Wikipedia:Reference desk/Archives/Mathematics/2012 May 24

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May 24

Weather info

If the average high for May 24 is 75 degrees, and the average low for May 24 is 46 degrees, does that neccesarily mean that the average range of temperatures must be 29 degrees? Legolover26 (talk) 14:54, 24 May 2012 (UTC)

Mean range = (1/n)∑(M-m) = (1/n)(∑M - ∑m) = (1/n)∑M - (1/n)∑m = mean high - mean low. That assumes the same number of readings n of high and low - if this isn't the case, there's insufficient information to calculate the mean range.→109.148.243.127 (talk) 15:20, 24 May 2012 (UTC)

Algebra course

Help. I need a crash course in Algebra 1 and Algebra 2. Math does not come hard to me, and I learn fast. I have already gotten up to quadratic equations. Now where? — Preceding unsigned comment added by Legolover26 (talk • contribs) 16:37, 24 May 2012 (UTC)

(ec) It will help if you explain why you want a crash course in algebra. Do you have a specific application, or are you trying to learn more math because you enjoy it, or are you trying to rapidly ramp up on prerequisite knowledge and skills to prepare for more advanced math or applied science study? Personally, I always found algebraic geometryanalytic geometry to be the most fun part of high school mathematics, and it's a good preparation for the applied field of computer graphics. Nimur (talk) 16:46, 24 May 2012 (UTC)

Somehow I don't think you looked at the article you linked to after you wrote that. (Analytic geometry is what you meant.) Looie496 (talk) 17:06, 24 May 2012 (UTC)

Thanks! Slip of the proverbial tongue. Analytic geometry is suitable for an intermediate high-school student, while algebraic geometry would typically refer to a subject that requires several more advanced concepts that are rarely taught until the third or fourth year of a university pure math curriculum. What I meant is "the application of algebra to define and analyze geometric problems." Nimur (talk) 18:39, 24 May 2012 (UTC)

How about:

1) Graphing equations, and finding slope, X-intercepts, Y-intercepts, maxima, minima, and intersections ?

2) Solving simultaneous equations ?

3) Converting story problems into algebra ? StuRat (talk) 16:44, 24 May 2012 (UTC)

I really want it for fun, and also for prerequisite knowledge for advanced math. I also need it for college, because I do not know of any college that would let me in with the current level of math that I have now. I would prefer that it be a free online course. Legolover26 (talk) 17:23, 24 May 2012 (UTC)

So why did somebody who likes math and intends to go to college skip algebra in high school ? StuRat (talk) 17:34, 24 May 2012 (UTC)

I "did" not skip math in high school because I am not old enough. I am in the seventh grade. I am not in public school math classes because they would hold me back. I think that there is no use to procrastinating algebra until high school if you want to learn calculus too before college. But all that is beside the point. Where can I find something like what I mentioned before? Legolover26 (talk) 17:56, 24 May 2012 (UTC)

I would recommend buying a textbook if possible -- you can probably get one cheap via Amazon. An alternative is to see if you can get one from your local high school or borrow one from your local library. There are online resources but I haven't seen one that includes a good set of exercises, and exercises are really the heart of any math class. Looie496 (talk) 18:55, 24 May 2012 (UTC)

Coolmath seems to cover the subjects you need, if you can stand the childish presentation ("let's understand what Standard Parabola Guy does for a living. He's a squaring machine, baby!"). Anyway,you can use the list of subjects as a guide. linear algebra, despite being a college subject, is not too hard to understand, for me it was way easier and more fun than highschool (middle school?) topics like conic sections, trigonometric identities or calculus (probably because those topics required memorising stuff). You may want to skip the vector spaces theory. Linear algebra course another one and an MIT course. That was my idea of fun in those days... Ssscienccce (talk) 20:18, 24 May 2012 (UTC)

I'm a bit confused about why your classes would be holding you back. Unless things have changed since the late 90's, you're right where you should be for an advanced track. Algebra I in 7th grade, then Geometry in 8th, then Algebra II, Trig, Pre-calc, and Calc to finish off high school.

Minkowski's cousins

If Euclidean 4-space geometry is $++++$ and Minkowski geometry is $-+++$ or $---+$ ... is there an interesting geometry with signature $--++$? —Tamfang (talk) 18:42, 24 May 2012 (UTC)

Neither the ++++ 4-space nor the ++-- 4-space have immediate physical interpretations, like the +++ space and the +++- space-time. Bo Jacoby (talk) 21:51, 24 May 2012 (UTC).

All those geometries are interesting for a pure mathematician, but maybe not if you want to do physics. Rschwieb (talk) 01:18, 25 May 2012 (UTC)

The space of lines in $\mathbb {R} ^{3}$ naturally carries a (conformal) metric of signature $++--$. This has direct applications to scattering theory. Sławomir Biały (talk) 14:02, 25 May 2012 (UTC)

I think that $++--$ appears in Twistor space. That might not sound immediately physical, but I believe they're working on that. 129.234.186.45 (talk) 08:56, 25 May 2012 (UTC)

Four dimensional Honeycombs (and the additional entries where not all the polytopes are identical)?

There are various articles on sets of polygons which can be used to regularly fill a plane and sets of polyhedra which can be used to regularly fill space. Does anyone have any suggestions on where to look for information on sets of polytopes which fill 4-space? I'm looking for the equivalent of the tables in Convex uniform honeycomb. I believe that four dimensional equivalents exists for most (all?) of the 28 in that article, but I'd like to find something more concrete on that. My default place to try and look would be Coxeter's Regular Polytopes, but I don't think it covers that.Naraht (talk) 18:57, 24 May 2012 (UTC)

Trivially you can extend all 28 into 4-space by stacking, just as the 11 uniform plane tilings are represented in prismatic 3-space tilings, but I guess that's not what you're after! — Indeed Coxeter lists only the regular three: {4,3,3,4}, {3,4,3,3} and {3,3,4,3}. — I guess George Olshevsky's paper "Uniform Panoploid Tetracombs" (listing 143 of them) is no longer on the web; I'll ask him for permission to put it on my site. —Tamfang (talk) 19:15, 24 May 2012 (UTC)

Uniform Panoploid Tetracombs —Tamfang (talk) 21:02, 25 May 2012 (UTC)

But I see that Richard Klitzing lists them here, with links to details on 21 of them. —Tamfang (talk) 19:23, 24 May 2012 (UTC)

The extensions I was looking at were not the stacking, but rather the equivalents where the three dimensional truncated cube and octahedrons becomes the four dimensional truncated tesseract and 16-cell.Naraht (talk) 19:52, 24 May 2012 (UTC)

Can't I yank your chain just a little bit? —Tamfang (talk) 20:14, 24 May 2012 (UTC)

Now you have me worried about being stung by 4th-dimensional bees. Would the stingers sting me at all points on my body simultaneously, even the inside ? :-) StuRat (talk) 16:17, 25 May 2012 (UTC)

No, only one point at a time, but one that you can't get at. —Tamfang (talk) 20:45, 25 May 2012 (UTC)

Sorry for not responding back. Thank you for the paper. I need to look at it more closely in terms of the vertex figures and the possible values the sides of the vertex figures can have and still be inscribed.Naraht (talk) 19:11, 30 May 2012 (UTC)