Talk:Geometry

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Covers major areas well, but needs references, general expansion, and examples. Tompw 16:13, 5 October 2006 (UTC)

Contents 1 Separation from History of geometry article 2 Suggestions on further expansion 3 Re: references and examples 4 Questionable 5 pictures 6 Geometrist 7 Different forms of geometry 8 History

[edit] Separation from History of geometry article

(Note: I couldn't find the message I composed to explain the move, so here it is to best of my ability from memory:)

"What the #%&%%^?! What happened to the geometry article?!"

I bet that's what you are thinking. Well, there wasn't one. What was here was the article "History of geometry" posted under the wrong name. This problem had been pointed out years ago by Larry Sanger, and has been a recurring theme on the talk page since, so I took the liberty to correct the problem. It's pretty amazing to find a stub on such a high-profile subject, isn't it? I'm sure Wikipedia's mathematics experts will have fun with this one.

Many students taking geometry at the middle- and high-school level will probably be visiting this article for help understanding the subject. Therefore, this article should be written with them in mind, as well as provide an overview to the overall subject leading to the various advanced subtopic articles on the subject.

I look forward to seeing what you guys/gals come up with.

Good luck, and have fun. --The Transhumanist 01:41, 3 October 2006 (UTC)

For previous discussions see Talk:History of geometry.

While I like the new article so far a lot better than the previous one as a general introduction to geometry, it all seems (except for the history summary) very much aimed at describing current research-level mathematics. Shouldn't there be something about high-school-level geometry, very early in the article? —David Eppstein 01:52, 3 October 2006 (UTC)

Definitely, this article is one of our most important summary articles so needs to cater for a wide readership. --Salix alba (talk) 08:18, 3 October 2006 (UTC)

The emphasis on research: Quine said there are people interested in philosophy, and people interested in the history of philosophy, and the implication was (partisan and) that these were different bunches of people. The history having moved out, it was interesting to me to tackle the question from the other end: what would be an acceptable survey of the 'state of the art'? Another analogy: a cosmology basic article could go back the Babylonians, and on the other hand school students might well expect to find the Big Bang, age of the Universe 14.5 billion years, dark matter discussed. It has been interesting so far ( a day or so): I hope some more can be added that does illuminate geometry. Charles Matthews 16:12, 3 October 2006 (UTC)

[edit] Suggestions on further expansion

Section(s) on analytic geometry, projective geometry, Non-Euclidean geometry, affine geometry should be added. (Igny 13:53, 3 October 2006 (UTC))

Also finite geometry. -- Cullinane 14:16, 3 October 2006 (UTC)

[edit] Re: references and examples

Examples don't seem appropriate. References should be restricted to general reading on contemporary geometry. References for individual topics make much more sense on a per article basis. Charles Matthews 17:53, 5 October 2006 (UTC)

[edit] Questionable

The article now includes a suspect sentence:

• The history of 'lost' geometric methods, for example infinitely near points, which were dropped since they did not well fit the Procrustean bed of Bourbakiste axiomatization trying to complete the work of Hilbert and Principia Mathematica, is yet unwritten.

Frankly, this sounds like obscure ax grinding. (Surely Procrustean bed and Hilbert should be linked.) Nor am I convinced by the claim. For example Abhyankar's 1990 monograph, Algebraic Geometry for Scientists and Engineers, AMS (ISBN 978-0-8218-1535-9), devotes Lecture 19 (pp.145–158) to “Infinitely Near Singularities” including points in N^th neighborhoods (a.k.a. infinitely near points). How lost is that? --KSmrq^T 00:39, 9 October 2006 (UTC)

Give me a little time, and I'll support this with a quote from Weil. Yes, infinitely near point is something that was recovered when birational geometry was put on a foundation. Cf. Manin talking about 'bubble space', when you blow up the projective plane everywhere, and again and again ... There is a genuine topic here. Charles Matthews 07:56, 9 October 2006 (UTC)

[edit] pictures

I noticed that the illustrations so far are historical. Perhaps some pictures, somehow illustrative of some aspects of "contemporary geometry" could be included. I think it would be cool for the lay-reader to see something like that, even if it appears quite mysterious. --Chan-Ho (Talk) 01:32, 9 October 2006 (UTC)

[edit] Geometrist

I had a dream the other day, in which I was studying to become a "geometrist" and I wondered (when I woke up), whether this is a real term, one I made up (which could be real), or the by product of all the drugs. Any insight into this problem would be appreciated. In any case it's my new favorite word. —The preceding unsigned comment was added by Verbally (talk • contribs) 15:26, 23 October 2006 (UTC).

The usual word for someone who does geometry is "geometer". —David Eppstein 15:53, 23 October 2006 (UTC)

[edit] Different forms of geometry

I think that there should be a section of this article explaining the different forms of geometry and the differences between their concepts. That is why I wrote that section about the different forms of geometry. But every time I put a section in about it it gets removed. But the readers of this article are not told anywhere in the article about what the difference between Euclidean and non-Euclidean geometry is. That is a very important aspect of geometry that should included in this article. There ought to be a section of the article explaining what Euclidean geometry is and what non-Euclidean geometry is and how they differ and also explaining what the other forms of geometry are. Prb4 16:15:12 February 14, 2007 (UTC)

Does anyone have a response to what I just said and would it be possible to reinsert a revised version of my explanation of the different forms of geometry into the article as a section titled different forms of geometry? Does anyone else here agree with me that the section should be reinserted into the article? The reason I feel this way is because the article does not deal with the issue of parallel lines which is the most important difference between Euclidean geometry and the two non-Euclidean geometries, hyperbolic geometry and elliptic geometry and because in general I think that this article does not give a sufficient overview of the differences between the concepts in different geometries and because in general I think this article is a second rate article which does provide enough information on geometry. Prb4 20:40:21 Wednesday February 14, 2007 (UTC)

[edit] History

Since this is a mathematics article does it really need to have a history section. I think the article should focus on current geometry and math concepts and the history of geometry should only be discussed in the history of geometry article. Prb4 19:20, 15 February 2007 (UTC)

Yes it does. It is hardly possible to explain what 'geometry' means in the 21st century without some history. The fact that you have been adding a late nineteenth century version of 'forms of geometry' rather tends to support that. Please don't remove historical context from mathematics article. It certainly helps the general reader, it may help mathematicians and physicists outside their specialisms; and we anyway have thousands of purely technical mathematical articles. Charles Matthews 19:40, 15 February 2007 (UTC)

I agree with Charles. Your insertions show a rather misguided idea of what "geometry" means today. Your proposed "different forms of geometry" is just a mess. Really, you should learn more mathematics before attempting to characterize the "different forms". --Chan-Ho (Talk) 22:32, 15 February 2007 (UTC)