Shortest distance

[Eurox]

Is it possible for the shortest distance between two points not to be a straight line?

[kempie]

Yes.

e.g. if the line is following the contours of a surface.

[JudgeJ]

Beware Kempie!

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.

[kempie]

I didn't confuse anything.

The question did not mention geometry and as such my example is possible.

[kempie]

oops... my previous post should have read 'geometry of a sphere'

[janesmythe22]

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.

[landie]

Yes, as kempie has said, aircraft fly a path akin to stretching a length of string aroung a sphere. Spacecraft use gravitational forces to aid their navigation past planetary objects and ships negotiate tides to reach their destinations.

[magicdice]

no - a line following the contours of a surface is longer than a straight line, is it not?

[kempie]

magicdice - that would depend on your definition of 'straight' when you apply it to surface geometry, as highlighted by janesmythe22.

[magicdice]

ahh i stand corrected. i only skimmed the other answers & you were all up to your elbows in it which put me off a touch.

no such thing as a simple question here!

[fo3nix]

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.

[Azimov]

In order to travel between any two points, one must first travel half the distance.

As there are infinite halves, the distance between any two points must also be infinite, therefore no matter what route you choose you'll never get there anyway.

So the answer to your question is no! ;o)

[fo3nix]

Azimov: not really related to the original question, but that is a mathematical problem that had many people stumped for a while. but has since been solved. :P

[mikola]

Well...what about worm holes, in theory? Couldn't you travel through a worm-hole (if you could survive it) and be sent to any point in space?

[fo3nix]

a wormhole is just a theoretical warping of spacetime within a certain region. If this theory is correct, then again the shortest distance between two points in spacetime may not be straight.