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Shortest distance
Is it possible for the shortest distance between two points not to be a straight line?
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The shortest practical distance may well not be a straight line (e.g. from England to Australia. One has to follow the contours of the earth, and so travel about 12,000 miles).
However, the true shortest distance in this case is actually via the earth's centre, only about 8,000 miles.
You must be careful not to confuse the shortest distance between two points on the surface of an impenetrable solid body, and the true, geometric, shortest distance.
If you were thinking of the Earth, it's never a straight line. It's a geodetic line. Related to the Cosmos, if Einstein is right, then again, it's not a "straight" line. On the other hand if you define the straight line as "the shortest distance between two points etc...", in that case, by definition, it always applies. That's the problem with "common sense". See "Euclid: The Elements" and his five postulates (and what happened to his fifth postulate, also what may be "wrong" with his fourth postulate). Well, we don't know what "electricity" is, but still people are paying electricity bills.
for flat space (a plane of glass, for example), the geometry here is called Euclidean. here, the shortest distance between two points is a straight line.
for non-flat space (a sphere, such as the earth, for example), the shortest distance is not necessarily a straight line. it's often called a geodesic.
the sort of geometry you may want to use for non-flat space is known as Riemannian geometry.
for non-flat space (a sphere, such as the earth, for example), the shortest distance is not necessarily a straight line. it's often called a geodesic.
the sort of geometry you may want to use for non-flat space is known as Riemannian geometry.