PPT Slide
Another representation leads to a more useful display of the azimuthal projections. The X axis represents distance on the sphere. The Y axis represents the same distance on the map. Take an increment (one centimeter, say) on the X axis, then move up to the curve. Then move across to the Y axis to find the amount by which the spherical distance has changed. The advantage of this representation is that the slope of the curves quickly reveals the distance change. It is an approximation to the areal enlargement. For example, if the slope is greater than one, the map area is enlarged. If the slope is less than one the map distances shrink. If the slope is equal to one we have the azimuthal equidistant projection.