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To whomever add the 3rd series ("Another that converges even more rapidly is the arcsine series" ) into the "Rate of Convergence" section. I don't think a 3rd series is needed to demonstrate the convergence principle: there are hundreds of series for pi; it takes only 2 to illustrate the point to lay readers. Why stop at 3? why not 4? 5? But, in any case, that 3rd series needs a citation or it should be removed. -- Noleander ( talk) 03:00, 8 January 2013 (UTC)
There is currently an RfC underway at User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant) over whether to have a full Wikipedia article about tau. (You may want to read through it if you haven't already.) Among other new sightings of tau listed there is that the UC San Diego math department has begun teaching tau in one of its Calculus courses. There's plenty of other evidence, but when an accredited math department at a major university has begun using tau instead of pi in one of its courses, you can no longer claim tau is just "popular culture". I'm not asking for tau to be given more lines in the pi article. Just that it be moved to a more appropriate section. -- Joseph Lindenberg ( talk) 23:16, 28 February 2013 (UTC)
They're also teaching tau in some courses at Queen Mary University of London. I haven't had time to sift through their website yet and determine the full extent of it, though. -- Joseph Lindenberg ( talk) 22:13, 1 March 2013 (UTC)
Tau is a very silly choice for 2π anyway. Just look at it, it's more like half a π, or like a π with one leg missing, so it would have been a good choice for π/2 or perhaps π/3, but 2π? No, definitely not. - DVdm ( talk) 14:16, 3 March 2013 (UTC)
I removed a "who" tag. A sentence that says "proponents" and then has two references by different people is perfectly clear about "who" is making the claims: the people being referenced.
However, I am mildly troubled by labeling people who write or say anything in favor of τ as "proponents". I find it too dualistic; I don't see an need to divide people into "proponents" and "opponents" when actual opinions will be more nuanced. — Carl ( CBM · talk) 13:44, 12 March 2013 (UTC)
Implying that there is only a link between pies and pi puns because of the shape of a pie is ridiculous as pies come in any such shape they are made in, and plenty are not circular. Whether a pie is baked round or square, it's almost certainly the name association that leads people to make jokes regarding the two, not the shape. Most people aren't so mathematically enthused as to make the effort to make a math-enthusiast-only-audience joke. — Preceding unsigned comment added by 121.215.129.230 ( talk) 09:08, 14 March 2013 (UTC)
This is actually pretty good. (Not tau propaganda, though it does mention tau at one point.) www.youtube.com/watch?v=wCEhvenbfYM -- Joseph Lindenberg ( talk) 10:27, 15 March 2013 (UTC)
It really is a new MIT tradition. They've announced that again this year, admissions decisions for the fall freshman class will be posted online on Pi Day (3/14) at Tau Time (6:28pm). For anyone who missed it last year, here is a link to the formal proclamation, written in official MIT crayon: mitadmissions.org/blogs/entry/i-have-smashing-news -- Joseph Lindenberg ( talk) 02:53, 8 March 2013 (UTC)
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Samiwala78652 ( talk) 17:50, 19 March 2013 (UTC)mention that 22/7 is a rational number which is a approximation of pi and pi by itself is a irrational number.If you divide 22/7 you will get 3.1428571 and then it will just keep on repeating.Also because of pi we can do solve many math problems like area of circle,cone,cylinder,many geometrical figures volumes,etc.
