Deducing Mollweide's Projection
Although mathematically very simple, the previous Sanson-Flamsteed projection
is not completely satisfactory at high latitudes, due to
excessive shearing and crowded meridians. A slightly more
complicated analysis leads to a new, somewhat
complementary projection.
Given the Earth's radius R, suppose the equatorial
aspect of an equal-area
projection with the following properties:
- A world map is bounded by an ellipse twice broader than
tall
- Parallels map into parallel straight lines with uniform
scale; only the Equator is a standard
line
- The central meridian is a straight standard line; all
other ones are semielliptical arcs
Suppose an Earth-sized map; let us define two regions,
S1 on the map and S2 on the Earth, both bounded
by the Equator and a parallel. The equal-area property
can be used to calculate y given 
. Given
y and 
, x can be calculated immediately
from the ellipse equation, since horizontal scale is constant.
 |  |  |  |  |  | | www.progonos.com/furuti September 21, 2002 |