Is A Straight Line Always The Shortest Distance Between Two Points?

The video tutorial explores the concept of the shortest distance between two points, emphasizing that it varies based on geometry. On a flat surface, a straight line is the shortest path, but on a sphere like Earth, the shortest path is an arc called the great circle distance. This concept is crucial in air travel, where flights follow curved routes to minimize distance and fuel consumption. The video also discusses map distortion, explaining how 2D maps can misrepresent distances. It defines great and small circles mathematically and highlights the practical implications and limitations of using great circle distances, considering Earth's shape as a flattened sphere.

Explain the difference between a great circle and a small circle on a sphere.

Why do great circle distances have a tolerance of about ±5%?