Earth's Curve, Flat Maps, and the Fastest Route Between Two Points

Imagine, say, that you wanted to travel from New York to Madrid, two cities that are at almost the same latitude. If the earth were flat, the shortest route would be to head straight east. If you did that, you would arrive in Madrid after traveling 3,707 miles. But due to the earth's curvature, there is a path that on a flat map looks curved and hence longer, but which is actually shorter. You can get there in 3,605 miles if you follow the great-circle route. which is to first head northeast, then gradually turn east, and then southeast. The difference in distance between the two routes is due to the earth's curvature, and a sign of its non-Euclidean geometry. Airlines know this, and arrange for their pilots to follow great-circle routes whenever practical.

Notes:

Because the Earth is a sphere and maps are flat, the fastest route between two points on a map is actually a curved line and airlines take this into account when plotting flight paths.

Folksonomies: geometry models maps

Taxonomies:
/science/mathematics/geometry (0.518712)
/travel/transports/air travel/airlines (0.500288)
/sports/football (0.496782)

Keywords:
fastest route (0.909952 (negative:-0.436227)), curved line (0.751659 (neutral:0.000000)), shortest route (0.739678 (neutral:0.000000)), flight paths (0.727254 (neutral:0.000000)), earth (0.696611 (negative:-0.145974)), New York (0.695341 (neutral:0.000000)), gradually turn (0.690903 (neutral:0.000000)), non-Euclidean geometry (0.681735 (neutral:0.000000)), Flat Maps (0.670470 (negative:-0.508408)), great-circle routes (0.659825 (positive:0.243413)), great-circle route. (0.650392 (neutral:0.000000)), flat map (0.631499 (neutral:0.000000)), Madrid (0.562051 (neutral:0.000000)), airlines (0.551663 (neutral:0.000000)), points (0.515166 (negative:-0.436227)), miles (0.515165 (neutral:0.000000)), sphere (0.480026 (negative:-0.436227)), latitude (0.475726 (neutral:0.000000)), account (0.462773 (neutral:0.000000)), difference (0.459325 (positive:0.250381)), cities (0.458191 (neutral:0.000000)), pilots (0.457734 (positive:0.243413)), distance (0.451506 (positive:0.250381))

Entities:
Madrid:City (0.937408 (neutral:0.000000)), New York:City (0.519687 (neutral:0.000000)), 3,605 miles:Quantity (0.519687 (neutral:0.000000)), 3,707 miles:Quantity (0.519687 (neutral:0.000000))

The Grand Design

Books, Brochures, and Chapters>Book: Hawking , Stephen W. and Mlodinow , Leonard (2011-09-01), The Grand Design, Bantam, Retrieved on 2011-12-12

Source Material [books.google.com]

Folksonomies: science quantum physics m-theory