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I have been told that the only straight lines on a sphere are great circles. Great circles are circles which pass through the "equator" of the circle. Why are these considered straight? They certainly look curved, because they are on a sphere.

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Straight isn't a good description. However, the shortest path between any two points on a sphere lies on a great circle just like in flat space, the shortest path between any two points lies on a straight line.

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  • $\begingroup$ Nice, short and to the point. +1 $\endgroup$ – DonAntonio Oct 2 '13 at 15:45
  • $\begingroup$ Straight is the best description. Consider the straight path from the north pole to Cape Town. Arriving in Cape Town keep up going straight away further to get back to the home of St. Claus. Geodesics rely on straightness, not on minimal distance. For that -1. $\endgroup$ – Michael Hoppe Oct 2 '13 at 18:31
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They are as straight as they can be, given that they have to lie on a sphere. Lines in Euclidean space and great circles on spheres are examples of what's called geodesics in differential geometry.

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