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.

What is the shortest distance between two points on a sphere called?

• Great circle distance

• Straight line distance

• Flat Earth distance

• Curved path distance

Why do airplanes often take curved routes instead of straight lines?

• To save time by flying over more countries

• To follow air traffic control instructions

• Because curved routes are shorter on a spherical Earth

• To avoid bad weather

How does a 2D map affect the perception of distances?

• It shortens distances for convenience

• It makes distances appear longer

• It accurately represents all distances

• It distorts distances due to flattening

What defines a great circle on a sphere?

• A circle with a smaller radius than the sphere

• A circle that is parallel to the equator

• A circle that is perpendicular to the poles

• A circle whose center coincides with the sphere's center

What is a limitation of great circle distances?

• They ignore the curvature of the Earth

• They assume Earth is a perfect sphere

• They are only applicable to small circles

• They are not used in modern navigation