# What are the strengths and weaknesses of these projections?

## Gall-Peters Mercator Azimuthal Equidistant Robinson

Oct 11, 2016

See explanation.

#### Explanation:

There could be no listing of map projections in Cartography, sans

reference to the elliptical (19th century ) Mollweide projection. , for

both the (poles inclusive ) hemispheres, over an ellipse.

The semi of the ellipse are in the proportion a = 2b.

in appropriate scale (say 1.2" to 10^8" , for a = 3" ), there is

no distortion for the equatorial circle of length $2 \pi R$, with a

representing $\pi R$..

Alternately, we can make the total surface area $4 \pi {R}^{2}$ truly

represented. Here, area of the ellipse $\pi a b = \pi {a}^{2} / 2 \to 4 \pi {R}^{2} \to$ a

representing $2 \sqrt{2}$R.

The 20th century A. H. Robinson.s map is similar, with the

weaknesses that it is neither conformal ( in preserving surface

angles ) nor keeping local areas on the same scale. The strength is

in Meredian ( longitudinal ) great circles turning gently towards

poles. In my opinion, Mollweide's projection is a basis for National

Geographical Society (NGS)-supported Robinson projection.

Oldest is G. Mercator's cylindrical map for the globe. When spread

over a Table, it is rectangular. We cannot map polar regions here,

The scale distortion is $0 \to \infty$. This method for the then sailors

is the forerunner for all the subsequent improvements.

I break here, to continue after some hours, in my next edition of

Mercator's map preserves the stretch along the equator.. As

latitude increases, lengths are zoomed. In other words, the

Scandinavian countries would be very much stretched. Using

this, we could easily make out finer details for places over

higher-latitude small circles

.The projection contributed by J. Galli and A. Peter in in 20th

century was adopted in British schools. It is cylindrical equal-area

projection and is better for sub polar latitudes. The area for USA

will be thrice the area for India. The ratio is preserved.

In equidistant maps , each location is dragged relative to the

other so that the distance scale is preserved. This is good with

respect to instant location, for relative distances.

Azimuthal circular projection .is centered at a pole and is good if it

ends with the equator great circle. Locations with same longitude

lie on a radius, Latitude circles are really small. The globe can be

presented separately in two circular maps, for the northern and

southern latitudes, respectively.

Despite relative merits, all are good and meticulous. for local (

spherical cap ) neighborhood, .

For graphical depictions, see respective wiki pages, for these

projections.