Wikipedia:Reference desk/Archives/Mathematics/2007 November 28

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[edit] November 28

[edit] Approaching mathematics in non-American cultures

I have heard that different cultures have different approaches to learning mathematics and focus on different areas, leading to different strengths and weaknesses. Is there any truth to this? Where can I find information on non-American approaches to learning mathematics?

Advance thanks.

lvlarx (talk) 06:50, 28 November 2007 (UTC)

Have a look at articles in Category:Mathematics education. There are some articles on non US education, but it is week on mathematics in non English speaking countries. The article Mathematics education has an overview of different approaches, for example Rote learning and New math. --Salix alba (talk) 18:20, 28 November 2007 (UTC)
Not to mention New Math (song). Confusing Manifestation(Say hi!) 21:53, 28 November 2007 (UTC)

[edit] Am I correct?

Doing past papers for revision, I came upon this question:

A courier firm has a restriction on the size of parcels that it will carry at the normal rate.
The sum of the length, width and height of any parcel must be less than 162 cm.
The length of a box parcel is twice its width.
Find the maximum possible volume of the parcel that can be carried at the normal rate.

The official solution is 139968cm3 (full workings can be seen here, page 3), but I think I can find a higher value: 162/4 = 40.5; 40.52*(2*40.5) = 149262.75, bigger than 139968. Even disallowing decimal points, 402*92 is still bigger. Is the exam wrong, or did I miss something? Also, by asking the area between a curve and the x-axis within a limit, does this usually mean the net area where area below the x-axis is subtracted (ie. the conventional integral way) or where all the area are added together (ie. the area below x-axis is positive is well)? --antilivedT | C | G 10:33, 28 November 2007 (UTC)

Did you think that 40.5*2 = 91? Try again --tcsetattr (talk / contribs) 10:59, 28 November 2007 (UTC)
Eeek, need sleep... --antilivedT | C | G 11:01, 28 November 2007 (UTC)

[edit] How 2m * 3m results 6m^2

If 2m and 3m (lines) have no extension, how can it be that after an operation (*) the result (6m^2) do have extension? Where does this extension comes from? Mr.K. (talk) 12:33, 28 November 2007 (UTC)

In what sense do lines have no extension? One might as well say that the result has no extension, since it has no volume. Or, more reasonably, we could say the two inputs have extension in one direction, and the output in two (i.e. dimensions add under multiplication) which is hardly mysterious. Algebraist 13:11, 28 November 2007 (UTC)
What if we multiply 3m * 3m^3, what is this 9m^4 that we obtain?Mr.K. (talk) 13:51, 28 November 2007 (UTC)
If you are asking how we can interpret the unit (meter)^4 that we get when we multiply a length by a volume, then the answer is that it has no standard physical meaning. In a real world calculation, if you get such a result it probably means you made a mistake. However, sometimes our units are not measures of length, and in that case four dimensions may be possible. In any case, mathematicians do constrain themselves to 3 dimensions. You'll often see them working with an infinite number of them. nadav (talk) 14:19, 28 November 2007 (UTC)
Please define your terms and variables. I have no idea what you are talking about. nadav (talk) 14:11, 28 November 2007 (UTC)
You've got an object with a 4-space "volume" of 9. Think of it as extending 3 "meters" back and forth in "time" if you must -- though that's hardly an apt visualization, it'll do. We can't do things physically with 4-D spaces and volumes, though, since we can only work in 3 dimensions. But if you were measuring 4-space volume, mathematically, that's what you'd get. Gscshoyru (talk) 14:23, 28 November 2007 (UTC)
If by 'extension' you mean exponent, then note that 2m = 2m^1; an exponent with value 1 is usually omitted. Phaunt (talk) 15:47, 28 November 2007 (UTC)
No, by 'extension' I mean the property of taking up space. Mr.K. (talk) 01:03, 29 November 2007 (UTC)
That asterisk may in some way resemble the Cartesian product: You have an element of \Re, and another element of \Re, and a pair of both elements belongs to \Re^2, which is a "more complex" than the original set (\Re^2). In your case, you have a product of elements of linear extension, and get a result of planar extent. (Please forgive my "Real" \Re)Pallida  Mors 00:53, 29 November 2007 (UTC)
In simple cases is clear you combine basic units into more complex units. 2m^2 and 2m don't take up space, but if you multiply them, they do. Both elements contribute somehow to this new one. However sometimes these operations result in a qualitative difference. So, multiplying two units, you can get a unit that have different qualitative properties -not a combination of the properties of the members of the multiplication - or that do not even exits. Mr.K. (talk) 01:03, 29 November 2007 (UTC)
I think I know where do you want to get. However, this is not exactly a math problem, but a problem of dimensional analysis - a physical discipline. When resolving physics problems, we are required to determine the numerical result and the units of this result in an equation. The numerical result normally isn't too difficult to get, however, the same can't be said for the units. A unit can be dimensionally correct or incorrect, so as the numerical value can be correct or not. 217.168.3.246 (talk) 03:34, 30 November 2007 (UTC)

[edit] Göttingen University anecdote

I vaguely remember an anecdote about the waiters in some cafe at Göttingen University not wiping the table lest they would remove valuable formulae written on the table top. It is said of a period when some famous mathematicians worked there. Does somebody know the full anecdote and involved parties? 87.126.142.54 (talk) 18:05, 28 November 2007 (UTC)

Sounds like the story of the Scottish Book and the Scottish Café, but that was in Lwów, not Göttingen. Gandalf61 (talk) 10:05, 29 November 2007 (UTC)