www.youtube.com/watch?v=nnZk_YuIYkA (This is apparently a follow-up to www.youtube.com/watch?v=G2lFfH6Rknk, in case you haven't seen that video. It includes an actual serious teacher's lecture starting about 5 minutes in.)-- Joseph Lindenberg ( talk) 22:13, 20 March 2013 (UTC)
sin 18=1÷(1+sqrt5) and in radian asin(1÷(1+sqrt5))=π÷10 Twentythreethousand ( talk) 21:10, 28 February 2013 (UTC)
the difference from 180 to 18 is 162 as for pi to pi/10=162*1radian,why is this not correct? Twentythreethousand ( talk) 22:31, 23 March 2013 (UTC)
Take any rational or irrational numbers under 180,divide those numbers by 180 and take the sine of those digits in radian mode or by the use of Taylor series.Invert the sine in degree mode and divide the numbers that were divided by 180 using the answers that were given by Taylor series or in radian mode reverted to degree mode(the dividend), and you obtain pi. — Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 20:40, 28 February 2013 (UTC)
Twentythreethousand ( talk) 22:38, 27 March 2013 (UTC)
Editors (both from [3], meat puppets?) appear to be trying to recreate Tau_(2π) contrary to prior discussions. Can some others keep an eye? IRWolfie- ( talk) 23:59, 11 March 2013 (UTC)
Is there anything controversial about the following removed sentence? "Salman Khan, named in Time's 2012 annual list of the 100 most influential people in the world,[149] advocated the use of τ before π in one of his educational videos at Khan Academy.[150]" – St.nerol ( talk) 01:47, 12 March 2013 (UTC)
The John Machin method is inaccurate past the 16th digit. See WolframAlpha. -- 72.219.142.167 ( talk) 20:29, 6 April 2013 (UTC)
Please review WP:NOTFORUM as articles talk pages are not a place to discuss new ideas that are not based on reliable sources. Johnuniq ( talk) 07:02, 12 April 2013 (UTC) |
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1. Any point in 2-dimension or 3-dimension is not a point, unless below described exceptions Consider the points below: .... Which of the above is a point – fourth dot or fifth dot (so small, that it can not be seen with the naked eye)? If we enlarge the fourth point and the fifth point with a lens or a microscope, we will see it as big as probably the first dot, if not bigger. Thus, the fourth and fifth points are spheres (or something else) and they are not points. However small and accurately we describe the position of the point, it will still have a left, right, above and below to it, besides the sides / diagonals. The position of a point can be defined only if the coordinates are in multiples of 1 or other exceptions below. Also, it will not be possible to represent the point diagrammatically, even if all its coordinates are in multiples of 1. If we put a point in that coordinate, then, some part of the point will be above the coordinate, some part below and so on. Even here, it is only a hypothetical point and any attempted representation of the point will only be an approximation, with the spreading across of the minute point (when enlarged through a lens, as described above). Exclusions: The fact of the matter is that there is no point in 2-D or 3-D, excluding certain exceptions. Let us take 2-D for starters. If we have coordinates of (1, 2), then 1 and 2 being whole numbers, this will exactly represent a point in 2-D with respect to origin i.e. (0,0). A point with the coordinates in 2-D of (3.23, 4.69) cannot be a point. This is because, 0.23 lies between 0 and 1 or between 0.22 and 0.24. What it means is that if it is not in multiples of 1 or an equally divided proportion of 1 and its multiples, then it cannot be a point. If we take 1m as the length of a line, then the line can be divided into exactly equal and measurable parts only by 2, 5 and multiples and powers and other combination of products and powers of these two numbers; of parts. This is so, because 1 cannot be divided into exactly 3 equal parts; nor 6; nor 7; nor 9. But, it can be divided into 2, 4, 5, 8 equal parts. It can also be divided into 1000 equal parts or 25 equal parts. This is so because; the division of 1 by the other numbers does not have a finite number of decimal places. So, how much ever precision we go to, we can never represent any point accurately, with the other decimal representations. So, (1, 1.1) can be represented for a point and similarly, (1, 1.25) can also be represented. But not (1, 1.35). 