangular pieces. Distortion values are radially symmetric across the center of the map.

## Usage

The Berghaus star projection was used for world maps in several atlases in the nineteenth century. The American Association of Geographers uses a version of the Berghaus star projection in its logo.

## Parameters

Berghaus star parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Latitude Of Origin
• XY Plane Rotation, which rotates the projection on the central point. If set to zero, the default, the star is oriented with a point extending down. When set to 36°, the star is rotated counterclockwise so that a point extends up toward grid north.

## Sources

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.