Talk:History of geometry
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| Mathematics grading: | B Class | High Importance | Field: Geometry and topology | ||
This doesn't strike me as a very good way to introduce geometry to a general audience: "Geometry is a branch of mathematics concerning spaces together with some sort of symmetry relations defined on it. Objects are said to be congruent if there is a symmetry mapping one to the other, and quantities unaffected by all symmetries are called invariants. The study of invariants is the main part of geometry." Those sentences should come about eight paragraphs into the article, I think. -- Larry Sanger
Really meant as a stop until something better comes along...
What is the relationship to trig? Is trig a subfield of geometry in general? Of analytic geometry? Do "real mathematicians" not say "trigonometry"?
The discussion of congruency was apparently ripped out of this page, and poorly done, as a later paragraph refers to "figures" which are not present on this page, but the context is compatible with the figures on the congruency page. Brent Gulanowski 17:59, 30 Nov 2003 (UTC)
Should there perhaps be some mention of geometric series here? There is a redirect from geometric to geometry and I suspect it does get linked when talking about things like geometric growth. --fvw 11:46, 2004 Jul 27 (UTC)
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[edit] "definitions"
In the opening paragraph to this article I find the wording "in conjunction with mathematical definitions for points, straight lines[...]" problematicsince points and lines, among other things, are usually left as undefined terms in Euchlidean geometry. Servais 17:08, 27 Nov 2004 (UTC)
Though these definitions are often absent from a course in Euclidean geometry, Euclid himself defines them (see [1]), though it has often been argued that his definitions aren't that much good! However, in the context of being only 3 or 4 generations after Leucippus and 2 or 3 after Democritus, Euclid's "a point is that which has no parts" could have been a reasonable stance in stating Euclid's position with respect to atomic theory. Again, it may be useful to have a "history of geometry" section because it is sometimes hard to distinguish between Euclid's own geometry and the framework that became "Euclidean geometry".
It might also be useful to cite Felix Klein's Erlangen Program since this definition was seminal in balancing Euclidean and non-Euclidean geometry back into a single subject. (Sorry, I couldn't get this link to 'take', but there is a good article there already.) Dominic Widdows 19 Apr 2005
[edit] A better introduction
Algebra and Geometry are the 2nd largest branches of mathematics (after Mathematical_analysis). It's possible to divide geometry into six main branches:
1) Euclidean geometry (the basic geometry)
2) Analytic geometry (could also be an offshoot of algebraic geometry but is more basic)
The more advanced and complex branches are:
- Probably Riemannian geometry and symplectic geometry and other geometries that live on manifolds should be sub-branches of differential geometry. -Lethe | Talk 19:32, May 30, 2005 (UTC)
6) Non-Euclidean geometries; this includes:
6a) Riemannian geometry (also called elliptic geometry) and 6b) Lobachevsky-Bolyai-Gauss Geometry (also called hyperbollic geometry). Basically the Riemannian metric can account for an infinite number of non-Euclidean geometries.
- Why are these seperate branches? Can't those hyperbolic geometries be modeled on Riemannian manifolds? -Lethe | Talk 19:29, May 30, 2005 (UTC)
7) Topology which is the youngest and most sophisticated branch of geometry which also meets modern algebra.
- I don't agree with you that Topology should be considered a branch of geometry. -Lethe | Talk 19:29, May 30, 2005 (UTC)
8) Noncommutative geometry is currently an active area of research, especially in the area of advanced theoretical physics. -- Orionix 04:36, 13 Mar 2005 (UTC)
- And where are symplectic geometry and Kähler geometry on your list? -Lethe | Talk 19:32, May 30, 2005 (UTC)
Topology is no longer young. Noncommutative geometry isn't really geometry - it has a geometric language, but so does (for example) Boolean algebra theory. It might be better to concentrate on Euclidean geometry, algebraic and differential geometry, and geometric topology, as the basic classification.
Charles Matthews 22:04, 22 Mar 2005 (UTC)
Everything which explores structure & spatial relationships has a 'geometric language'. -- Orionix 16:40, 8 Apr 2005 (UTC)
the mention of pick's theorem on this page is highly inappropriate. (and suffers from spelling issues). It should go somewhere else. Dmharvey 14:45, 30 May 2005 (UTC)
Fans of Pick's theorem would be disappointed. Seriously, it isn't far from geometry of numbers, which might be worth a mention. But the whole page probably should be reconsidered, since it has probably been given little attention. Charles Matthews 15:46, 30 May 2005 (UTC)
[edit] Total rewriting, August 2005
I agree, as others have noted, the old article was not very good. I could not see any way to fix it.
The article I have written is long, but since geometry is one of the 5 items listed under "areas of mathematics", I think it deserves a long article.
I have written the article as a historical account. Geometry is such a large and varied field, I think it would be difficult to give an adequate definition of it apart from its historical development.
I did not put "Greek geometry" in an article of its own because most of it is needed to understand the rest of the story. The reader should not have to go read a separate "Greek geometry" articlle in order to make sense of the "Geometry" article.
I have left the "20th century" section as a stub, because I am not as interested or qualified to write it. There are a couple of topics I would like to put in, but I would appreciate help on this. I think it would be good to keep the article general and self-contained, ie the reader shouldn't have to be a mathematician to follow it.
Aftermath 03:35, 28 August 2005 (UTC)
[edit] Needs rewrite
Seriously. The current article doesn't fit in with the ideas of wikipedia. It is too jumbled and unstructured. It should be possible to just look at the article and find what most people want to know:
1. What geometry is, distinguishing between the formal definition and the public conception of geometry. 2. What are the current fields of study in geometry. How the field divides into subfields. 3. How study of geometry is applied, and how geometry fits into maths as a whole.
The history section should be separated from that - if neccessary, onto another page.--Fangz 01:55, 14 October 2005 (UTC)
- I agree. Almost the whole article is about the history of geometry rather than actually explaining aspects of geometry. If I remembered geometry well enough I would rewrite this, but I don't. It should have how to use geometry to solve problems and things like that- as it is it is not very helpful. -Chocolateluvr88 00:25, 10 January 2006 (UTC)
[edit] Images?
What's geometry without images? This important page is seriously lacking. Gflores Talk 05:16, 17 December 2005 (UTC)
[edit] Thales of Miletus
I decided to change where it said "Thales of Ionia" to "Thales of Miletus" because, although Miletus was part of Ionia, "Thales of Miletus" is the name under which Thales is most commonly known (along with "Thales the Milesian"). When I read that line I wondered if Thales of Ionia was a different person than the Thales of Miletus I was familliar with. When I followed the link to the Miletus page, I found that they were one and the same, so I was bold and made the change to the more familliar name. Normally I wouldn't post such a ridiculous comment for such a minor edit, but apparently this page isn't actually part of a wiki, you have to have all your edits approved by the almighty lords who watch this page. Is that to your liking, Your Majesty, Oleg Alexandrov? I'm so regretful to have failed you in my edit summary. --Someones life 05:17, 2 February 2006 (UTC)
- Yeah, it is good that you explained your edits. It is entirely appropriate to document your edits with an edit summary, for the benefit of your fellow contributors and my own majesty. Oleg Alexandrov (talk) 19:53, 2 February 2006 (UTC)
[edit] This should be at History of geometry
This article is more about history and less about mathematics. When people think "geometry", they think of modern geometry, and would expect to see Geometry talk about topics in modern geometry, not about the history of geometry. — 0918BRIAN • 2006-03-7 23:52 Bold text