2. Any line is not a line; except the hypothetical line measuring in length as above Consider below lines (assume of varying widths): ________ ________ ________ ________ Similar to a point, a line, too, cannot be represented as a line. For, which of the above 4 lines is a line and which are combination of multiple parallel lines? Same as above, if we expand the third and fourth (so small, that it is not visible to the naked eye) lines under a microscope, we will see it as big, if not bigger that the first line. Obviously, the first one is not a line and similarly, other 3 are also not lines. Any straight line drawn is as good as a rectangular thin rod (or something else), as we will have points on the line, which will be like other geometrical objects like sphere, etc. So, a straight line is only a hypothetical line, joining two points that can be defined as above. In reality, it would not exist. When it comes to the length of a line, again, it has to be as described in the previous point (point no. 1). Otherwise, it will have a range of length. Let us see how? If we have a length of a line of 1 m, then it is exactly measurable. However, if we have the length of a line which is not in multiples of 1 or multiples of parts of 1 divisible by any combination product / power of 2 and 5; then, it is never a line. In those cases (e.g. 2.53 m), the line is not a line, it is a function of numbers, whose size falls between 2.5 m and 2.625 m (which are multiples of 1 + numeric multiples of equally divisible parts of 1 i.e. divisible by 4 and multiples of 8 and hence exactly measurable). Thus, any line is hypothetical, like points. And any two points in space (even if defined as per point no.1) will never be able to form a line, unless the length of the line joining the two points (shortest distance between the two points) is as described in this section. And, if they don’t follow this principle, then the distance between the two points can never be measured accurately. 3. A circle can have diameters only as defined above in point no.2 Any line (even if hypothetical) will have a measurable and constant length, only if the previously stated conditions hold for the length of the line. Thus, this holds for even the diameter of a circle. Thus, any diameter other than of length as described in point no. 2 is neither measurable, nor constant. And, if the diameter is neither constant nor measurable, then, it cannot form a perfect circle. Thus, you can have a diameter of 1 m or 1.5 m; but not a diameter of 1.59 m. Or maybe, you can also have a diameter of 1.59 (= 1 + ½ +1/25 + 1/20); which the mathematicians should ascertain. In this case, by rotating the diametrical line by 360 degrees, we will get a circle – or we thought so! Let see more surprise below. 4. The circumference of a circle can never be determined Assume that the diameter of a circle is 1 m. Then the circumference of the circle = π x d = π. The circumference of a circle is nothing but a straight line of same length as the circumference, turned into a circle. Thus, the length of the line representing the circumference is π, in this case. However, π is not a number that can be represented in any of the manner mentioned in the previous point nos. 2 and 3. That is, it is not a finite number, which can measure a line accurately and precisely. It is represented by an infinite series. So, definitely, it cannot be a measurable and constant length, as should define a line or the length of the circumference of this circle. Thus, if we were to split the circle at any point and then stretch the two ends to form a line, then, if the length of this line is π or any multiples thereof, then it is definitely not going to be measurable or constant or finite. Anything finite (circumference of a circle) cannot be represented by and infinite number / series. Although π is termed to be a constant; since it does not follow the above rules, it is not a measurable constant for a line; and, hence for the circumference. Thus, there are two options: a. Either π x d is not the circumference of a circle or b. The circumference of a circle can never be determined accurately, despite an accurate and measurable diameter. And a circle can be formed only by a measurable diameter, as described above. E.g. 1/3 meters can never be the diameter of a circle, as it is not finite. Likewise, 1/6 or 1/7 or 1/9 meters also cannot be the diameter of a circle, as the resulting fractional number is not finite and the length of the line is not an exact equal divisor of 1. In case (a), mathematicians have to determine the new circumference of a circle, if it is exactly measurable from point to point. In case (b), what it means is that the so