Talk:Pi/Archive 6

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alternative symbols

before the widespread use of the pi symbol on computers pi was often expressed as "II" on computers. —Preceding unsigned comment added by Danafton (talk • contribs) 04:09, 4 April 2008 (UTC)

Historical rectifications

This article fails to mention many of the Chinese efforts in evaluating pi, and actually makes no mention of China at all. This should definitely be addressed, since it is now known that the Chinese had a very precise approximation of pi long before the Greeks. I'd be happy to provide references for this, but the work of Joseph Needham, British scholar on the history of Chinese science, is a good place to start. —Preceding unsigned comment added by 132.206.186.82 (talk) 16:08, 28 January 2008 (UTC)

Three different spellings of one word, in just one article. Only on wikipedia. :)

Ok, so there is formulas (9 occurrences), formulæ (5 occurrences) and formulae (6 occurrences). Randomblue (talk) 22:58, 11 December 2007 (UTC)

I will go with whatever the majority likes. I like formulas, since it is more accessible and common in contemporary professional mathematical logic. — Carl (CBM · talk) 23:01, 11 December 2007 (UTC)

I like formulae, although I think using the ligature is unnecessarily pretentious. 'Formulas' seems to be slightly more common in American literature (from a quick search), but I suspect the Plain English campaign would support its use. :-) Angus Lepper^{(T, C, D)} 10:28, 12 December 2007 (UTC)

Done, all changed to "formulas". It is the most widely used spelling in mathematics (even British mathematicians use it). Randomblue (talk) 17:55, 30 January 2008 (UTC)

Geometrical calculations - pentagons?

Nice picture with the inscribed pentagon, hexagon and octagon. But I couldn't help wondering, when was the exact trigonometric formula for sin(36°) first known? (Or chord(72°) equivalently).

If I remember rightly, I thought most of the early inscribed polygon approximations were based on 6 x 2ⁿ-agons, with the successive chord lengths calculated using the half-angles formulas.

Were there early instances of calculations based on pentagons, and if so, who by and when? Jheald (talk) 14:38, 12 December 2007 (UTC)

Okay, so you can use Ptolemy's theorem to show that chord(36°) = 1/φ, the reciprocal of the Golden ratio. And presumably this was maybe known as a special case even earlier?

But it might be an idea to have a pic of 6, 12, 24 sided inscribed polygons, alongside the 5,6 and 8 one, to show the calculation as actually done by Archimedes. Jheald (talk) 15:13, 13 December 2007 (UTC)

The Basis for determing Pi's value of 3.14159265358... is Radian

It should be clear from this example that the ratio of "Radian length : sC length" is the FOUNDATION for the Pi Theorem which I'll paraphrase: The length of a Circumference is 3.141597.. times the length of the Diameter.

Pi is two things. It is the 16th letter of the Greek alphabet

with an associated value of 80. It is also Latin for "Perimeter". Pi is used in the context of "Perimeter" in Archimedes Pi Theorem.

Any attempt to determine the ratio between Circumference length and Radius length must first answer this crucial question: " When is Arc length 1:1 with Radius length". (1:1 is equal, expressed as ratio)

Archimedes stated his answer to that question, with this statement. "Rad (57.2957.. degrees of Arc) is 1:1 with Radius length". From that answer,it can easily be demonstrated how 3.141597.. was determined.

sC length (180 degrees) / Rad length (57.2957.. degrees)= 3.141597.. The value of 3.14597. is directly applicable to sC where

"180* length is  3.141597.. times Radius/Rad"  

C length (360 degrees) / Rad length (57.2957.. degrees) = 6.283194.. The value of 6.283194.. is directly applicable to C where

"360* length is 6.283194. times Radius/Rad"

When Radius length is doubled to become Diameter length, the ratio of "6.283194.. : 1" becomes ratio of "3.141597.. : 1" The Pi Theorem states this latter ratio.

