Talk:Euclidean geometry

Where are the Axioms?

Some people say that Euclid's book don't contain axioms; I have no reason to argue that, not knowing Ancient Greek. But we are in 21st century, and more than one set of axioms of Euclidean Geometry is available, and I am sure must be either listed or refered. Any Mathematicians present here? I could write a section describing an axiomatic Euclidean Geometry, as it is what people expect from a geometry theory. Using a set-theoretical model of geometry is not enough for describing a theory. First, I hope at least some people know that there's more than one set theory; second, we are talking here about a theory, not about models, right?

I'd love to hear your opinion. Vlad Patryshev (talk) 15:29, 14 May 2022 (UTC)

The article mentions Playfair's axiom, perhaps you could develop that. You can also expand the logical basis section Lbertolotti (talk) 23:16, 9 June 2022 (UTC)

Some of the best known axiomatic formulations of Euclidean geometry are listed in section § Axiomatic formulations. Sure that this section should be made more visible and could be improved, but there is no reason for rewriting it from scratch.

You wrote "I could write a section describing an axiomatic Euclidean Geometry". As you do not say which existing axiomatisation you have in mind, I suppose that this would be your own axiomatization. This would be WP:OR, and, as such, would be strictly forbidden in Wikipedia. D.Lazard (talk) 08:58, 10 June 2022 (UTC)

Euclid's Geometry

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

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

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)

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)

"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)

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

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)