calculated circumference of the circle is either less or more than the point to same point distance traversed through the circumference of the circle. What this means is that, a circle as defined generally as traversing from one point to the same point around a 360 degree arc, around a center, with the same diameter, is never possible in reality to draw. Thus, we always draw somewhat lesser or somewhat more of a circle. In other words, a circle can only be defined as an infinite loop, with no beginning or no end, with every point in the circle being exactly the same distance from a central point. Of course, the distance of each point from the center should follow the above description of a proper line (point nos. 2 and 3). Conclusion: It is thus, for the mathematicians to define the exact laws and review formulaes again. For, this article can sound the death knell for the most vouched for and most wowed constant π! I am sure the above theories will apply to all geometrical figures, their lengths, their circumferences, their areas, their volumes and so on. -- Annienaras ( talk) 14:48, 11 April 2013 (UTC)
Why PI x D cannot represent the circumference of a circle? Gentlemen, I accept your comments; however, please look at the below logic, which explains my rationale better:
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I don't think I've ever seen Π used for the circle constant, ever. It's production, just about always, isn't it? Twin Bird ( talk) 18:16, 24 April 2013 (UTC)
I think Simple Harmonic Motion rates a mention. Pi crops up whenever we are discussing things that oscillate or wobble. — Preceding unsigned comment added by Paul Murray ( talk • contribs) 05:14, 1 May 2013 (UTC)
The actual method of approximation for pi with 96 gons within a circle of 1 diameter is sin(180/96)*96=3.141031950890509638111352....,correct to 3 digits to the decimal places. Twentythreethousand ( talk) 20:18, 11 May 2013 (UTC)
We propose here to set up and run, on a spreadsheet, the calculation of Pi using the idea of Archimedes to inscribe in a circle the regular polygon with 6 sides (regular hexagon), then (by halving the central angles) one with 12 sides, then 24, 48 and 96 sides, calculating for this a perimeter equal to: " three times the diameter plus a certain portion of it that is smaller than a seventh and largest of 10/71 of the same diameter " which is the approximate value of Pi suggested by Archimedes.
Draw a circle of unit diameter and inscribe in it the regular hexagon. Divide by half the angle AOB through OC, then the angle AOC through OE and continue indefinitely, resulting in the succession of regular polygons of 12, 24, 48, ... etc.. sides, inscribed in the circumference, which associate with positive integers n (n = 1 is associated with the hexagon, n = 2 with the dodecagon, etc..).
The arrow CD of the arc AB, denoted by f, is:
CD = OB-(OB2-DB2)1/2 cioè:
f1 = r-(r2-(l1/2)2)1/2
where r is the radius of the circle and l1 the side of the hexagon (r = l1 = 0,5). It has, in general:
fn = r-(r2-(ln/2)2)1/2
and the lengths of the sides of the polygons are calculated in succession:
ln+1 = (fn2+(ln/2)2)1/2
Entering formulas in a spreadsheet, as shown in figure (Inserting formulas):
you get the table (Calculation):
The last column of the table contains the succession of values of pn, the perimeter of the regular polygon of n sides inscribed in the circle of unit diameter. By induction will be lim pn = Pi as n tends to infinity. — Preceding unsigned comment added by Ancora Luciano ( talk • contribs) 16:56, 24 May 2013 (UTC)
In theory, pi has to conclude. It is the ratio of a circles diameter to its circumference, and it has to be a rational number. — Preceding unsigned comment added by Dakoolst ( talk • contribs) 22:11, 28 May 2013 (UTC)
See User talk:Tazerdadog/Tau (Proposed mathematical constant) at the bottom. Chutznik ( talk) 19:26, 6 May 2013 (UTC)
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We need to find some way of finally resolving this issue. Martin Hogbin ( talk) 10:15, 11 May 2013 (UTC)
Certian Solutions to PI π the ration of diameter & parameter of a circle, square, hexagon, etc where the diameter is the max dameter measured thru the center of the 2- or 3=dimensional object was first published as part of a High School Project @ Golden Sr Hich, Golden Colorado(Golden Demons), in 1975. These Postulates, Theorems, etc were not independantly confirmed during the 9 wk-course which also contains solutions to √ square root and cube root of 2 necessary to get a euclidian solution to PI.
