Alternative to Euclid's Concept of Straight Line

[pjunky]

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:

 

[arildno]

I'm sure you are not the only one.
The following link is to an online version of the Elements, with neatly arranged commentaries to euclid's text. It is frequently critical of him:
http://www.mathcs.clarku.edu/~djoyce/java/elements/toc.html

 

[Tac-Tics]

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.

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.

 

[arildno]

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:

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)

 

[pjunky]

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.