Talk:Nome (mathematics)

Tag

What, exactly seems too technical or needs to be clarified? Any specific comments? linas 15:34, 27 January 2006 (UTC)

Tag removed. Technical tag requires an explanation, no matter how brief or vague, to be left on the talk page. --C S (talk) 06:31, 19 February 2009 (UTC)

Unclear

The article states that the special function "is given by ...", and then for the dots we see an equation. It is not clear to me which symbols in that equation represent the function, and what it is a function of. Should we read this as

$q(\omega _{1},\omega _{2})=e^{\frac {{\rm {i}}\pi \omega _{2}}{\omega _{1}}},$

or what?

Or is it perhaps the case here that "special function" is a misnomer, and that this is, rather, a real-valued quantity that is better called a "parameter", like the eccentricity of an ellipse, the clique-width of a graph, and the fundamental period of a periodic function?  --Lambiam 18:47, 28 November 2016 (UTC)

q can be thought of as a function of either the periods omega, or the lengths K or the half-period ratio tau. Take your pick; they are interchangable. Alternately, one can invert: for example, K is a function of q, an explicit expression for it is given in the article on K.

So, In all cases, you are trying to paramaterize an ellipse; the K's are the major and minor axes of the ellipse, the omega's are one over that, because the ellipse tiles the plane, and the half-period ratio just tells you how squashed the tiling is. Its called a "special function" because its a classic 18th and 19th century thingy that resulted from the study of ellipses. Abramowitz and Stegun have 50 pages of tables of the values of this function. Its the bedrock foundation for elliptic curves. 67.198.37.16 (talk) 19:10, 9 January 2019 (UTC)

Summer 2023

During the summer of 2023, this article became 10x larger, and now contains a waterfall of intriguing, beguiling algebraic relationships. It's all very nice, but is there some geometric interpretation to all of this? I've encountered such waterfalls before, and it makes me wonder. For example, pick a Lie algebra, any one will do. Say, su(3). Pick a unit vector v in it. Write down exp(v). You will get a waterfall of relationships, each more stunning, and stunningly opaque, than the one before, all of them resembling the contents of this article. And for what? One is just lost in the bowels of the Baker-Campbell-Hausdorff formula; but su(3) has a geometric interpretation and exp(x) has a geometric interpretation that are somehow "clear" in a way that the waterfall is not. Besides saying "its all ellipses", is there some easier way of stating what these new additions are all about? 67.198.37.16 (talk) 02:39, 20 December 2023 (UTC)