The solutions were dubbed Ken- where '-' is the actual abbreviation for solution invarious bases which then were used for various objects like sphere, cube, etc
Remote terminal to School of Mines computer
[Kenneth Maurice Rogers May 14, 2013 6:13PM] — Preceding unsigned comment added by 98.245.71.86 ( talk) 00:34, 15 May 2013 (UTC)
I removed two things from the tau section: (1) an illustration; and (2) a sentence about Albert Eagle. The illustration was a bit UNDUE, considering that tau is not used seriously, and an illustration is very suggestive - and also there is a lot of info about pi that is not in this article. The sentence about Eagle was perhaps okay, but was not supported by a cite (at least, I could find no mention of Eagle in the cites). -- Noleander ( talk) 11:51, 11 May 2013 (UTC)
It may be of interest to record that Oxford University hosted a day school (June 2013) on Tau and Pi. The proceedings are here. Robinwhitty ( talk) 21:52, 3 June 2013 (UTC)
somebody please add this:
The day after New Zealand legalised same-sex marriage, [1] a Catholic priest appeared on a television news show and drew parallels between legalising same-sex marriage and the 1897 attempt to regulate pi, saying pi – and heterosexual marriage – were both "pre-existing" realities that couldn't be changed. [2] 46.11.30.197 ( talk) 20:26, 6 June 2013 (UTC)
I found the reference to Euclidean and non-Euclidean geometry confusingly written, since the preceding definition of Pi, which it refers to, does not directly mention geometry at all. To parse the reference to EG / NEG, one has to already be familiar with the idea that generalized geometries can be defined, and that the notion of circle can be defined in such a way so as to generalize to any geometry. I do strongly believe that this should be fixed somehow, but I'm not particularly wedded to my own fix, so feel free to replace it if you think you have something better. Lewallen ( talk) 18:30, 7 June 2013 (UTC)
OK, I don't know what to think with Pi#cite_ref-153. Should I treat it as a notable source and start a real article on tau, should it be taken out because it is just another newspaper article on a subject which Wikipedia just can not handle, or, the third option, add to it with a counter journal article like http://digitaleditions.walsworthprintgroup.com/display_article.php?id=1013141 ? John W. Nicholson ( talk) 23:34, 14 June 2013 (UTC)
Added ref/source and will continue to do so in Electronics section. Many issues in this field NOT covered in physics. Please add references rather than just deleting whole section because of "unsourced"!! I will continue to add sources as I expand. Thanks. Pdecalculus ( talk) 01:14, 3 August 2013 (UTC)
The History section now has 9 subsections, which is a lot. The focus of most of those subsections is the quest for more digits. In the middle are subsections 4 and 5, which are not about the quest for more digits. Subsection 6 again resumes the quest for more digits, this time with modern computers. That seems like a natural point to break off a new major section, especially since all those additional digits are considered unnecessary for practical use. The modern quest for more digits is a different kind of pursuit, so much so that subsection 7 has to explain to the reader why they're still doing it. But mainly, I'm just looking for a natural breakpoint, and this seems like a good place to do it. -- Joseph Lindenberg ( talk) 07:28, 4 August 2013 (UTC)
It is astounding that the article only briefly mentions the Fourier transform (and doesn't mention Fourier series at all). These applications come from the fact that in harmonic analysis π appears naturally as an eigenvalue of the translation group (actually the Casimir eigenvalue—on the torus for Fourier series, Rn for the Fourier transform). The Fourier decomposition is then the spectral decomposition of (convolution with) a function. In my opinion, this is where π comes in nontrivially into most physical formulae. Sławomir Biały ( talk) 12:34, 4 August 2013 (UTC)
Please see the electronics discussion also. I added a section on electronics, and had intended to expand it, then add sections on molecular biology and physical chemistry, but an editor kept deleting with "already covered" (not true) as a strategic explanation for deletion, instead of contribution to the section or discussion of the bigger issue of balance.
