Wikipedia:Reference desk/Archives/Mathematics/2016 April 22

= April 22 =

Notation in combinatorics
In the article "3-dimensional matching" (version of 02:28, 22 April 2016), there are several instances of an inequality sign preceded by a space but not followed by a space. Is that a typographical error, or is it correct for this particular field of mathematics? If it is correct, what does it mean, besides inequality? I did not find answers to these questions at Manual of Style/Mathematics. —Wavelength (talk) 20:01, 22 April 2016 (UTC)
 * Typographical error. --JBL (talk) 20:13, 22 April 2016 (UTC)
 * Now fixed in all 3 instances, I believe. --JBL (talk) 20:16, 22 April 2016 (UTC)


 * Thank you for your reply and your corrections. I just noticed, further down, an equation without spaces around the equals sign, and I inserted two non-breaking spaces.
 * —Wavelength (talk) 20:43, 22 April 2016 (UTC)


 * Heh, I remember when a coworker on a programming project objected to my habit of putting spaces around operators. —Tamfang (talk) 07:33, 24 April 2016 (UTC)
 * Bet he cut his teeth as a C programmer.Naraht (talk) 21:02, 25 April 2016 (UTC)
 * Dunno about that; he seemed old enough for Fortran. I can say he was a big fan of Petri nets, to the bafflement of the rest of us. —Tamfang (talk) 01:48, 28 April 2016 (UTC)

indirect derivatives
Given $$r = r(u,v)$$ and its partial derivatives $$r_u, r_v, r_{uu}, r_{uv}, r_{vv}$$; suppose u,v are themselves linear functions of t, with $$u_t = a, v_t = b$$. Is this right?
 * $$r_t = ar_u + br_v$$
 * $$r_{tt} = a^2r_{uu} + 2abr_{uv} + b^2r_{vv}$$

(Context: $$r(u,v)$$ defines a point on a surface which I seek to represent by facets whose size is determined by local curvature and the resolution of a 3d printer; I need to compare the second derivative, in various directions on the surface, with the first.) —Tamfang (talk) 23:13, 22 April 2016 (UTC)


 * Yes. The second equation is two applications of the first equation. The first equation follows from the multivariate chain rule. Our article isn't as readable as it could be on this point (imo), but the example gives
 * $$\frac{\partial u}{\partial r}=\frac{\partial u}{\partial x} \frac{\partial x}{\partial r}+\frac{\partial u}{\partial y} \frac{\partial y}{\partial r}$$
 * which is what you need modulo a few letter changes. Btw, it's interesting that you can apply calculus to 3d printers. This type of practical application usually has a hard time making into the classroom. --RDBury (talk) 05:19, 23 April 2016 (UTC)


 * I showed off my creations to the mother of a 4yo who was already showing interest in math. "See? Anton made these with math!" —Tamfang (talk) 08:58, 25 April 2016 (UTC)