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The Sinusoidal Projection

This projection, also known as the Sanson-Flamsteed projection, and the Mercator Equal-Area projection, is the simplest pseudocylindrical equal-area projection.

As we saw previously,

the width of a degree of longitude is proportional to the cosine of the latitude. Hence, if we space the parallels of latitude uniformly on the map, and make the scale of longitude always proportional to the cosine of the latitude, areas will be correct.

However, as you can see, continents distant from the prime meridian are sheared, giving them a very distorted appearance in this projection.

Since the scale on the Equator is uniform, and the meridians cross it at right angles, and the vertical scale of the projection does not change along the equator for different longitudes, it is possible to considerably reduce distortion with this projection by using an interrupted version of it.

The image above is an example of an interrupted sinusoidal projection.

The scale of the Sinusoidal projection is true along both the Equator and the prime meridian. This property is preserved, at least for half of the Equator, if we consider the transverse aspect of the Sinusoidal projection as well:

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