My general problem with this article is the paucity of "use" coverage and the overbearing corpus of information on finding additional digits! Can we look at the whole article from a 30,000 foot view of balance? If you Google pi in electronics or physics, bio, chemistry, etc. you will find a real opportunity for Wiki to contribute here. I've checked 6 current texts in computational electronics alone, and there are over 33 pages of very important material on pi in that "use" (which probably should be called "applications") alone. This is a subset of the broader, and changing, field of pure vs. applied math, which of course have converged. Instead of a 50/50 balance, the article relegates "use" to a small section, and one which seems the subject of a trend to compress and defeature rather than expand. I'm hoping we have an attitude of supporting STEM in addition to gleefully adding a bunch of pop culture facts that admittedly will help us win at trivia at our favorite pub (not a small benefit), but not ignore topics (like electronics) that themselves make this site itself possible.
Whoever had the idea to add "outside mathematics" had a good idea. That would be the section I'd add apps in chem, bio, physics, electronics, as "outside" probably is intended to mean "outside pure math." I mean, some of the examples of algorithms in the article get beyond math (AND their intended topic of adding digits) and into computational complexity; unless you want to lump the whole field (big O etc.) under "discrete math" (meaning, all the material relevant to IT that high schools no longer teach in the US), or regroup that under an outside math topic of "computing," which it actually is. The distinction is subtle: as soon as I start using pi, even in a compiler equation in Scheme, to produce a model of a molecule, I've transitioned "into" rather than outside of math!! — Preceding unsigned comment added by Pdecalculus ( talk • contribs) 15:36, 4 August 2013 (UTC)
I'm happy to put in the work to expand applications in chemistry, biology, physics and electronics if anyone thinks that this would be of value, but with a busy semester of teaching coming up I don't want to do so just to have global deletion if there is no agreement on the need in GENERAL for expanded applications (forget the specifics, they can be built). Pdecalculus ( talk) 13:55, 4 August 2013 (UTC)
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In the fourth paragraph of the introduction, I suggest changing "ubiquitous nature" to "ubiquity". "Nature" means "birth", and so should only be used to describe an inborn characteristic of something living -- or at least metaphorically alive -- and even then only when a suitable noun for the characteristic can't be found. 66.108.3.12 ( talk) 00:33, 19 August 2013 (UTC)
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template.. I'll note that the Oxford American Dictionary includes among its definitions of nature "the basic or inherent features of something, esp. when seen as characteristic of it" and includes the example "helping them to realize the nature of their problems", which is roughly analogous to the usage here.
Rivertorch (
talk)
19:58, 19 August 2013 (UTC)Not sure where to post this. Can't seem to find history or a discussion page. Article used to say, as I recall, that 39 digits of pi were enough to calculate the circumference of the universe to the width of an atom. That's about right. Now it says 39 digits is enough to calculate the volume of the universe to within the volume of an atom. I believe that is incorrect, notwithstanding a reference to a source. My calculation says it takes 113. (FWIW, I have a MA in math, so I know how to figure.) Details of my calculation are in Yahoo Answers at http://answers.yahoo.com/question/index?qid=20130918143934AA8vutk . I'm reluctant to change this myself since this is a featured article. Here's a video confirming that 39 digits applies to circumference, (it would not also apply to volume): http://gizmodo.com/5985858/how-many-digits-of-pi-do-you-really-need. — Preceding unsigned comment added by Freond ( talk • contribs) 02:15, 19 September 2013 (UTC)
I think the current history section focuses too much on historical approximations of π whereas the adoption of the symbol π for the particular ratio of periphery to diameter of a circle is only scratched on briefly at the end. In my view, the history section should discuss in more detail how historical sources particularly before 1706 actually formulated the geometrical relationships between perimeter/volume on the one hand and side length/diameter/radius on the other. For example, it might be misleading to interpret historic clay tablets as implying a value for the ratio of perimeter to diameter if they actually describe for example the ratio perimeter to radius or area to side length of some polygon. How about subdividing the history section in two subsections, where the first discusses the development of the particular ratio perimeter to diameter as circle constant, including historical notation, and the second discusses the development of numerical approximations for π? Isheden ( talk) 20:50, 26 September 2013 (UTC)
On looking at the "Page length (in bytes) 89,180" I was wondering if pi is too big and needs to be split? -- John W. Nicholson ( talk) 00:21, 28 September 2013 (UTC)
In the section titled: "Motivations for Computing Pi", you cite Arndt & Haenel who state that 39 digits of Pi are necessary in order to calculate the volume of the known universe to an accurracy of the volume of one hydrogen atom. Being suspicious of this number,I found their book, and they report this number without comment or proof. They cite another paper by other authors, and I have to admit that I did not researtch this paper. Instead, I and a colleague calculated this quantity ourselves, and we determined that 111 or 112 digits are required. I am cutting and pasting our analysis. What do you think?
