Maps & Spherical Geometry
Math · Intermediate · Lesson 6 of 7

The Mercator Map

Why Greenland looks huge

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

  • No flat map can show a sphere without distortion (Gauss, 1827).
  • Mercator preserves angles but stretches lengths by 1cos⁡φ\frac{1}{\cos\varphi} and areas by 1cos⁡2φ\frac{1}{\cos^2\varphi}.
  • Equal-area projections keep sizes fair but distort shapes.

Steps

  1. No perfect map
  2. Inflating circles
  3. Greenland and Africa
  4. Scale bars
  5. Far north on Mercator
  6. Choosing a projection