Talk:Euclidean geometry

I disagree that Euclidean geometry refers primarily to plane geometry. Certainly I have never thought of it that way. Euclid also did not restrict him to plane geometry in his "Elements". So I hope you don't mind, but I changed that bit. mike40033 07:18, 12 Mar 2004 (UTC)

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Should this article be merged with Non-euclidean geometry? -- The Anome

No, I don't think so. This article ought to discuss Euclidean geometry. At the moment it doesn't actually say much about Euclidean geometry, and instead spends too much time discussing non-euclidean geometry, which is already discussed in Non-euclidean geometry. So it needs a lot of work, and some of it should be moved to Non-euclidean geometry, but it should remain a separate article. --Zundark, 2001 Dec 22

The five postulates are:

1. To draw a straight line from any point to any point.
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any center and radius.
4. That all right angles equal one another.
5. That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Source: http://s13a.math.aca.mmu.ac.uk/Geometry/M23Geom/Euclid/Euclidbook1.html
looxix 21:51 Feb 23, 2003 (UTC)

Currently, the article includes:

 As Godel proved, all axiomatic systems -- excepting the very simplest -- 
 are either incomplete or contradict themselves, and this is no exception.

It seems to me that a sufficiently simple axiomatization of Euclidean geometry might actually be complete. I don't see any way to embed the natural numbers in Euclidean geometry, which is the usual way to verify that Gödel's theorem applies. -- Carl Witty

Isn't there some work on showing how to make computations with ruler-and-compass constructions, providing you have a pre-existing "program"? The Anome 19:36 21 May 2003 (UTC)

It's:

• Simon Plouffe.The Computation of Certain Numbers Using a Ruler and Compass. Journal of Integer Sequences, Vol. 1 (1998), Article 98.1.3

The Anome 19:56 21 May 2003 (UTC)

Contents

1 Is not enough! 2 Parallel postulate 3 removed part 4 Euclidean geometry sometimes means geometry in the plane

Is not enough!

In deed,the article is well constructed showing us the basics of Euclidian Geometry but i think is a little short for those who are intrested to learn more about this subject.I hope to find out more in the future!

Parallel postulate

The fifth postulate is equivalent to parallel postulate, which can be phrased as follows

• Through a point not on a given straight line, one and only one line can be drawn that never meets the given line.

I don't believe this is true, nor the correct way or naming things. The "parallel postulate" to be completely accurate should always refer to Euclid's axiom as he stated it. I believe what is being called the "parallel postulate" here is actually what is rightly called "Playfair's axiom", although to be perfectly honest, there is even some doubt in my mind as to whether this term is meant to mean "exactly one line" or "at most one line" (Playfair used the former phrase, Legendre the latter, so there is some confusion for me, or if it matters.) Revolver 06:30, 20 Mar 2004 (UTC)

removed part

I just removed new subsection, it was correct but irrelevent, might go somewhere else... Tosha 00:00, 30 Mar 2004 (UTC)

Thanks for stating your points of view regarding the correctness and relevence (sic) of the characterizations of physical spaces in terms of Euclidean geometry succinctly, yet explicitly and separately.

Thanks also for the generous scope of your suggestions where else within this encyclopedic representation of what's considered correct (at least: rather than "any where else but ...") this topic might be addressed instead.

Being left to narrow this considerable selection down, perhaps (at least) to

- the discussion of Euclidean planes and spaces by the author of A Modern View of Geometry, W. H. Freeman (1961),

- derivations and statements of certain expressions (such as that attributed to one Tartaglia) which some do seem to find noteworthy after all,

- considerations rather less frivolous than [[Talk:Why 10 dimensions]], or

- being an [[Wiktionary:Also-ran]] to what appears already established,

the choice appears nevertheless daunting ...

Regards, Frank W ~@) R 03:44, 30 Mar 2004 (UTC).

Euclidean geometry sometimes means geometry in the plane

I would sugest at least

Euclidean geometry often means geometry in the plane

for me (I'm russian) Euclidean geometry means plane geometry if not stated otherwise, maybe for all of you it is different, but then it is not clear why the article on Euclidean geometry explains what plane geometry is...? Tosha 12:43, 29 Jul 2004 (UTC)