Gall-Peters Projection
"Equal-area cylindrical projection with standard parallels at 45°N and 45°S"
Championed by Arno Peters in the 1970s as a politically just corrective to Mercator, Gall-Peters preserves absolute surface area proportions across the globe at the cost of extreme shape shearing at the poles and vertical elongation at the equator.
Forward Mathematical Formulation
x = \frac{R (\lambda - \lambda_0)}{\sqrt{2}}y = R \sqrt{2} \sin \phih = \sqrt{2} \cos \phi, \quad k = \frac{1}{\sqrt{2} \cos \phi}, \quad hk = 145°N, 45°SCartographic Application & Critique
Primary Applications: UNESCO educational charts, Post-colonial geopolitical advocacy, Area comparisons.
Critical Analysis: While solving the area distortion problem, Gall-Peters trades angular fidelity for severe tropical stretched distortion ('wet rags hanging on a line'), ignoring that dozens of equal-area pseudocylindrical alternatives (Mollweide, Boggs, Goode) preserve area with far superior aesthetic shape preservation.
Tissot Profile Across Latitudes
| LATITUDE | SCALE h | SCALE k | AREA hk | 2θ' DEFORM |
|---|---|---|---|---|
| 0°N | 1.41 | 0.71 | 1.00× | 41.8° |
| 30°N | 1.23 | 0.82 | 1.00× | 23.1° |
| 45°N | 1.00 | 1.00 | 1.00× | 0.0° |
| 60°N | 0.71 | 1.41 | 1.00× | 41.8° |
| 80°N | 0.24 | 4.08 | 1.00× | 83.2° |