Wikipedia:Reference desk/Archives/Mathematics/2009 June 8

= June 8 =

statistics
can you explain more on validity and reliability of statistics. the truthfulness of statistics —Preceding unsigned comment added by 81.199.149.148 (talk) 09:58, 8 June 2009 (UTC)


 * See Statistics. Bo Jacoby (talk) 20:54, 8 June 2009 (UTC).
 * You may also be interested in a (radio/podcast/online) series from the BBC called 'Go Figure'. A Google search for 'BBC Go Figure' turns up various pages (like this one) from the online magazine feature - the dropdown box in the top right lets you access others in the series. It's more light hearted, and written for a general audience, but may be of some use. Angus Lepper(T, C) 23:31, 8 June 2009 (UTC)

Why doesn't 10 divided by zero equal infinity?
This seems like a really plausible result since division is nothing more than repeated subtraction. When I divide 10 by 1 then I in essence only count the number of times I can subtract 1 from the result of the previous subtraction, i.e. 10-1=9, 9-1=8... etc. until I am left with a value of zero or a remainder between zero and 1.

Therefore when I subtract zero from 10 I get 10 but the number of times I can do this subtraction and do it again and again and again is infinite. -- Taxa  (talk) 20:58, 8 June 2009 (UTC)


 * Because it could be positive infinity or it could be negative infinity. 10/x gets bigger and bigger as x approaches zero from above, but it gets more and more negative if x approaches zero from below. For a limit to exist, it has to exist and be equal in both directions. There are some number systems in which positive and negative infinity are considered to be the same thing, in those systems 10/0 really does equal infinity. See real projective line. --Tango (talk) 21:03, 8 June 2009 (UTC)


 * See also Division_by_zero. Friday (talk) 21:04, 8 June 2009 (UTC)


 * 10 / 0 = x is equivalent to saying what solves 0 x = 10, yes? But any value of x will not solve this equation. 10 / 0 isn't really meaningful. —Preceding unsigned comment added by 210.11.75.201 (talk) 02:54, 9 June 2009 (UTC)
 * Yes, but 0*infinity is indeterminate, which means it could be anything, including 10. That's why you can get meaningful and useful mathematics by defining 10/0 to be infinity (as long as you identify positive and negative infinity). --Tango (talk) 03:20, 9 June 2009 (UTC)


 * What you are telling is the limit (that too on the positive side) as the denominator approaches zero. 10/0 is simply not defined. Division by zero is not defined, which means there isn't any specified value for it. You can define it yourself, saying 10/0 is 10 from now onwards, but there wouldn't be much point in that as it wouldn't help you to solve any problem. Now the logic you are telling is the limit, which has already been clearly explained by others that it does not exist, as it can be both infinity or minus infinity. See One sided limit. Rkr1991 (talk) 03:59, 9 June 2009 (UTC)

For some purposes it makes sense to add just one "infinity" to both ends of the real line and say 10/0 = infinity. This serves the purposes of trigonometry, projective geometry, and complex analysis (where the whole plane has just one extra "point at infinity" tacked onto it. Michael Hardy (talk) 04:53, 9 June 2009 (UTC)

Plotting contour lines from discrete points
Suppose I have a number of discrete points with values attached to them. I want to now draw contour lines (isopleths) around these points. As a real example, plotting isobars on data from pressure data from weather stations.

Naturally, the plots such as these are performed by meteorological organizations are automated somehow.

What are the standard algorithms used to plot these points? Any online references I can look at? —Preceding unsigned comment added by 210.11.75.201 (talk) 23:24, 8 June 2009 (UTC)


 * I think the usual graphing packages like Gnuplot can do this. As for algorithms, hmm, what's there to know?  Just do some obvious interpolation around nearby points to estimate the function around known points, and fit some splines through them.  A graphics book like Foley and Van Dam  et al might say more.  Cite from computer graphics:


 * James D. Foley, Andries Van Dam, Steven K. Feiner and John F. Hughes (1995). Computer Graphics: Principles and Practice. Addison-Wesley 67.122.209.126 (talk) 02:10, 10 June 2009 (UTC)


 * Gnuplot can't really do this adequately in all circumstances, by it's own admission: see http://www.gnuplot.info/docs/node177.html. I know that one can krige around and interpolate this way, but what I'm really after is some knowledge of what the standard processes are in meteorology to produce automated isobar plots, ie., whether kriging is used, or whether it is not used and some other method done. —Preceding unsigned comment added by 210.11.75.201 (talk) 23:24, 8 June 2009 (UTC)  —Preceding unsigned comment added by 60.241.132.54 (talk)