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constantinople
A straight line
the shortest air route is a great circle
since air travel can fly a more direct route, not having to circumnavigate land mass, it would be the shortest distance.
chennai to tehran, paris and london
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Great Circle Route
The shortest route between two points on the surface of a planet, when routes are limited to the planet's surface, is the arc of the great circle that connects the two points. The shortest route between two points anywhere, without regard to intervening matter or energy preventing the route from being followed, is always the line connecting the two points.
It was the Suez Canal, which was a short cut between the Mediterranean Sea and the Indian Ocean, leading to India, Australia and Asia.
If you mean by the words "direct route" the shortest distance between two places, distances between two places are shortest at the equator, because of the shape of the planet. If you mean which direction should be traveled to minimize distance, the route taken should be as straight a line as possible.
The geographical position of the Suez Canal makes it the shortest route between East and West as compared with the Cape of Good Hope. The Canal route achieves saving in distance between the ports north and south of the Canal.
straight line