Jamietwells

I have a mathematical formula that would be a useful addition to one of the pages. The problem is I don't have a source. I can derive the formula and prove it is correct, but it is lengthy and probably not really suitable for the article. What should I do?

More context may help, but if no published source has mentioned the formula in connection with that article's topic, it's probably not a useful addition. This is also skirting original research, something we should not engage in. Huon (talk) 21:45, 27 June 2015 (UTC)

Thank you for taking the time to answer my question. I'll give you the full story. I was reading ages ago about Greek mathematicians and I can't remember who, but one of them was famous for discovering the formula for the surface area of a parabolic dish. I just closed the article without thinking about it, but earlier I got curious about the problem (it was more interesting than I'd first thought) so I had a little go at solving it myself. I got a little stuck and went to the Wiki article where there was a volume formula but not a formula for the surface area. Since this seems just as important as formula for volume I asked on the talk page why it wasn't included. The response was basically "The area formula is complicated and requires a computer to calculate". I don't think it is complicated actually (not much more so than the volume on anyway and even saying in the article that the area formula is very complicated would be an improvement imho) but I've not finished checking it yet since it's time for bed here. Jamietwells (talk) 22:17, 27 June 2015 (UTC)

My calculus is a little rusty, but the correct formula for the area of a parabolic dish with radius of the opening d and height h>0 should be

${\frac {\pi d}{6h^{2}}}\left((d^{2}+4h^{2})^{3/2}-d^{3}\right),$

which indeed tends to $\pi d^{2}$ as h tends to zero. This is a special case of a surface of revolution, whose area is well-known. I'm pretty sure we could find reliable sources for that formula, though going by a quick Google Books search, the collecting area, which is simply $\pi d^{2}$, seems more relevant and is already given in our article. Huon (talk) 00:53, 28 June 2015 (UTC)

Well I think the best place for this formula is on this article so I'm, going to add it to the end of the "Dimensions of a paraboloidal dish" section. It ends:

Of course, $\scriptstyle \pi R^{2}$ is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight a reflector dish can intercept.

so I think it'd look nice on the end reading:

Of course, $\scriptstyle \pi R^{2}$ is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight a reflector dish can intercept. The surface area of parabolic dish can be found using Pappus's centroid theorem which gives $A={\frac {\pi R}{6D^{2}}}\left((R^{2}+4D^{2})^{3/2}-R^{3}\right)$

What do you think? --Jamietwells (talk) 14:30, 28 June 2015 (UTC)

Using Pappus' centroid formula in this case seems unnecessarily complicated since the calculation of the centroid is non-trivial. Instead I'd rather add a link to surface of revolution#Area which describes a direct method of computation. Huon (talk) 18:42, 28 June 2015 (UTC)

Congratulations on solving the problem. I've tried putting some numbers into your formula, and it always produced plausible results. However, I'm still surprised that, since the calculation of the length of a parabolic arc involves a logarithmic term, the area of a dish produced by rotating an arc apparently does not.

Wikipedia purists may object that this is Original Research (OR), which is forbidden If they do, you may find a better welcome on some other websites. Appropedia.org, for example, does not forbid OR; it positively encourages it.

DOwenWilliams (talk) 15:25, 30 June 2015 (UTC)

I know what you're saying, and usually I wouldn't add something like this, but my stance on 'rules' is that they're really just guidelines that when followed usually produce an acceptable result. In this instance the OR rule is about trust. We can't trust that someone has done the research correctly, but I feel like with maths there is no trust. Maths is either correct or it isn't, so I think if someone has seen the formula and, because of the lack of reference, doesn't trust the formula, they can check the discussion of the talk page or post about it and hopefully they'll find the mathematical derivation which should be true no matter who says it's true, and then be convinced. So I feel in this case it's better to have the formula without a source than to not have the formula, but I'm open to being convinced and obviously a source would be nice. I shall have a look for one when I next get some time.

--Jamietwells (talk) 16:17, 30 June 2015 (UTC)

Someone said "Rules are for the guidance of wise men and the obedience of fools." One of the French revolutionaries, I think. Voltaire perhaps. And he probably said it in French. Anyway, I agree with him, and with you. Unfortunately, there are people here who do not agree.

I have tried to cite that piece I showed you about the focus-balanced paraboloid here on Wikipedia but have been blocked by people who say it is OR and/or that Appropedia and other websites are not reliable sources. It's all just plain math and computer programming, which is similarly indisputable, but rule freaks will be rule freaks. I have managed to post the result, without citing a derivation, on Wikipedia, and someone has plastered it with "citation needed" tags. There's no way to win.

Sigh....

DOwenWilliams (talk) 20:56, 30 June 2015 (UTC)

I copied your dish-area formula into Appropedia. Hope you don't mind.

http://www.appropedia.org/Sun_Related_Calculations#Dimensions_of_a_dish

DOwenWilliams (talk) 03:26, 4 July 2015 (UTC)