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Euclidstraight line

  1. Oct 24, 2008 #1
    I'm not getting satisfied with Euclid's concept of straight line and shortest distance b/w to given points is a Straight line,At present I'm studying "The Elements".

    Can you people know any alternatives on this topic?
    I'm interested to study them.


    Thanks:shy:
     
  2. jcsd
  3. Oct 24, 2008 #2

    arildno

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    Dearly Missed

  4. Oct 24, 2008 #3
    By today's standards, Euclid wasn't entirely rigorous. In 1899, Hilbert gave a course on axiomatic geometry from his own formulation. Whereas Euclid describes geometry in 5 axioms, Hilbert does the same with no less than 20.

    http://en.wikipedia.org/wiki/Hilbert_axioms

    Euclid relied more heavily on common sense in proofs. Granted, all proofs require an amount of common sense, it's clear that Hilbert assumed even less.
     
  5. Oct 24, 2008 #4

    arildno

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    As for Euclid's definition I.4 of the straight line, it is NOTORIOUSLY vague, so you are not alone.

    (For the a-culturalists here on PF, check out the link)
     
  6. Oct 24, 2008 #5
    wow..! thank you all people
    I think I'm alone but so many are here,its great.
    I'm very confusing with dimension concept too,not satisfying with concept of 3rd Dimension.
     
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