A Method to demonstrate the ratio between "length C : length R" 1.Take a perfectly round object and place it on a horizontal surface. 2.Mark the Start and End of one precise rotation of the object, on the horizontal surface. 3.Measure the distance between the Start and End point. 4.Measure the "length of Radius", or "length of Diameter", of the object 5.Divide the "length of Radius", or "length of Diameter", into the length of C, which was measured at step 3. The result that step 5 provides is the "ratio of " length C to length R, or length C to length D, (It should approximate either 3.14597 or 6.283194..)

Note: What is occurring in step 2, is this. The objects length of Circumference is transformed to a Linear length, which can be precisely measured at step 3. Length of Radius & Diameter are already Linear.

The simpler the explanation of "how Pi's value is determined", the more easily it is understood. Is there a more simple and more clear explanation than the one offered? If there is,someone should link it to the Pi main page, for the benefit of the very young enquirers. Or perhaps someone could edit this offering.

Question for Wiki; Would the intent of the Main Page animation be more clear if it was stated that the "separation shown between 1, 2, 3, 4," is representative of Diameter length? Or is that too obtuse? --58.186.119.151 (talk) 22:00, 12 December 2007 (UTC)

Sammie finds Pi to be sophistecated.

70 Billion decimals of PI

Can this link be included in the article on PI ? I do not know where the trillion digits are available ! [1]

(GeorgeFThomson (talk) 20:35, 31 January 2008 (UTC))

Wrong information about Dase

According to the links below, Johann Martin Zacharias Dase did his 200 digit pi calculation the year 1844. The article claims he did it 1814, ten years before he was borne. I couldn't edit the article so I wrote it here instead. Why can't the article be edited? http://en.wikipedia.org/wiki/Zacharias_Dase http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Dase.html —Preceding unsigned comment added by 130.242.107.27 (talk) 00:38, 9 February 2008 (UTC)

Thanks for the correction; I have edited accordingly.

We've had to restrict editing of this article to registered users because there is a large number of bored dimwits out there who think it funny to insert stuff such as "I LIKE PIE!!1!!" into the article. Forcing such vandals to register before they can deface the article seems to keep the problem down to a manageable level.

For some reason that is not well understood, pi seems to be a particularly loved target of mathematics vandals. Perhaps it is because pi is the only Greek letter one typically sees in pre-college mathematics; some people who did not do well in math classes may have latched on to it as a symbol of all that is wrong and hard to understand about math.

Unfortunately the policy also prevents participation by unregistered users who happen not to be dimwits. We hope it does not scare away too many. Fortunately, registering a username is easy, quick, free and anonymous, so why not just do it? –Henning Makholm 00:53, 9 February 2008 (UTC)

PI has 2 end

look at it this way if u take a string and cut it the lenth of the radius of the circle it will supposidly wrap around the circle 3.14....... times but pi i said 2 go on forevr which is known as infinity but the string cannot wrap around the circle infinity times becasue eventually it will reach apoint were it starts to overlap the string at the begining of the circle.

Please Correct ME if im wrong and PLEASE explain it in laymons terms why im wrong! im only 14 yeasr old and i only came accross this studdin math! —Preceding unsigned comment added by 142.167.133.230 (talk) 00:31, 26 February 2008 (UTC)

It's not the size of π that is infinite. Of course π is less than, for example, 3.15, which is finite. It is the number of digits in its decimal expansion that is infinite. -- Meni Rosenfeld (talk) 19:04, 26 February 2008 (UTC)

The precision gets infinitely smaller rather than infinitely larger, kind of like how the elements (hydrogen, carbon, nitrogen, oxygen) were though of to be the smallest form of matter, then we found atoms, then we found electrons/protons, then etc. etc... But now I am intrigued with the teacher who claims the radius is 3.14 times the circumference of the circle?!? --Billy Nair (talk) 19:49, 3 March 2008 (UTC)

It's a difference of "infinite" AND "continuous." Continuous means that a given area may have a beginning and end, but has an infinite number of points within it. Like a circle. Because a circumference is continuous when in ratio to the circle's finite parts, π is continuous (it -is- the ratio between circumference and the finite parts). Because it is continuous it can never be finished, only made more precise; however, while making it preciser is fine and good, it only adds to the length of π. By adding to the length of the written number, it becomes unusable (what, you gonna write all day and night forever and ever?) in my opinion, and is thus the least practical method of finding an accurate circumference.--97.91.175.154 (talk) 16:07, 14 March 2008 (UTC) aka MilquetoastCJW

