Pseudocylindrical Family·Inventor: Arthur H. Robinson·Year: 1963

Robinson Projection

MATHEMATICAL SPECIMEN · ROBINSON

"Visually balanced compromise projection adopted as the National Geographic standard"

Commissioned by the Rand McNally publishing company, Robinson created an empirical lookup table of coordinates designed to minimize both shape and area distortion across the global oceans and continents simultaneously.

Forward Mathematical Formulation

X-COORDINATE:

x = 0.8487 \cdot R (\lambda - \lambda_0) \cdot X(\phi)

Y-COORDINATE:

y = 1.3523 \cdot R \cdot Y(\phi)

DIFFERENTIAL METRIC:

Tabulated numerical interpolation (not an analytical algebraic function)

Cartographic Application & Critique

Primary Applications: Thematic global atlases, National Geographic Society world maps (1988–1998), Educational publishing.

Critical Analysis: Because it is neither conformal nor equal-area, Robinson cannot be used for precision mathematical measurement or navigation, but stands as a masterwork of perceptual visual compromise.

TISSOT INDICATRIX (Lat: 60°N)Area: 0.91×

MERIDIAN (h)

1.16

PARALLEL (k)

0.78

ANGULAR (2θ')

22.3°

Tissot Profile Across Latitudes

LATITUDE	SCALE h	SCALE k	AREA hk	2θ' DEFORM
0°N	0.98	1.00	0.98×	3.2°
30°N	1.02	0.95	0.97×	12.4°
60°N	1.15	0.82	0.94×	31.8°
80°N	1.38	0.58	0.80×	54.0°

Interdisciplinary Geometric Links

The Chromologium (Color Physics)APPLIES

Visual Balance & Harmonization

Narrative SemioticsMANIFESTS

Geographic Compromise Rhetoric

Academic Provenance: Robinson, A. H. (1974)