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Pi in multiple bases
What is the point of the infobox showing pi in multiple bases etc.? The best rational approximations are helpful, and I can sorta see the point of having binary and continued fractions, simply to show that there's no obvious pattern of the digits, but why octal, hexadecimal, and sexagesimal? They don't give any useful insight, and have no practical value. You might think the sexagesimal represention has some antiquarian value because of the Babylonian use of sexagesimal, but apparently the Babylonians didn't calculate with pi as a sexagesimal fraction (and certainly not to so many digits), but as the fraction 25/8 (not even 22/7). --Macrakis (talk) 14:37, 17 September 2011 (UTC)[reply]
I went ahead and removed the sexagesimal as trivia. The base 11 expansion is more notable since it appeared in Contact. The octal and hexadecimal are basically extensions of binary and might be used as a way of defining the number in a low level computer language, though I doubt that's come up much in the last 20 years. I have doubts about the generalized continued fraction; it doesn't converge particularly quickly and there are dozens of other series, products, etc. that might go in its place.--RDBury (talk) 18:33, 17 September 2011 (UTC)[reply]
Octal and hexadecimal may (very rarely these days) be useful constants for computer applications, but WP doesn't need to be in that business: converting the decimal to binary is trivial. --Macrakis (talk) 18:52, 17 September 2011 (UTC)[reply]
Agreed that having multiple bases may be excessive, but either octal (3 binary digits each) or hex (4 binary digits each) should be retained, binary would be unnecessary. As for generalized continued fraction, I reset it in the more standard format; it does converge at 3 decimals per 4 iterations, much faster than the other GCFs in the linked article, and surprisingly the same speed as the GCFs for both the natural logarithm and the nth root of 2 in unfolded notaion. — Glenn L (talk) 01:17, 18 September 2011 (UTC)[reply]
Huh???? Sexagesimal is not notable, although it was used in Ptolemy's Almagest, but base-11 is notable because it appeared in some obscure novel?? I don't see any great need for so MANY digits in base-60 as what we saw there, but it's historically significant that base-60 was once standard in some eastern Mediterranean countries and was used in the most famous of all books ever written on astronomy. Michael Hardy (talk) 02:18, 18 September 2011 (UTC)[reply]
I agree about base 11 (which I don't think has been in the article recently anyway), but don't follow your logic about base 60. Should we also say, instead of 22/7, κβ' δια ζ' or whatever Euclid used as notation? Is Ptolemy's base-60 notation for pi in fact attested (I don't think it is -- but if it is, can you cite chapter and verse)? Do secondary sources mention Ptolemy's base-60 value? If so, we should use that value, not a modern value translated into base-60. And is it useful to have any base-60 value in the infobox? The very fact that the textual explanation is too big for the infobox tends to indicate that it doesn't belong there. --Macrakis (talk) 03:12, 18 September 2011 (UTC)[reply]
I'll let somebody else tackle base-60. But since nobody seems to object to substituting hex or octal for binary, I'm restoring hex and removing binary. Beginning with the traditional decimal value looks nicer anyway. — Glenn L (talk) 05:27, 18 September 2011 (UTC)[reply]
Let's discuss for a minute why it is useful to have binary/octal/hex in there at all. I'd think that the main reason is to demonstrate to the reader that there is no obvious pattern in the binary digits. Of course, you and I know that there is no obvious pattern in the digits of most irrational numbers (in fact, irrational numbers with obvious patterns often seem to be transcendental! ***). But for the general reader, I think that's a useful demonstration. But most general readers -- I'd venture to say in fact even many mathematicians who aren't computer scientists -- won't be familiar with octal or hexadecimal as compact ways of writing binary. So I think binary is better than octal or hex here.
Another possible reason for including hex is for programmers who want to include constants in assembly-language programs or some such. But (a) there are vanishingly few such people; (b) very few applications need fixed-point representations (as opposed to floating-point -- and I hope no one is suggesting we include the IEEE 754representation in hex); (c) it is trivially easy to generate the hex from the decimal representation.