But MilquetoastCJW, your argument could also be applied to the perimeter of a square in terms of its side, and that certainly has a decimal expansion which terminates (i.e. 4)! (This probably isn't that useful to the original questioner though - for my answer to that, see below.) Olaf Davis | Talk 09:03, 13 April 2008 (UTC)

Perhaps this example will help too: you know that 1/3 = 0.33333... right? Of course 1/3 isn't infinite since it's less than 1, but when you write it as a decimal it goes on for ever. It just means that no matter how many digits you write down it won't be quite right. 1/3 is a little bigger than 0.33333 but a little smaller than 0.33334 - and the same if we add a hundred 3s instead of five. The only difference with pi is that the digits don't repeat! Olaf Davis | Talk 08:58, 13 April 2008 (UTC)

Special Sections of Pi

I thought it would be interesting to add a section to the page that talks about special "pieces" of pi. I found a great website that mentions all of the repeating numbers and even includes a search engine where you can look for any sequence of numbers up to the first 100,000,000 decimal places in Pi. This Pi "trivia" is actually pretty interesting, even if you're not a geek like me. Here is the website: http://www.angio.net/pi/bigpi.cgi --Terpfan19 (talk) 21:22, 2 March 2008 (UTC)

Other occurences of Pi

Would it be interesting / useful to add a section on the other occurences of Pi in the built and natural world. For example, this BBC news article ( http://news.bbc.co.uk/1/hi/magazine/7296224.stm ) mentions it's presence in the Great Pyramid at Giza and in the calculation of river flows/basins. Just a thought... Aaron-Cork (talk) 13:25, 14 March 2008 (UTC)

How do we know pi is infinite?

Totally elementary question here, but how do we know that we won't some day find an end of Pi? —Preceding unsigned comment added by 69.62.140.50 (talk) 21:04, 13 March 2008 (UTC)

That would prove it is rational. Georgia guy (talk) 21:41, 13 March 2008 (UTC)

Which would be both hilarious and awesome. PeterMottola (talk) 10:49, 14 March 2008 (UTC)

In more detail: If a number has a decimal expansion which ends, then it is a ratio of some integer and a power of 10 (for example, $7.235={\frac {7235}{1000}}$) and is thus rational. π has been proven to be irrational - a proof can be found here for example. Thus, its decimal expansion cannot end. -- Meni Rosenfeld (talk) 10:58, 14 March 2008 (UTC)

Happy Pi Day! —Preceding unsigned comment added by ArdClose (talk • contribs) 13:59, 14 March 2008 (UTC)

PI IS NOT INFINITE. It is continuous.--97.91.175.154 (talk) 16:09, 14 March 2008 (UTC)

Describing a real number as continuous really doesn't make much sense either.169.237.88.59 (talk) 20:05, 21 April 2008 (UTC)

Duodecimal?

I've removed Pi's representation in "duodecimal" from the infobox on the right. I believe it is merely trivia and does not add to the article. As the duodecimal article says, "Languages using duodecimal number systems are uncommon."

Hexadecimal is arguably not helpful either, but I'm leaving it in because it's a number system in active use today.

If there were an article about (possible) patterns in Pi's digits, then these other base representations may be appropriate. As it stands, I think only the decimal representation is appropriate for this encyclopedia article on Pi. I have taken the conservative step of removing only "duodecimal".

Thoughts? Xiphoris (talk) 18:41, 14 March 2008 (UTC)

Agree with the removal of duodecimal. However, since binary and hexadecimal representations (of any quantity) are so prevalent in computing, I think it's appropriate to retain those. (For example, I was just reading that the bzip2 file format uses as one of its magic numbers the hexadecimal representation of pi.) —Steve Summit (talk) 14:57, 15 March 2008 (UTC)

Animation

Is there any way to slow down the animation next to the article? This would make it easier to see what happens in it (and it may also be less "blinking" next to the article during reading). -Philwiki (talk) 10:42, 20 March 2008 (UTC)

Wrong definition of transcendental

I'm referring to the following sentence, which appears in the introduction (second paragraph): "...it is a transcendental number, which means that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) could ever produce it".

