Great Circle Routes: The Shortest Way Home

Introduction

A straight line on a flat map is not the shortest path between two points on a sphere. Using Great Circle Map (greatcirclemap.com), students can plot routes between cities — for example Geneva, Dubai, and Tokyo — and discover that the shortest route curves dramatically on a flat projection. This exploration connects spherical geometry, trigonometry, and the haversine formula to real-world navigation. Students can investigate why airlines choose certain stopover cities, how wind patterns and geopolitics affect routing, and how different map projections distort our perception of distance. The mathematics reveals why the 'obvious' route is rarely the optimal one.

Guiding Questions

• Why does the shortest flight path appear curved on a flat map?
• How can you calculate the great circle distance between two cities using their coordinates?
• What factors other than distance affect which route an airline chooses?
• How do different map projections distort the appearance of routes and distances?
• If you had to choose one stopover city between Geneva and Tokyo, which minimises total distance?

Key Mathematical Concepts

Helpful Resources

• https://www.greatcirclemap.com/