Some time later this month it will become possible to write two archaic Greek letters in TeX in Wikipedia articles. Those two letters were used in Ptolemy's Almagest in the numeral system he used, with base 60 and subbase 10. So after that I will go check out his book from the library again, and do some further editing of the article about his table of chords. At that time, I will see exactly what he says about π, and probably say something about it in this article. Michael Hardy (talk) 22:15, 18 September 2011 (UTC)[reply]
More than slightly modified I would say. You are right about the quality which has a number of problems: it's badly pixelated, badly compressed and is difficult to read at that size. It's also not clear the point it's making: without a lengthy explanation it's not obvious the curved sections are the same length as the diameter. Finally it's not a good idea to use colour to convey important information, for readers with non-colour displays and colour-blind readers. In light of all this I've restored the previous version which does not have these problems.--JohnBlackburnewordsdeeds22:31, 18 September 2011 (UTC)[reply]
Here's the image so people can see what's being discussed. Your comments have merit, but all the same I think there are features of this image that could be used to improve the present top image (which isn't bad).The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.Anythingyouwant (talk) 22:36, 18 September 2011 (UTC)[reply]
I like this image a lot.
Repeats indefinitely
Yes, "its decimal representation never ends or repeats indefinitely" is vague compared to a longer explanation like "... repeats infinitely like 5/6=0.8333333 ... or 3/22=0.13636363636 ...". But "repeats indefinitely" is less vague than just "repeats", which is simply wrong; the decimal representation does repeat finitely. Art LaPella (talk) 06:35, 10 October 2011 (UTC)[reply]
True. I guess that's why you linked repeat to repeating decimal. I've just changed the page back to "... never ends or repeats", because someone else had changed it to "... has no end", which is slightly misleading (the decimal expansion of 1/3 also has no end). Since we're phrasing it in the negative, I think "repeats forever" doesn't work in this context: "... never ends or repeats forever" strikes me as clumsy. But I don't mind if someone can think of a better solution. I guess what we really want to say is "... never ends and never becomes periodic", but we're trying to keep the lead non-technical, right? Jowa fan (talk) 00:47, 11 October 2011 (UTC)[reply]
"has no end" is true as far as it goes. It doesn't say it isn't like 1/3, but readers don't expect us to list everything it isn't; they just want to be able to trust what we say it is, even if they don't click the link. Not mentioning repeating is better than saying it doesn't repeat, because it does repeat. So "has no end" without mentioning repeating, is less misleading than saying it doesn't repeat. I would also prefer "never ends and never becomes periodic" to "never ends or repeats". Art LaPella (talk) 01:38, 11 October 2011 (UTC)[reply]
How about "never ends, and never reaches a point after which it repeats forever". It's true that it's a little longer-winded, but maybe it should be, because the "never repeats forever" is on its face of higher logical complexity than "never ends". (At a slightly deeper level, of course, no decimal expansion ever "ends", but only turns into repeating zeroes, but we don't have to go there.)
I like to say that first off Wikipedia is an encyclopedia, not a course in advanced astrophysics. Even so calculating Pi() to 40 digits would suffice in all possible uses in astrophysics. This page is deeply flawed in its emphasis. Pi critical function is in defining circular parameters and derivation of trigonometric phenomena. Pi, for instance, tells us the number of radians in a circle. E.g. (180/pi() = 1 radian in degrees). The radian is essential for the calculation of sines and cosines based on alpha, because it defines how many radians there are in a circle and because it makes if possible for us to relate angles in radians to angles commonly used in daily life (30, 45, 60, 90, 120, etc.). Several aspects of the mathematical usefulness of pi are virtually glossed over for this numerology which is nothing more than amateur science taken to an extreme. Most pages would place 80% of whats on this page into a paragraph "Pi in popular culture". This page is on the same caliber as the Apollo 16 page.
pi/2 = 90 (an arbitrary base 360' system in which is better based on the pi/radian based system)
pi/3 = 60', in a right triangle the adjacent side is 1/2 the hypotenuse.
pi/4 = 45', in a right triangle both the opposite and adjacent sides are equal, and the length is 1/(2^0.5) the hypotenuse
pi/6 = 30', in a right triangle the opposite side = 1/2 the hypotenuse.
This page is an excellent example of the fact that mathematics is not a pure science, but a representative language-tool for science. Pi() has scientific meaning in that its properties supercede base-systems. But knowing the digital representation in base 10 is therefore meaningless, even less meaningful in the age of computers when its precision is arbitrarily set to 8, 16, 32, or 64 digits and can be implemented without any knowledge using terms like pi(). Memorizing 100,000 digits is even more meaningless. These numerologistic analysis are the equivelant of a page on supercalifragilisticexpialidosious.
PB666yap22:13, 14 October 2011 (UTC)[reply]
What's in the article is what books an articles specifically about pi talk about. And that's what qualifies material for inclusion in Wikipedia. And by the way I do not view mathematics as a science, and while it may be used as a representational tool in science that isn't what it is either. It just is mathematics, one of the endeavours people get up to. Dmcq (talk) 08:42, 20 October 2011 (UTC)[reply]
