Talk:Non-Euclidean geometry

Diagram with hyperbolic

That diagram is only true for Poincare hyberolic disc lines, not other kind of hyperbolic geometries like the Klien model.

Absolute Geometry

Absolute geometry does not take a position on Euclid's fifth postulate, the rule of Euclidean geometry that states that parrallel lines go on to infinity and never intersect. So it is wrong to refer to absolute geometry as a non-Euclidean geometry because it is compatible with both Euclidean and non-Euclidean geometry and the first 28 Euclidean theorems don't involve parralell lines so they could be considered absolute geometry so absolute geometry is really not neccessarilly a non-Euclidean geometry and should not be referred to as such in this article. NikolaiLobachevsky 6:03:14 1/4/2007 (UTC)

long url in article body pointing to edit

This is in the article body, it seemed a little wierd (not the content itself, the big/edit url in the text):

Another practical model of hyperbolic space was developed by Dr. Diana Taimina in 1997 using crochet (please see http://en.wikipedia.org/w/index.php?title=Non-Euclidean_geometry&action=edit&section=5 for more information).

Lovecraft

The current version of the article says, regarding The Call of Cthulhu, "It is heavily implied this is achieved as a side effect of not following the natural laws of this universe rather than simply using an alternate geometric model, as the sheer innate wrongness of it is said to be capable of driving those who look upon it insane.[35]" and [35] is The Call of Cthulhu. Which is false, what Lovecraft described *was* an alternate geometric model (gravity/perspective working differently, angles looking differently depending on the point of view, that it was easy to get lost), and he did not claim that "innate wrongness is capable to drive insane". See the article "H. P. Lovecraft and non-Euclidean geometry". 178.42.226.17 (talk) 22:09, 10 April 2023 (UTC)

Importance

The discovery of non-Euclidean geometries was a major turning point in the foundations of Western philosophy. It caused a re-examination of the concept of "truth" and the basic assumptions we had made about the world in which we live. This little piece of mathematics has had a profound impact on our culture and intellectual history, yet so many people are totally unaware of it. This section should be the centerpiece of the article, the reason for actually having this page instead of just redirects to the hyperbolic and elliptic geometry pages. The impact in physics certainly belongs here, but there is so much more that should be present. Wcherowi (talk) 22:01, 21 August 2011 (UTC)

Hi, I'm placing my comment here because it relates to this section and what you, Wcherowi, have written in it. I'm still not very familiar with Wikipedia, so if this should instead be a new section please let me know/simply move it.

I am no mathematician, so perhaps my understanding of Euclidean geometry is too elementary. But I take issue with the sentence "Unfortunately for Kant, his concept of this unalterably true geometry was Euclidean." After reading it, I wondered "why is that unfortunate?" My understanding is that our physical world (as we perceive it using our human senses) is best described by Euclidean geometry. Assuming this is true, I fail to see how the discovery of Non-Euclidean geometries had any consequences for Kant's "unalterably true geometry". Again, from my (limited) perspective Non-Euclidean geometries have no bearing on the reality that humans experience via their visual and spatial senses. In this case I am talking solely about our experiences on Earth.

I'm sure you disagree(d) with me, otherwise you would not have written what you did. So my request boils down to: care to explain? I believe that this should (eventually) be explained in the article text. Firvqipo (talk) 15:23, 28 January 2022 (UTC)