Pseudocylindrical Family·Inventor: John Paul Goode·Year: 1923

Goode Homolosine Projection

"Equal-area interrupted hybrid joining Sinusoidal at the equator with Mollweide in the polar zones"

Goode combined the Sinusoidal projection (between 40°44'N and 40°44'S) with the Mollweide projection for higher latitudes, interrupting the ocean basins to allow each major continental landmass to be centered on its own local meridian.

Forward Mathematical Formulation

X-COORDINATE:

\text{Sinusoidal below } 40^\circ 44', \quad \text{Mollweide above } 40^\circ 44'

Y-COORDINATE:

Coincident parallels at } \phi = \pm 40^\circ 44'12''

DIFFERENTIAL METRIC:

Equal-area across all segments (h \cdot k = 1)

Cartographic Application & Critique

Primary Applications: Rand McNally Goode's World Atlas, Global distribution of climate, agriculture, and forestry.

Critical Analysis: Known colloquially as the 'orange peel map', it achieves pristine continental area fidelity by transferring the inevitable distortion into the oceans.

TISSOT INDICATRIX (Lat: 60°N)Area: 1.02×

MERIDIAN (h)

1.13

PARALLEL (k)

0.90

ANGULAR (2θ')

13.2°

Tissot Profile Across Latitudes

LATITUDE	SCALE h	SCALE k	AREA hk	2θ' DEFORM
0°N	1.00	1.00	1.00×	0.0°
30°N	1.08	0.93	1.00×	14.2°
60°N	1.22	0.82	1.00×	28.5°
80°N	1.45	0.69	1.00×	48.1°

Interdisciplinary Geometric Links

MorphologiumUSES

Composite Manifold Blending

VeridianumREPRESENTS

Ecological & Resource Distribution

Academic Provenance: Goode, J. P. (1925)