The Mercator map of the world has been the most popular during the last few centuries because correct angles and shapes are preserved throughout the map. Its straight, parallel meridians allow angle measurement with a protractor. Consequently, it is particularly useful for both air and marine navigation. Its principal disadvantage is that distances are greatly distorted – Greenland appears larger than South America when it’s actually one-ninth the size. The extreme latitudes of the map are also exaggerated.
A Stereographic projection is a true perspective projection that has been popular since the 16th century. It is frequently used to map a complete hemisphere. And when this projection is used to map the world, complete hemispheres are commonly rendered as two circles. While useful for navigation, it is poor for showing correct areas or scale. The Stereographic is constructed by projecting the earth onto a plane tangent to the surface from a point directly opposite the point of contact – or the antipode (parts of the earth diametrically opposite).
The Mollweide projection compresses the extreme latitudes vertically and stretches them horizontally. This remedies the ‘pointed’ result of the Sinusoidal at the poles and spreads the extreme latitudes, giving better shape there. The disadvantage is that the equatorial regions become stretched on the opposite direction giving a ‘long’ look to Africa and South America.
The Hammer-Aitoff projection is another attempt to improve shapes on an equal-area projection. By curving the latitude lines, meridians are crossed at angles closer to a right angle (as would be the case on earth). However, shapes still stretch severely at the perimeter. Despite the slight improvement in shapes, the curved latitude lines make the map harder to construct and use.
In 1923 Paul Goode of the University of Chicago grafted two projections together – the equatorial region of the Sinusoidal projection with the extreme latitude region of the Mollweide – to utilize their virtues while eliminating their weaknesses. Goode’s Interrupted Homolosine projection provides a vast improvement in shapes while maintaining equal area. By using interruption, selected parts of the map – like land formations – can be kept centered, further diminishing distortion. Whenever interruption is used on any map, nearby points can become split apart and the relationship between them lost.
Transverse Elliptical projections are a common approach to equal-area mapping. True distances on the earth from pole to pole (180 degrees) and along the equator (360 degrees) yield a 1:2 ratio that can be proportional to an ellipse with the same 1:2 ratio. The Mollweide is another example of an elliptical map. The ‘traverse’ aspect of an elliptical projection puts the pole in the center of the map instead of the equator.