Talk:Geometric transformation

Near misnomer

The term geometric transformation nearly always means a linear transformation or matrix transformation. The examples given show this to be true. Reference to the "What links here?" shows few exceptions. The operation of multiplicative inverse used to generate Mobius transformations involves exceptional formality to cope with zero. Proponents of "geometric algebra" may find this article important, but traditional terms in mathematics do not include the modifier "geometric" since linear algebra is studied with other referents. Rgdboer (talk) 23:18, 20 October 2024 (UTC)[reply]

I do not understand what point you are trying to make. It is clearly false that geometric transformations are either linear transformations or matrix transformations: geometric transformations are maps from geometric points to geometric points, while linear transformations are maps from vectors to vectors. What is true is that many common types of geometric transformations can be modeled using linear transformations of one kind or another (after the geometric space in question has been given an appropriate [arbitrary] choice of coordinate system), which can be convenient because mathematicians and computer programmers have developed conceptual and practical tools for dealing with linear transformations which can then be applied as-is.

What is also true is that this article is currently quite mediocre, does a poor job of describing its subject, and needs a lot of help in every way. –jacobolus (t) 23:55, 20 October 2024 (UTC)[reply]

The phrase "geometric transformation" is redundant as transformations in mathematics are usually treated geometrically. Preferred precision is taken with homography (for projective geometry), affine transformation, or Euclidean motion. Geometers often just say motion once the universe of discourse has been set. Asserting "high priority" is inappropriate. — Rgdboer (talk) 22:06, 21 October 2024 (UTC)[reply]

The prhase "geometric transformation" appears in 44,200 results in Google scholar, mostly in the sense described here. Many (probably thousands) of sources describe "geometric transformations" as a topic of study per se (encompassing homographies, affinities, Euclidean motions, Möbius transformations, etc.), and this shows up in many places around the world as a topic of the secondary school curriculum, as evidenced by many books/papers on the subject aimed at high school students or teachers. It also appears in papers about a wide variety of applied science and engineering topics. Even though this article is currently mediocre, I think this makes for a good top-level topic article, alongside transformation geometry, from which we can provide an overview and comparison of specific types of transformations. The word "transformation" is used much more generally in mathematics. –jacobolus (t) 02:43, 22 October 2024 (UTC)[reply]

Books with substantially this phrase as a title include Yaglom 1955, Modenov & Parkhomenko 1961, Johnson 1989, Amir-Moéz 1998, Mortenson 2007, Gelca & Onişor & Shine 2022, not to mention numerous book chapters and several other books dedicated to the topic and using the term but titled something else (e.g. Transformation Geometry, Geometries and Transformations, Transformations and Geometries, ...). –jacobolus (t) 04:46, 22 October 2024 (UTC)[reply]

OK. True, this is part of mathematics education before college. The view that a geometric transformation is just a group element in the Erlangen program shortchanged me. — Rgdboer (talk) 02:16, 23 October 2024 (UTC)[reply]