OOOPS! This page does not support "Equation Editor" in Microsoft Word. This is my very first time I have ever commented on a Wikipedia page, and, as you can tell, I'm not that good at it yet. Is there some way I can attach a Word document? In any event, our procedure was to calculate the volume of the universe twice: Once using an exact expression for Pi, and the second: using (π-δ) where δ is the error one would need in their approximation of Pi to get the required error in the calculation of the volume of the universe. Subtract these two expressions for the volume, this difference in volumes is then set equal to the volume of a hydrogen atom. Solving for δ yields a value of approximately 5 times 10 to the negative 111.
What do you think?
Bob Michaud 74.78.5.64 ( talk) 13:09, 3 November 2013 (UTC)
Really? The 'circular shape of a pie' makes it a frequent subject of pi puns? Not, uhm, I don't know, the fact that it is a homophone? Small detail, but if you're going to make a caption to a picture, at least have it make sense. 92.109.161.68 ( talk) 17:38, 5 October 2013 (UTC)
Pi day (March 14) is also the birth date of Albert Einstein. Josh-Levin@ieee.org ( talk) 03:03, 11 November 2013 (UTC)
i wonder why pi even existed? — Preceding unsigned comment added by 108.45.142.191 ( talk) 01:13, 11 November 2013 (UTC)
Assuming that the hypotenuse of the right angle triangle equals to 180^2+180^2=64800 and sqrt 64800 equals 180*81*(sqrt 2 /81) then it is without no doubt that pi have a hypotenuse as well that is equal to pi^2+pi^2 where the sqrt of the result equals pi*81*(sqrt 2/81) therefore pi can be squared. 74.12.28.38 ( talk) 00:55, 28 January 2014 (UTC)
The article's sub-section entitled Infinite series contains the following:
This is several years before John Machin's improved algorithmic variations on that series. The subsequent sub-section entitled Rate of convergence indicates that:
The implication of the second statement on the first statement is that Abraham Sharp evaluated the first 50,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 terms. The world's fastest computer would take a lot more than trillions of years to directly evaluate that many terms, so Sharp as he was, I claim there's a contradiction. The second claim is easily verified "manually" by basic error bounding in Numerical Analysis, therefore the pre-Machin-like efforts of Abraham Sharp did not use the Gregory-Leibniz series to directly produce 71 decimal digits of π (or if he did, he hasn't finished yet; he won't have even really got going yet).
Both of the article's statements are cited to a source, but the former is a book I cannot afford, and the latter requires a paid subscription I do not have.
On a related but almost pedantic matter, mathematicians are usually not interested in the number of correct digits in an approximation. The resultant error of an approximation is much more important, and these metrics are not the same thing. As an example of the difference, I have a wonderful approximation for 1. It is the sum of the series of terms where the nth term is defined to be 10^(-3(n-1)) - 10^(-3n). After just three terms, the approximation is 0.999999999 with an error of very nearly one part in a billion. But the number of correct decimal digits is zero, and will stay that way no matter how many terms are taken.
With thanks from
ChrisJBenson (
talk)
06:32, 11 January 2014 (UTC).
