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

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

  1. ShawnBlueNote

    ShawnBlueNote New 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. Didactylos4

    Didactylos4 Star commenter

    No it isn't
     
  3. Eureka!

    Eureka! Lead commenter

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

    Lascarina Star commenter

    And that ShawnBlueNote was an infant prodigy.:rolleyes:
     
  5. Mangleworzle

    Mangleworzle Star commenter

    You should have seen the mayhem before Newton invented gravity.
     
    Noja likes this.
  6. nomad

    nomad Star commenter

    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.
     
  7. Eureka!

    Eureka! Lead commenter

    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. lanokia

    lanokia Star commenter

    Aren't flat surfaces purely theoretical since space-time is curved so all surfaces are curved to some degree?
     
    Noja likes this.
  9. FritzGrade

    FritzGrade Senior commenter

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

    nomad Star commenter

    Not if they have a curvature of zero.
     
  11. lanokia

    lanokia Star commenter

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

    nomad Star commenter

    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. lanokia

    lanokia Star 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...
     
  14. nomad

    nomad Star commenter

    Or equidistant from two equally massive bodies.
     
  15. Vince_Ulam

    Vince_Ulam Star commenter

    All the cool kids are non-Euclidean:


     
    lanokia likes this.
  16. Vince_Ulam

    Vince_Ulam Star commenter

    Apples - everywhere.
     
    Burndenpark likes this.
  17. emilystrange

    emilystrange Star commenter

    did they invent apple crumble after that, then?
     
  18. racroesus

    racroesus Star commenter

    Do we know if the Universe is curved?
     
  19. Eureka!

    Eureka! Lead commenter

    Well I quite admire him now for being inquisitive about how intuitive basic science is. The fact is it isn't - but it is only through such "experiments" you realise that.
     
  20. lanokia

    lanokia Star commenter

    Aye again, accept that but that strikes me as another idealisation... I mean Jupiter and the Sun could be such a system and the Earth, Mars etc are just pin ****** but they still distort S-T.
     

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