This sentence is wrong, or at least very confusing. Indeed, pi is transcendental, and indeed, being transcendental implies that no sequence of algebraic operations can produce it, but this is not an equivalent definition of being transcendental. Many algebraic numbers cannot be produced in this manner as well (in some sense, this is what Galois theory is all about: showing that you cannot produce the roots of polynomials of degree higher than four in this way).

Two ways to correct this sentence:

1. Writing: "...it is a transcendental number, which implies that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) could ever produce it".

2. Writing: "...it is a transcendental number, which means that it is not a root of any polynomial with rational (/integer) coefficients", or "...it is a transcendental number, which means that it doesn't solve any equation of the form p(\pi)=0, where p is a polynomial with rational (/integer) coefficients.

ImSoft (talk) 12:41, 27 March 2008 (UTC)

Right. I'm not sure if mentioning transcendentality even belongs in the introduction, as its accurate definition is not really intro material. For the time being I've replaced it with "...is a transcendental number, therefore no finite sequence...". -- Meni Rosenfeld (talk) 12:49, 27 March 2008 (UTC)

Being transcendental is part of the interest of pi, and so should be mentioned in the intro, but I agree that a full definition isn't really necessary there. The beauty of a wikilinked encyclopedia is that we don't need to give a full definition inline, just a hint of why it's interesting. Not sure about the exact wording, though. --Macrakis (talk) 13:20, 27 March 2008 (UTC)

Biblical History

I added a section about pi in the Bible. It was deleted because it was "gibberish". I understand. But then can someone please add something about it then?Wikimichael22 (talk) 18:12, 5 April 2008 (UTC)Wikimichael22

It does no such thing. I assume you are talking about the quote from Kings:

"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26

Which says nothing about Pi for three reasons:

1. A cubit is a non-standard measurement. It's defined as the length from your elbow to your wrist, but this tends to be different for different people. Simmilarly your arm that does the cubit-measuring tends to not map very well to the curve of the circumference of the circle.

2. This is a documentation of the construction of a physical object, and thus will not have been a perfect circle.

3. I have yet to see any architectural plans which use the complete value of pi as part of their computation (since it would take infinitely long). Thus such numbers are quoted to a number of significant places. Thus all we can say is that in this passage the numbers were quoted to one significant figure. —Preceding unsigned comment added by 87.194.49.123 (talk) 19:07, 4 May 2008 (UTC)

On this topic, Here is an interesting link from the article on Gematria: * π in the bible Fintor (talk) 06:10, 14 May 2008 (UTC)

But a cubit may be proportional, if the diameter is one cubit (which it may not state), than the the perimeter would measure three cubits as it says. A cubit is just another unit, does it make a difference if you say 3 cm, or 3 cubits, or 3 inches (which is another measurement, pharaoh's thumb). Androo123 (talk) 00:45, 23 May 2008 (UTC)

Pi Day

Supposedly Pi Day is on March 14 at 1:59:26 P.M. Well the truth is that this would make it 13:59:26. So wouldn't that make it 1:59:26 A.M.?Wikimichael22 (talk) 18:22, 5 April 2008 (UTC)Wikimichael22

1300 is 1:00 PM. Dicklyon (talk) 18:45, 5 April 2008 (UTC)

I believe that was the point, Dicklyon. They probably just keep it at 1:59 P.M. to make it easier for those who want to ... celebrate? Or at least observe. Phoenix1304 (talk) 19:56, 11 April 2008 (UTC)

Vandalism

Pie? Einstein in 1687? Come on. I'd do a rvv edit now if I felt I could accurately do that. 67.8.55.66 (talk) 05:00, 10 April 2008 (UTC)