Talk:Euclidean geometry

This is the talk page for discussing improvements to the Euclidean geometry article.
This is not a forum for general discussion of the article's subject.

Put new text under old text. Click here to start a new topic.
New to Wikipedia? Welcome! Learn to edit; get help.

Article policies

Archives: 1, 2: 12 months

Euclidean geometry was one of the Mathematics good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Article milestones
Date	Process	Result
July 19, 2006	Good article nominee	Listed
October 6, 2007	Good article reassessment	Delisted
February 24, 2009	Good article nominee	Not listed
Current status: Delisted good article

Mathematics Top‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Top	This article has been rated as Top-priority on the project's priority scale.
	This was a selected article on the Mathematics Portal.

Greece High‑importance

	Greece portal This article is within the scope of WikiProject Greece, a collaborative effort to improve the coverage of Greece on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.GreeceWikipedia:WikiProject GreeceTemplate:WikiProject GreeceGreek
High	This article has been rated as High-importance on the project's importance scale.

Classical Greece and Rome Mid‑importance

	This article is within the scope of WikiProject Classical Greece and Rome, a group of contributors interested in Wikipedia's articles on classics. If you would like to join the WikiProject or learn how to contribute, please see our project page. If you need assistance from a classicist, please see our talk page.Classical Greece and RomeWikipedia:WikiProject Classical Greece and RomeTemplate:WikiProject Classical Greece and RomeClassical Greece and Rome
Mid	This article has been rated as Mid-importance on the project's importance scale.

Euclid's Geometry

What are postulates ? 103.170.68.3 (talk) 14:33, 29 June 2022 (UTC)[reply]

Follow the link: postulate. D.Lazard (talk) 15:27, 29 June 2022 (UTC)[reply]

consider this image for your article

https://upload.wikimedia.org/wikipedia/commons/5/59/Picture_euclidean_geometry_123.png Fausto!'20045 (talk) 00:07, 20 April 2023 (UTC)[reply]

This image does not really seem useful or relevant here. It is a low-resolution screengrab of a Geogebra (?) demonstration that three angles of a triangle (specifically the isosceles triangle with base length 2 and altitude 2) sum to a straight angle. There are many bizarre choices: poorly placed labels, an ugly color scheme, the unexplained inclusion of a Cartesian coordinate grid relative to which the triangle seems to be randomly located, etc. –jacobolus (t) 00:28, 20 April 2023 (UTC)[reply]

"An absolute, often metaphysical sense"?

According to the current article:

For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century.

I think the main idea being conveyed here is basically correct, but as these sentences stand, they're not very well-written.

I would point out a few problems:

1. The language used here is very strong, probably too strong: "For more than two thousand years...no other sort of geometry had been conceived." If somebody here thinks this language is appropriate, can they cite a source for keeping the current wording? The SEP makes the point that I think is trying to be made here in a more measured way: "The epistemologically convincing status of Euclid’s Elements was uncontested by almost everyone until the later decades of the 19th century."

2. Similarity, "any theorem proved from [Euclid's postulates] was deemed true in an absolute, often metaphysical, sense" is not well-written. Deemed by whom? And what is the "absolute, often metaphysical sense" being spoken of in this sentence? There were lots of competing systems of metaphysics in the ancient world and likewise in the Medieval world. In whose "metaphysical sense" were the theorems of Euclidean geometry deemed absolutely true? Again, the SEP makes the point that I think is trying to be made here, but in language that is a lot clearer: "Euclid’s treatment of geometry has, through the ages, been celebrated as a perfect deductive presentation of a science, and certainly Euclid made great efforts to obtain a most careful logical chain of truths." DefinitelyNotAnExtraterrestrial (talk) 02:57, 20 May 2023 (UTC)[reply]

Fixed. D.Lazard (talk) 10:38, 20 May 2023 (UTC)[reply]

Two rotten edit summaries: my apologies

In "System of measurement and arithmetic" I have just changed "congruent" to "equal", and in the Edit Summary I twice tried to say "Hasn't an earlier sentence just said that 'congruence' applies to the entire figure?"

While editing the Edit Summary I have now learned the hard way that pressing Enter does not go to a new line, it IMMEDIATELY SUBMITS the edit, before I was ready.

I am using a tablet and I suppose that mobile editing works differently to what (I hope) the WP creators intended. If anyone with more WP knowledge can get the system changed so it doesn't do that, please do. 203.220.1.139 (talk) 13:55, 30 September 2023 (UTC)[reply]

It may be worth clearly distinguishing multiple senses of "Euclidean geometry" here

The term Euclidean geometry can refer either to Greek deductive geometry per se, deductive synthetic geometry based on it (including in the medieval Islamic world, in Renaissance Europe, etc.), or the geometry of Euclidean space (of other styles, including vectors, transformation geometry, analytic geometry, etc.). This article focuses on Greek deductive geometry, but many of the places where a wikilink to Euclidean geometry appears, the sense of the geometry of Euclidean space is intended instead. I think both senses should be discussed here, possibly as separate top-level sections. –jacobolus (t) 01:30, 9 May 2025 (UTC)[reply]

I agree. As it is, Euclidean geometry is essentially an historical artile, while incoming links are intended to modern geometry. An example of the current bias of the article is that it is entierely based on the synthetic approach, and there is no mention of the equivalence between analytic and synthetic approaches of Euclidean geometry (I know that this is mentioned somewhere in Wikipedia, but I do not remember where) D.Lazard (talk) 09:21, 9 May 2025 (UTC)[reply]