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Daily Dose · Maps/Sep 14, 2026/Projections & Distortion

Fourteen
Greenlands

Every flat map of a round planet has to lie somewhere. Mercator chose to lie about size — and put the whole lie in the north. On the map the world has used for 457 years, Greenland is drawn the size of Africa. Africa is fourteen times larger.

14×
Africa is 30,365,000 km².
Greenland is 2,166,086 km².
Mercator draws them the same size.

The rule is one line of trigonometry: on a Mercator chart, area is multiplied by sec²φ — the square of the secant of the latitude. At the equator that is 1. At 60° it is 4. At 80° it is 33. Greenland sits between 60°N and 83°N and is inflated roughly fourteenfold; Africa straddles the equator and is drawn almost true. The distortion is not a mistake. It is the price of the one thing the chart was built to do.

45°S ×2 30°S ×1.33 15°S ×1.07 0° EQUATOR ×1 15°N ×1.07 30°N ×1.33 45°N ×2 60°N ×4 75°N ×15 LATITUDE AREA DRAWN GREENLAND 2.17M km² DRAWN 14× TOO BIG AFRICA 30.37M km² CANADA RUSSIA U.S. BRAZIL INDIA AUSTRALIA SCANDINAVIA GREENLAND, TRUE SCALE 1/14 of Africa · equal-area ANTARCTICA CANNOT BE DRAWN — ON MERCATOR THE POLES LIE AT INFINITY. THE MAP IS CUT AT 83°N / 58°S. AREA SCALE = sec² φ AS MERCATOR DRAWS IT DRAWN NEAR TRUE SCALE TRUE AREA TINT = HOW MUCH THIS LATITUDE IS INFLATED
THE MAP OF THE STRETCH. Every horizontal band is tinted by how much this projection inflates it — pale at the equator, saturated toward the poles. Greenland is shown as Mercator draws it. The small outline in southern Africa is Greenland at its true area, one fourteenth of the continent around it. Coastlines are hand-simplified; the projection is the real Mercator equation.
01 · The rule

The map multiplies as you go north

Mercator holds angles true by stretching east–west to match the shrinking circles of latitude — then stretching north–south by exactly the same amount to keep shapes honest. Area pays for both. It is inflated by sec²φ, and it runs away fast.

×1 15° ×1.07 30° ×1.33 45° ×2 60° ×4 70° ×8.55 75° ×15 80° ×33 85° ×132 EQUATOR TOWARD THE POLE →
LatitudeRoughlyArea drawn
the equator×1
15°Dakar, Manila×1.07
30°Cairo, New Orleans×1.33
45°Milan, Portland×2
60°Oslo, Anchorage×4
70°Tromsø, central Greenland×8.55
75°northern Greenland×15
80°Alert, Nunavut×33
85°the Web Mercator cut-off×132

The inflation is unbounded. At the pole itself, sec²φ is infinite — which is why no Mercator map has ever shown a pole. Google Maps and every other web map cut the world off at ±85.05113°, the latitude that makes the world a convenient square.

This is not a flaw anyone can engineer away. In 1827 Gauss proved the Theorema Egregium: a sphere has curvature a plane does not, so it cannot be flattened without distortion. No flat map can keep both area and angle. Every projection is a choice about what to sacrifice.

02 · The comparison

Ten places the map draws too small

True land areas, on one linear scale. The dashed line is Greenland. Everything above it is larger than Greenland in the world — and smaller than Greenland on the wall.

TRUE LAND AREA · MILLION km² Africa 30.36 United States 9.83 China 9.60 Brazil 8.52 Australia 7.69 India 3.29 Argentina 2.78 Kazakhstan 2.72 Algeria 2.38 DR Congo 2.34 Greenland 2.17 GREENLAND
DR CONGO AND ALGERIA ARE EACH LARGER THAN GREENLAND. SO ARE KAZAKHSTAN AND ARGENTINA. IN 2010 KAI KRAUSE NESTED THE USA, CHINA, INDIA, JAPAN AND MUCH OF EUROPE INSIDE AFRICA — A DELIBERATELY SYMBOLIC FIT, BUT THE ARITHMETIC BEHIND IT HOLDS.
03 · What the chart was for

It was never meant to be a picture of the world

Mercator built a machine for sailors. On his chart a course of constant compass bearing — a loxodrome — is a straight line you can rule with a straightedge. That single property is worth every distortion it costs.

