Why Can't a Flat Map Be Perfectly Accurate?
Every two-dimensional flat map of the Earth is an unavoidable mathematical compromise. Because our planet is an oblate spheroid, Carl Friedrich Gauss proved in his famous Theorema Egregium that a sphere's surface cannot be flattened onto a plane without stretching, shearing, or tearing.
Consequently, cartographers must choose which geometric properties to preserve and which to sacrifice:
- Conformality: Preserves local shapes and angles (critical for navigation and aviation), but severely distorts surface area.
- Equivalence (Equal-Area): Preserves the exact surface area of every country relative to one another, but requires varying degrees of angular distortion.
- Compromise Projections: Balances shape and area without strictly preserving either (e.g. Robinson or Winkel Tripel).
The Mercator Projection (1569)
Created by Flemish geographer Gerardus Mercator in 1569, the Mercator projection is a cylindrical conformal projection. Its defining mathematical genius was that rhumb lines (lines of constant compass bearing) are rendered as straight lines. A navigator on a sailing ship could draw a straight ruler line between Lisbon and New York, read the compass heading directly off the chart, and sail continuously on that bearing without constantly adjusting course.
However, to preserve local angles, Mercator stretches east-west and north-south distances equally by the factor secant(latitude). This means:
- At the Equator (0°), area distortion is 1.0 (exact).
- At 60° latitude (Oslo, Anchorage, southern tip of Greenland), areas are exaggerated by 4.0×.
- At 80° latitude (northern Greenland, Svalbard), areas are exaggerated by over 33.0×.
- At 90° (the North and South Poles), area distortion approaches infinity, which is why standard Mercator maps must be cut off near 85° latitude.
The Equal Earth Projection (2018)
In August 2018, cartographers Bojan Šavrič (Esri), Bernhard Jenny (Monash University), and Tom Patterson (US National Park Service, retired) published the Equal Earth map projection in the International Journal of Geographical Information Science.
For decades, educators seeking an equal-area world map had to choose between:
- Gall-Peters: Strictly equal-area, but infamously creates severe north-south elongation near the equator, giving tropical nations a "stretched rubber" appearance.
- Robinson / Winkel Tripel: Visually attractive, but neither is equal-area, meaning relative country sizes are still inaccurate.
Equal Earth answered this historical challenge: it strictly guarantees equal relative area across the entire globe while maintaining smooth, visually pleasing continental outlines inspired by the Robinson projection. Curved meridians emulate the curvature of the spherical Earth, and straight, parallel latitude lines make it simple to compare climates and latitude bands.
Direct Comparison Table
| Feature | Equal Earth (2018) | Mercator (1569) | Gall-Peters (1973) | Robinson (1963) |
|---|---|---|---|---|
| Primary Property | Equal-Area (Equivalence) | Conformal (Shapes/Angles) | Equal-Area (Equivalence) | Compromise |
| Area Preservation | 100% Exact | Extreme polar distortion | 100% Exact | Approximate (~10-20% error) |
| Equatorial Shapes | Natural, balanced curves | Exact local shape | Severely squashed vertically | Pleasing curves |
| Polar Representation | Gracefully rounded pole lines | Mathematically infinite (cut off) | Flat rectangular line | Flat rectangular line |
| Best Use Case | Thematic maps, education, true size comparison | Marine navigation, local web zoom tiles | Historical equal-area advocacy | General atlas reference |
The Takeaway: Tradeoffs, Not "Right vs Wrong"
It is common to hear people argue that Mercator is "wrong" or "evil." In truth, Gerardus Mercator created one of the greatest mathematical navigational instruments in human history. The error is not the projection itself, but rather misusing Mercator as a general-purpose world map for classrooms and geopolitical comparisons.
When the goal is to compare country sizes, understand global demographics, or teach geography fairly, the Equal Earth projection is the state-of-the-art solution.