Wikipedia:Reference desk/Archives/Mathematics/2009 July 1

= July 1 =

Triangle with all angles less than 180º
I know that, in elliptic geometry, it's possible to have a triangle with three right angles — thus adding up to 270º rather than the Euclidian 180º. Is there any system in which it's possible to have a triangle with less than 180º between its angles? I've looked through Hyperbolic geometry, but it's been a few years since I last took any maths, so I can't understand whether this is such a system. Nyttend (talk) 04:00, 1 July 2009 (UTC)


 * Yes, triangles having angles totalling less than 180 degrees characterises hyperbolic geometry. I'm surprised our article doesn't make that clear - I'll take a look at it. --Tango (talk) 04:07, 1 July 2009 (UTC)
 * I've added a bit about hyperbolic triangles to the lede of hyperbolic geometry. Somebody may want to review it. It would also be good if someone found a reference, I haven't had a chance to look for one but any geometry textbook that touches on non-Euclidean geometry will do. --Tango (talk) 04:15, 1 July 2009 (UTC)
 * [ec] Actually, it does, in the Escher section; I missed it. However, your assurance made me look more carefully and confidently, so thanks :-)  Nyttend (talk) 04:16, 1 July 2009 (UTC)
 * I missed it too! I think it is good to mention it early on, it's a pretty key characteristic. --Tango (talk) 04:20, 1 July 2009 (UTC)

MathPsy and QuantPsy: Difference
What is the difference between Mathematical Psychology and Quantitative Psychology, if any?```` —Preceding unsigned comment added by Ultraluna (talk • contribs) 18:01, 1 July 2009 (UTC)


 * I can't speak to Psychology, but the distinction also exists in Economics. In Mathematical Economics, one builds mathematical models to describe economic phenomena. What results from the models are (generally) qualitative solutions (e.g., an increase in X accompanies a decrease in Y). The focus is on mathematically representing the dynamics of a process so as to better understand the process rather than predicting what outcome the process will yield. In Quantitative Economics (we call it Econometrics), one fits data to mathematical models in an attempt to obtain quantitative solutions (e.g., an increase in X of one unit accompanies a decrease in Y of 10 units). The focus here is more on measuring the outcome of a process. Wikiant (talk) 18:28, 1 July 2009 (UTC)

Thanks for your response. That helps, albeit, somewhat. Without demeaning Econometricians in any way, from what I understand then is that Mathematical Economics is more important than Econometrics. The former builds the model on which the latter works on: like an Architecht and a Mason+Civil Engineer.```` —Preceding unsigned comment added by Ultraluna (talk • contribs) 04:51, 2 July 2009 (UTC)

Solve for z
Hi, I'd like guidance on solving the following equation for z,

$$xy+yz+xz-z-z^2 = 0 \,$$

The presence of the $$z^2$$ term makes this trickier; normally you might be able to extra the z term through factorisation and seclude it that way. I know I probably need to factorise the left hand expression in some way, but I don't really know any factoring techniques that apply here. Thanks. 94.171.225.236 (talk) 20:51, 1 July 2009 (UTC)

It's just a quadratic equation
 * $$ az^2 + bz + c = 0 \, $$

where

\begin{align} a & = -1 \\ b & = y + x - 1 \\ c & = xy. \end{align} $$

Michael Hardy (talk) 21:10, 1 July 2009 (UTC)


 * Understood, thankyou! Can I just ask why c isn't equal to xy? Wouldn't all terms lacking z imply that they constitute the constant term? 94.171.225.236 (talk) 21:21, 1 July 2009 (UTC)
 * Because Michael Hardy made a typo. Algebraist 21:25, 1 July 2009 (UTC)

Sorry. Typo. xy is correct. Michael Hardy (talk) 01:41, 2 July 2009 (UTC)
 * Is there a better way than using the formula $$a(x-r_1)(x-r_2)$$ (where $$r_1, r_2$$ are roots of the polynomial) in order to achieve a factorisation? The roots in quadratic formula form are, if my calculations are correct, something like this:


 * $$r_1, r_2 = \frac{(y+x-1) \pm \sqrt{y^2+6xy-2y+x^2+2x+1}}{2xy}$$


 * Which seems unecessarily complicated, considering this is an exercise. I haven't tested to see wether the whole expression for $$a(x-r_1)(x-r_2)$$ for the above polynomial expands to its original form, but I'm fairly certain there's a more elegant approach to this. 94.171.225.236 (talk) 08:07, 2 July 2009 (UTC)

The equation
 * $$z^2-(y+x-1)z-xy = 0 \,$$

has the solutions
 * $$z_1, z_2 = \frac{y+x-1 \pm \sqrt{y^2+6xy-2y+x^2+2x+1}}{2}$$

Your calculation was almost correct. Bo Jacoby (talk) 09:15, 2 July 2009 (UTC).


 * I believe the $$+2x\,$$ term should be $$-2x\,$$ in the above equations. -- Tcncv (talk) 04:24, 7 July 2009 (UTC)


 * I agree. —Tamfang (talk) 00:59, 22 July 2009 (UTC)