Talk:homology

Replication of definitions from homologous

In general, homology could be defined only in terms of homologous. I do not see whether it is a good idea; a replication of the definitions stated in homologous seems better. Why it seems better and whether it indeed is better remains unanalyzed at this point. --Daniel Polansky 17:55, 12 March 2008 (UTC)

That may be fair enough for some of the cases. As far as mathematics is concerned, it's likely true for the original meaning of homologous. (See the 1655 citation in homologous, which is a translation of a proposition from (a Latin version of) Euclid's Elements.) The case for the more recent mathematical meaning of homology is less convincing: the time homology theory arose seems to have overlapped the time (late 19th to early 20th C) when algebra began to be concerned more explicitly with mathematical objects. (See abstract algebra and Abstract algebra on Wikipedia.Wikipedia ) It seems likely that homology was already sometimes used in the older sense of homologous relationship and was reused in the new sense. I think there's also a missing projective geometry sense (see below).— Pingku^dimmi 07:05, 11 November 2020 (UTC)

Mathematical etymology

The following definition from OED seems to predate and underly the modern use in math. The note about Poincare is thus incomplete. "4. Mod. Geom. The relation of two figures in the same plane, such that every point in each corresponds to a point in the other, and collinear points in one correspond to collinear points in the other; every straight line joining a pair of corresponding points passes through a fixed point called the centre of homology, and every pair of corresponding straight lines in the two figures intersect on a fixed straight line called the axis of homology. 1863 G. Salmon Conic Sections (ed. 4) iv. 59 Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point. 1885 C. Leudesdorf tr. L. Cremona Elements Projective Geom. 11 Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology."--Zekelayla (talk) 00:33, 13 January 2018 (UTC)

This looks like the (still missing) projective geometry sense described here.— Pingku^dimmi 07:12, 11 November 2020 (UTC)