Wikipedia:Reference desk/Archives/Mathematics/2008 February 11

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February 11

Indefinite integral of erf^3

Does anyone know of a reference to express the following integral in closed form?

$\int \operatorname {erf} ^{3}(x)\,\mathrm {d} x\,\!$

erf is the error function. I can get the square with a CAS, but I have found nothing through either googling, CASs, MathWorld, etc. Any help would be appreciated. Baccyak4H (Yak!) 04:39, 11 February 2008 (UTC)

Is this equation dimensionally balanced?

This popular article http://news.bbc.co.uk/1/hi/magazine/7238637.stm includes an equation which looks to me as if it is not dimensionally balanced. In other words dimensional analysis would cast doubt on its validity. Am I right? 80.3.47.33 (talk) 18:02, 11 February 2008 (UTC)

That depends on what dimensions each variable has - they are probably dimensionless quantities (eg. there aren't really units of wittyness, so to give it a number you need to compare to an average person, or something, so W is actually the ratio of your wittyness to the wittyness of an average person, which is dimensionless), so it's fine. --Tango (talk) 18:42, 11 February 2008 (UTC)

That is, it's fine dimensionally. It shouldn't really take dimensional analysis to doubt its validity. This is the same source, for instance, that blithely published a claim that 0^0 equals "nullity", whatever that is. It's not that a formula like this couldn't be useful, see, since it is sometimes possible to reduce a complex statistical situation to a compact, reasonably accurate formula. What I doubt is that he put any more work into confirming its effectiveness than he mentioned in the article. Black Carrot (talk) 18:50, 11 February 2008 (UTC)

There are so many situations in everyday life when mathematics (or, more importantly, mathematical thinking) actually can be useful, and yet few people use it. We don't need to pay any heed to some bogus formula that someone made up one day. -- Meni Rosenfeld (talk) 22:27, 11 February 2008 (UTC)

Mandelbrot and Julia sets

Map of 221 Julia sets

Can anyone get me a picture similar to this, but centered, and with a separate picture of a Mandelbrot set (just the black part) the same size and in the same place to use as a mask? I only need the main cardioid part. (Technically, I only need half, as it's symmetric). I'm trying to make my own version of quantum weather butterflies. — Daniel 18:05, 11 February 2008 (UTC)

Can't you just do it yourself in any image editing package? Just crop the image so that it's centred wherever you like, and then get a picture of the Mandelbrot set (which you can easily find online) and shrink it to the right size. --Tango (talk) 18:44, 11 February 2008 (UTC)

If anyone can help you might want to be a bit more specific - any particluar colours for the julia set and how do you want the mandelbrot to be as a background? as a negative effect? or replacing the low value(s) in the julia. (I don't have access to microsoft basic so I can't actually help sorry)87.102.79.203 (talk) 19:33, 11 February 2008 (UTC)

Take a look at this one, I hope this helps. I also have the code to draw the picture (if you want it), it's in python. --George (talk) 20:05, 11 February 2008 (UTC)

There's some complex number in the (equation? algorithm?) for a Julia set. There's some relation between a Julia set with a complex number and the corresponding complex number in the Mandelbrot set. If you look on the map of 221 Julia sets, you'll notice an area shaped roughly like the Mandelbrot set.

Come to think of it, I don't need the map centered (what I meant by that was to have a Julia set a 0+0i and the rest of the grid built around that), and can use the one I posted. I can also find just the black part of Mandelbrot sets easily. The problem is I need them to be the same size and be in the same position.

I'd prefer the Julia sets to be yellow, as that's the color of a quantum whether butterfly. I think map of Julia sets and Mandelbrot set need to be separate pictures. I plan to use them to make the wings of butterflies on an image in POV-Ray. I don't get how the transparency works, but you might be able to do it by having the Julia set map where the Mandelbrot set is black, and just having a background color everywhere else. The images don't need to be very big. As I've said before I only want the main cardioid part (real > -3/4). — Daniel 22:04, 11 February 2008 (UTC)

I've been experimenting. The one-picture system will work (so long as it's PNG, GIF, or IFF). — Daniel 01:16, 12 February 2008 (UTC)

Disconnected set

I'm working in the standard topology R¹, and I need to prove that the set [0,1]U(2,3] is disconnected. Intuitively it looks obvious, but an accurate proof requires, for example, that [0,1] is both open and closed in [0,1]U(2,3]. Any idea why is that true? I'm pretty new to topology, so the answer might be pretty simple. Thanks, deeptrivia (talk) 23:07, 11 February 2008 (UTC)

Presumably [0,1]U(2,3] is topologised as a subspace of R. So you'll need to know the definition of open sets in the standard topology, and also the definition of the subspace topology. Given these definitions, showing that [0,1] and (2,3] are both open is trivial. Algebraist 23:33, 11 February 2008 (UTC)