Wikipedia:Reference desk/Archives/Miscellaneous/2011 April 6

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April 6

Wonderwall Cover on BBC3 documentary 'My brother the Islamist'

Hi, could you please tell me who the cover version of oasis' 'Wonderwall' is featured in the background of the BBC3 program 'My brother the Islamist' which was on TV on Monday 4th April?

Thanks in advance —Preceding unsigned comment added by 195.157.179.249 (talk) 07:06, 6 April 2011 (UTC)

If there is a 10 second section when there is no one talking over it, then try watching the program on iPlayer, and then phone 2580 (Shazam) on your mobile. Make sure that your phone doesn't cause your computer's speakers to click. CS Miller (talk) 08:07, 6 April 2011 (UTC)

I believe it was the version by Ryan Adams, which I'm sure you can find on YouTube to check. --Colapeninsula (talk) 09:05, 6 April 2011 (UTC)

Area of an irregular shape

How does one calculate the area of an irregular shape such as a country? Note, I am posting this on the miscellaneous desk rather than the mathematics desk because I would like the answer to be comprehensible to a non-mathematician. And I don't trust the pointy-heads over there to be able to do that. Thanks very much, --Viennese Waltz 07:58, 6 April 2011 (UTC)

I googled [calculating land area] and many entries came up, of which this was the first: www.ehow.com/how_4924590_calculate-area-piece-land.html, which for some reason is being kicked out by the spam filter, so beware. I don't know if it's the definitive answer, but it squares with what I've heard in the past, namely that they slice it up into simple geomtric shapes and figure out the area of each piece and add them up. In effect, the end result is a calculated estimate. ←Baseball Bugs ^{What's up, Doc?} carrots→ 08:14, 6 April 2011 (UTC)

The reason is that eHow is accused of being a low-quality, SEO-driven "content mill": eHow#Criticisms. AlmostReadytoFly (talk) 09:40, 6 April 2011 (UTC)

See also planimeter. My grandfather owned one, and I thought it was one of the coolest mechanical instruments ever. ---Sluzzelin talk 08:22, 6 April 2011 (UTC)

Neat. That, of course, assumes that the map was drawn correctly. But it's a nifty invention. ←Baseball Bugs ^{What's up, Doc?} carrots→ 08:39, 6 April 2011 (UTC)

Surveying seemed like it would be a logical place to look, but there isn't much there about figuring land areas. ←Baseball Bugs ^{What's up, Doc?} carrots→ 08:42, 6 April 2011 (UTC)

Surveyors divide the land up into lots of triangles and add together the area of each.--Shantavira|^{feed me} 11:18, 6 April 2011 (UTC)

You cut up the area into lots of small shapes whose areas you can calculate directly (typically triangles or rectangles), then add up all the little areas. This is what integral calculus is all about. If you don't want to learn calculus, use a planimeter or a computer program to do it. Staecker (talk) 12:51, 6 April 2011 (UTC)

While it is possible to think of the area of a shape in terms of integral calculus (and comfortable for someone familiar with calculus to do so), I suspect that "learn calculus" as a strategy for solving this particular problem is more than a bit of overkill. For arbitrary shapes (like geographical regions) there is rarely a convenient mathematical function describing the perimeter of the area in question. We must therefore fall back on numerical integration methods anyway, which – as Staecker says – is just "cut[ting] up the area into lots of small shapes whose areas you can calculate directly". (See also the trapezoidal rule.) TenOfAllTrades(talk) 14:38, 6 April 2011 (UTC)

True mathematicians will cringe at this, but the way integral calculus is done is by cutting up the region under a curve into an infinite number of infinitely small rectangles and adding up their areas. The methods described here are using the same idea. ←Baseball Bugs ^{What's up, Doc?} carrots→ 15:16, 6 April 2011 (UTC)

Integral calculus depends on there being an analytic expression which describes the size of the infinitesimal small rectangles, however. This is of limited use when dealing with irregularly- or arbitrarily-shaped objects whose form is not described by a mathematical function, which leads us to fall back on numerical methods. 192.75.165.28 (talk) 19:05, 6 April 2011 (UTC)

Yes. Hence the Trapezoidal rule that TOAT pointed out. It implies the basic problem with the measuring of bodies of land (or water), in that they are typically "round" and we want "square". So it has to be computed by creating squares, rectangles, triangles, etc. - which is the high-level basic idea of integral calculus, except that, as you note, it's hard to come up with a mathematical function that equates to a rugged shoreline. ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:14, 6 April 2011 (UTC)

I suppose I meant something like "numerical methods from calculus", since those are the most likely to be useful for this purpose. You don't really have to know much (any?) calculus to perform the trapezoid rule. You don't even have to know much calculus to INVENT the trapezoid rule! Staecker (talk) 19:19, 6 April 2011 (UTC)

