# The shortest distance between two points is a straight line!!

Discussion in 'Personal' started by ShawnBlueNote, Jan 29, 2016.

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1. ### ShawnBlueNoteNew commenter

Everybody knows that a straight line is the shortest distance between two points. I knew this from the time I was a nursery kid. However, it appears that Euclid, the Greek mathematician is credited with the discovery of this simple fact. This is ridiculous as far as I am concerned. Does one have to be a genius to discover this????

2. ### Didactylos4Star commenter

No it isn't

Bear in mind that it took a long time to invent/discover zero....

4. ### LascarinaStar commenter

And that ShawnBlueNote was an infant prodigy.

5. ### MangleworzleStar commenter

You should have seen the mayhem before Newton invented gravity.

Noja likes this.

It is only the shortest one on flat surfaces (i.e., Euclidean geometry). On spheres and other shapes, it may not be.

Your statement (above) fails when applied to non-Euclidean geometries, such as spheres and more complex geometries like saddles (hyperbolic paraboloids). Indeed, all the rules you learned in school (or nursery, in your case) like parallel lines staying parallel, only refer to Euclidean geometry. In the non-Euclidean universe, parallel lines may actually diverge or converge.

In Y8 we had a physics teacher who tried to get us to define "force" with none of us ever having any knowledge of Newtonian mechanics whatsoever. Needless to say, nobody had a clue.

8. ### lanokiaStar commenter

Aren't flat surfaces purely theoretical since space-time is curved so all surfaces are curved to some degree?

Noja likes this.

One of those teachers who tries to get the kids to do his job.

Not if they have a curvature of zero.

11. ### lanokiaStar commenter

But if space-time is curved [especially here on a body with mass] then all surfaces have to be curved surely?

No. Think of a plane or a line curving in one direction and slowly decreasing the amount of curvature so that it eventually begins to curve in the other direction. At some point its curvature will be zero.

wanet likes this.
13. ### lanokiaStar commenter

Aye I can accept that... but that curvature zero won't happen in an area with mass? Maybe in deep interstellar or even intergalactic space... but not here...

Or equidistant from two equally massive bodies.

15. ### Vince_UlamStar commenter

All the cool kids are non-Euclidean:

lanokia likes this.
16. ### Vince_UlamStar commenter

Apples - everywhere.

Burndenpark likes this.
17. ### emilystrangeStar commenter

did they invent apple crumble after that, then?

18. ### racroesusStar commenter

Do we know if the Universe is curved?