DATUM: WGS 84 / EPSG:4326
|SPATIAL EPISTEMOLOGY
CARTOLOGIUMATLAS
Spatial Representation & Projections
MATHEMATICAL ATLAS · 14 PROJECTIONS INDEXED

The Projection Lab

Every map projection is a mathematical compromise between area, conformal angle, distance, and direction. Explore 14 landmark projections with real-time Tissot indicatrix deformation metrics.

THE PROJECTION DISTORTION CRUCIBLE

Mercator Projection (1569)

Inventor: Gerardus Mercator · Family: Cylindrical

TEST LATITUDE:60° North
0° (Equator)30° (Subtropics)60° (Greenland)85° (Arctic)
Conformal (Angles)
Equal-Area (Sizes)
Compromise Map
Uninterrupted
CONTINENTAL SCALE DISTORTION RATIO:
True geographic area of Greenland (2.16M km²) is 1/14th (0.07×) of Africa (30.37M km²).
Projected Visual Ratio:1:1 (Equal Size!)
TISSOT INDICATRIX (Lat: 60°N)Area: 4.00×
h=2.00k=2.00
MERIDIAN (h)
2.00
PARALLEL (k)
2.00
ANGULAR (2θ')
0.0°
Cartographic & Political Critique:

"When co-opted into classrooms and wall atlases, Mercator visually inflates imperial powers in North America and Europe while drastically shrinking the African continent, South America, and the equatorial belt."

Formula: h = k = \sec \phiFull Mathematical Dossier

Complete Mathematical Projection Directory

CylindricalGerardus Mercator (1569)

Mercator Projection

Engineered strictly as a marine navigation tool, Mercator stretches latitude intervals toward the poles at the exact rate needed to preserve loxodromes (rhumb lines) as straight lines. This produces monumental area inflation in polar latitudes.

Conformal
Greenland: 1.00×Explore Dossier
CylindricalJames Gall (1855) / Arno Peters (1973) (1973)

Gall-Peters Projection

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.

Equal-Area
Greenland: 1:14Explore Dossier
PseudocylindricalArthur H. Robinson (1963)

Robinson Projection

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.

Compromise
Greenland: 1:8Explore Dossier
PseudocylindricalOswald Winkel (1921)

Winkel Tripel Projection

Tripel ('triple') refers to Winkel's objective to simultaneously minimize three distortions: area, direction, and distance. Adopted by National Geographic in 1998 to replace Robinson.

Compromise
Greenland: 1:11Explore Dossier
PolyhedralR. Buckminster Fuller (1954)

Dymaxion Projection (Fuller)

Projected onto the 20 triangular facets of an icosahedron and unfolded flat with no standard 'North-Up' orientation, Fuller's Dymaxion map presents the Earth's continents as an almost contiguous landmass with minimal local shape or area distortion.

CompromiseInterrupted
Greenland: 1:13Explore Dossier
QuincuncialCharles Sanders Peirce (1879)

Peirce Quincuncial Projection

Invented by the American pragmatist philosopher and mathematician C.S. Peirce, this projection maps the globe onto a square where the North Pole is at the center and the South Pole is divided among the four corners, forming a tessellatable quincunx.

Conformal
Greenland: 1:9Explore Dossier
PseudocylindricalJohn Paul Goode (1923)

Goode Homolosine Projection

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.

Equal-AreaInterrupted
Greenland: 1:14Explore Dossier
PseudocylindricalKarl Brandan Mollweide (1805)

Mollweide Projection

Published in Leipzig as an improvement on Mercator for astronomical and global geographic distributions, Mollweide represents the entire spherical world within an exact 2:1 ellipse.

Equal-Area
Greenland: 1:14Explore Dossier
ConicJohann Heinrich Lambert (1772)

Lambert Conformal Conic (LCC)

Lambert’s mathematical tour de force projects the sphere onto a cone intersecting the globe at two standard parallels. Meridians are straight lines converging at the pole; parallels are concentric circular arcs.

Conformal
Greenland: 1:12Explore Dossier
ConicHeinrich C. Albers (1805)

Albers Equal-Area Conic

Using two standard parallels where scale is exact, Albers Equal-Area Conic preserves true proportional surface area across large east-west landmasses like the contiguous United States, Europe, and China.

Equal-Area
Greenland: 1:14Explore Dossier
AzimuthalAl-Biruni (c. 1000 CE) / Guillaume Postel (1581) (1581)

Azimuthal Equidistant Projection

Centered on any chosen point (such as the North Pole in the United Nations emblem or a radio broadcasting antenna), every straight line radiating from the center is a true great circle with exact linear scale.

Equidistant
Greenland: 1:11Explore Dossier
AzimuthalHipparchus (c. 150 BCE) / Classical Antiquity (-150)

Orthographic Projection

A perspective azimuthal projection where light rays originate from infinity. It portrays the Earth exactly as it appears from deep space, displaying exactly one hemisphere at a time with foreshortening increasing toward the horizon limb.

Compromise
Greenland: 1:14Explore Dossier
PolyhedralSteve Waterman (1996)

Waterman Butterfly Projection

Waterman developed this projection based on packing spheres and unfolding a truncated octahedron (WKS polyhedra). Continents remain remarkably compact and undistorted while displaying ocean connectivity.

CompromiseInterrupted
Greenland: 1:14Explore Dossier
PolyhedralHajime Narukawa (1999)

AuthaGraph Projection

Created by Japanese architect Hajime Narukawa, AuthaGraph divides the spherical earth into 96 regions, projects them onto an inflated tetrahedron, and unfolds into an approximate equal-area rectangle that can tile infinitely.

Equal-Area
Greenland: 1:14Explore Dossier