Why Do We Need Projections?

The Earth is round, but maps are flat! To show the curved surface of the Earth on a flat page, we use map projections—mathematical ways of transforming the globe onto a sheet of paper.

Types of Projections

• Mercator Projection: Good for navigation but makes places near the poles look bigger.
• Robinson Projection: Balances size and shape for a more realistic world map.
• Azimuthal Projection: Shows polar areas accurately.

Projection Distortions

Every projection distorts some aspect of reality: size, shape, distance, or direction. Choosing the right projection depends on the map's purpose.

Real-World Relevance

• Pilots and sailors use specific projections for charting courses.
• Classroom world maps use projections that balance accuracy.

Formula

The math behind projections can get advanced, but here’s a simple version for converting latitude and longitude to a flat map:

\[ x = R \lambda,\quad y = R \ln\left(\tan\left(\frac{\pi}{4} + \frac{\phi}{2}\right)\right) \] where \( R \) is Earth's radius, \( \lambda \) is longitude, and \( \phi \) is latitude.