An analog way of calculating the area of an irregular shape is to trace it onto a piece of paper or cardboard, cut out the shape, weigh it on a sensitive balance, and compare it to the weight of rectangle of known area. Edison (talk) 15:11, 6 April 2011 (UTC)

The 'analog' way above works (done it myself, then checked by the triangle method later), but this presupposes that the map is correct - and this will depend on the projection used. If you are trying to determine the area of Lichtenstein this isn't going to matter much, but could be problematic with say Russia. Sadly, if you want great accuracy, you will probably have to find a mathematician who can calculate the area of an irregularly-shaped section of an irregular oblate spheroid. Or look it up, and hope the answer given is right... AndyTheGrump (talk) 15:30, 6 April 2011 (UTC)

Yes, I was about to make the same point about the planimeter method - it's fine for an approximate answer, but it's measuring the area of the map, not the area of the country. The only really accurate method is surveying - which is, of course, how the maps were constructed in the first place. I'll go back and join my fellow pointy-heads on RD/MA. Gandalf61 (talk) 15:46, 8 April 2011 (UTC)

Sites like this will do world map areas "for you" although putting in the points is some work, and the projection appears to have been taken into account. But I think it works on some fairly complex mathematics, hence the word "great circle" cropping up. Grandiose (me, talk, contribs) 15:53, 6 April 2011 (UTC)

I'm no mathematician myself, but I think that fractals mean that technically, it's not possible to measure them. Mind you, round here, that'd be known as a "punch in the mouth answer", as that's what it seems to be requesting. --Dweller (talk) 11:06, 8 April 2011 (UTC)

No. A perimeter such as a coastline can be fractal which means its length is indeterminate but the area enclosed is finite. Nations that share a natural border may therefore agree on their respective areas but disagree on the length of the common border. Vulgar terms such a "pointy-head" and "punch in the mouth" are regrettable and uncalled for here. Please be civil. Cuddlyable3 (talk) 13:37, 8 April 2011 (UTC) Cuddlyable3 (talk) 13:37, 8 April 2011 (UTC)

If area is length x width, as soon as length is infinite, surely area is too? Like I said, I'm no mathematician, but... and I suggest you strike the comment... Your comment is apparently addressed to me and I've not used the term "pointy-head". Furthermore, if you reread what I wrote, I said it was a punch in the mouth answer, ie I should be punched in the mouth. As this page is not part of the encyclopedia, there is no problem with use of what you call a "vulgar term", as it is perfectly civil. If self-deprecation isn't permitted any more, then I give up.--Dweller (talk) 15:01, 8 April 2011 (UTC)

It was me who used the term "pointy-head" and I make no apology for doing so. What a strange thing to get worked up about. --Viennese Waltz 21:18, 9 April 2011 (UTC)

Dweller, see Koch Snowflake for an example of an infinite perimeter enclosing a finite area. ---Sluzzelin talk 15:18, 8 April 2011 (UTC)

Fascinating. So, one can prove that the area is finite (it shouldn't have changed, as I understand it) --Dweller (talk) 15:21, 8 April 2011 (UTC)

Better yet, see Sierpinski triangle for an infinite perimeter enclosing exactly zero area. TenOfAllTrades(talk) 15:56, 8 April 2011 (UTC)

The published areas are calculated by surveying triangulation and geoid trigonometry (no calculus needed), but they bear little relation to the "real" area because they reduce all slopes to a projection onto the "horizontal" geoid at sea level. Where individual areas are measured on a significant slope, the total of the individual areas of separate fields, gardens, roads etc. will far exceed the theoretical "map" area. Real areas need to be used for calculating how much tarmac is needed for roads, or how much fertiliser for fields, but otherwise the geoid projection area seems to be universally used as if no land rose above sea level. Dbfirs 16:12, 8 April 2011 (UTC)

The legal definition of land area (US) ignores slope. This is not a simplification or error, but a legal intention. A 1 acre tract is still 1 acre even if you build a hill and dig a deep pit. Edison (talk) 20:34, 9 April 2011 (UTC)

Yes, it's the same in the UK, so surveyor's measurements need to be adjusted if there is a significant slope. That's the only logically consistent way to measure area, but in a hilly region there can be a significant difference in what you get for your acre or hectare of land. To answer the OP's question, choose a hill or series of hills from which all of the coastline of the country can be seen, then measure the distance from this hill to a large number of points on the coast. Correct these distances by simple trigonometry to take into account the height of the hill (and apply some complicated geoid trigonometry if this is a large country and the curvature of the earth will make a significant difference). Then just add up the areas of all the triangles. The more triangles you consider, the more accurate your answer will be, but complex coastlines make the task very difficult. In practice, map-makers use multiple triangulations to construct their maps, and some map projections give accurate areas, so these can be used to calculate the area just by "counting squares" (easy with a computer). The answer will never be super-accurate because of the coastline problem discussed above. Dbfirs 19:28, 10 April 2011 (UTC)