30° 60° 75° ON THE MERCATOR CHART A STRAIGHT LINE HOLD 052° ON THE COMPASS — RULE IT WITH A STRAIGHTEDGE ON THE GLOBE A SPIRAL TO THE POLE THE SAME COURSE — A LOXODROME, ENDLESSLY CIRCLING
THE SAME COURSE, PLOTTED TWICE AT A CONSTANT 052°. ON THE CHART IT IS A STRAIGHT LINE; ON THE GLOBE IT IS A SPIRAL THAT CIRCLES THE POLE FOREVER WITHOUT REACHING IT. THIS IS WHY THE 2026 UN RESOLUTION EXPLICITLY LEAVES MERCATOR IN PLACE FOR MARINE AND AIR NAVIGATION.
04 · The corrected map

The same outlines, told without the stretch

Equal Earth, published in 2018, is an equal-area projection: every shape on it holds its true proportion of the planet. Shapes bend instead. That is the trade Gauss says you must make — the only question is which way you make it.

GREENLAND 2.17M km² AFRICA 30.37M km² EQUAL EARTH · ŠAVRIČ, JENNY & PATTERSON, 2018 · EVERY SHAPE HOLDS ITS TRUE AREA SAME OUTLINES. SAME PAGE. NO STRETCH.
SAME HAND-DRAWN COASTLINES AS THE HERO MAP, PUT THROUGH THE EQUAL EARTH EQUATIONS INSTEAD. GREENLAND GOES FROM 1.08× AFRICA'S DRAWN AREA TO 0.076× — ESSENTIALLY THE TRUE 1:14. NOTHING MOVED BUT THE MATHEMATICS.
1.08×
Greenland vs Africa
as drawn on Mercator
0.08×
Greenland vs Africa
as drawn on Equal Earth
40.4°
Latitude where Equal Earth's
shape fidelity peaks
05 · The record

457 years, and a vote of 164 to 1

The argument about this map is older than most countries on it. On 4 September 2026 it reached the floor of the UN General Assembly.

  • 1569Mercator publishes Nova et Aucta Orbis Terrae Descriptio — a chart “corrected for the use of sailors.”
  • 1827Gauss proves the Theorema Egregium: no flat map can hold both true area and true angle.
  • 1855James Gall describes an equal-area cylindrical world map. It is forgotten within a century.
  • 1973Arno Peters re-presents it at a Bonn press conference on 5 May, and the argument goes public.
  • 2005Google Maps launches on Web Mercator (EPSG:3857), which truncates the world at ±85.05°.
  • 2017Boston Public Schools swaps the maps in its 2nd-, 7th- and 11th-grade classrooms.
  • 2018Šavrič, Jenny & Patterson publish Equal Earth; NASA uses it that July.
  • 2025The African Union endorses the “Correct the Map” campaign on 14 August.
  • 2026The UN General Assembly adopts Correct the map (A/80/L.104), 164–1, on 4 September.
164
Member states in favour of
resolution A/80/L.104
1
Against — the United States,
the sole objector
6
Abstentions: Estonia, Georgia,
Lithuania, Moldova, Serbia, Ukraine

“A fair map does not change the geography of the world, it changes how we see the world.” — Robert Dussey, Foreign Minister of Togo, introducing the resolution. The text is not binding, and it does not ask anyone to stop navigating by Mercator. It asks for equal-area maps when relative size is what the map is about, and for schools to teach that flat maps of a round planet always cost something.

06 · Why it matters

What to notice on the map

Four things the hero map shows that a sentence cannot.

  1. The tint is the whole argument. The horizontal bands darken with sec²φ. Notice that the darkening is not gradual — it is nothing at all for most of the map, then almost everything in the last twenty degrees. Distortion hides until it doesn't.
  2. Greenland and Africa are the same size on the page. Put a thumb over the labels and you cannot tell which is bigger. That is the illusion doing its work, and it is doing it on almost every classroom wall and news graphic in the world.
  3. The small shape in southern Africa is also Greenland. Same island, correct area, drawn to the same scale as the continent surrounding it. Fourteen of it would fit.
  4. The bottom of the map is missing. Antarctica cannot be drawn at all — on Mercator the poles sit at infinity. A map that cannot show one of the seven continents is a very specific tool, not a portrait of the planet.
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