I removed the claim that "pi" is a Latin word. It isn't in any normal sense -- goodness knows what it says on page xi of the Greek grammar, but perhaps just something to generate the same confusion with the Latin alphabet. I think it is much more accessible to say "spelled out". I will change the Lede version as well: I confused myself into thinking (and wrote) -- "Romanized" is at least an accurate description -- but it isn't. The Romanization of π is 'p'; while 'pi' is its name. Imaginatorium ( talk) 08:54, 17 January 2014 (UTC)
In reviewing some of the more esoteric errors in the later sections over the last six months, I had missed a basic mathematical error featured quite prominently in the lead section. Since edit 563172535 on 6 July 2013 at 16:31 by Giraffedata, the third sentence of this article stated that no fraction can be exactly equal to π (the exact wording was: "no fraction can be its exact value"). A full rigourous proof (disproof) of this needs only one counteraxample. Here's a fraction that is exactly equal to π:
I've already reverted the text in the article. This is here just in case a proof was required. With thanks from ChrisJBenson ( talk) 07:43, 11 January 2014 (UTC)
I'm not too keen on the current version of the lead. There is a dangling sentence about approximation by rational numbers that for some reason is on a separate line. I think this should be put back into the preceding paragraph somewhere. (But that might just be me: I personally don't like extremely short paragraphs.) Sławomir Biały ( talk) 12:01, 22 January 2014 (UTC)
Divide numbers (whole number,irrational or rational )below 180 by 180 or digits in the middle of 180 and 360 or 360 and 540 all multiple of 180 ,and take sin of the result in radian mode or by the use of Taylor series then change it to degree mode and take the inverte sin from the resutlt in radian mode and you obtain digits of pi by choosing the number that was divided by 180 or 360 and 540....etc. example of a fraction 355/113(a fraction from the article). 355/360=0.98611111111111111111111111111111..... in radian=0.83388586828323059431360578387878.... in degree=56.500004797622844197953735997243....*2(because 360 is a multiple of 180)=113.00000959524568839590747199449... therefore 355/113=3.141592........
355/113.00000959524568839590747199449...=pi
70.55.23.230 ( talk) 19:18, 27 January 2014 (UTC)
The pi/tau controversy makes an appearance at xkcd: "Pi vs. Tau". — Loadmaster ( talk) 20:51, 12 December 2013 (UTC)
With respect to Tau=Pi/2 as proposed by Albert Eagle, the transformation of a unity length line to a two-dimensional semi-circular arc might serve as the defining example. Cerian Knight ( talk) 18:41, 17 February 2014 (UTC)
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Please change the following text: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of tencubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value.
To this: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of ten cubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value. Rabbi Eliyahu of Vilna (The Vilna Gaon) wrote in his commentary on the Bible that the correct reading of the Biblical text indicates to apply a factor of 111/106 which results in 1.04716981 to the approximate π value of 3. This means that the value of π used in the construction of the ceremonial pool was actually 1.04716981 X 3 which equals 3.14150943. It is accurate to the 4th decimal point. This factor is derived from the extraneous word "koh" (קוה) written in the original Hebrew of 1 Kings 7:23. It is to be pronounced however "ko" (קו). Similarly, in 2 Chronicles 4:2, the original Hebrew is actually written "ko" (קו). The Hebrew letters also have numerical values. (קוה) has a value of 111 and (קו) has a numerical value of 106. 108.2.9.169 ( talk) 16:42, 2 March 2014 (UTC)
With reference to Ludolph van Ceulen, "pi" was for a period of roughly 200 years often called the Ludolphine number&Ludolphsche Zahl, from his death in 1610 into the 19th century.
at present, the history section does not explicitly name this fairly important naming practice (to the extent that previous namings ARE important!), and a single sentence or so, for example along the line: "For about 200 years, pi was occasionally referred to as the Ludolphine number, in honour of Ludolph van Ceulen, who calculated pi correctly to 35 digits in the 16th century". Or something like that. Arildnordby ( talk) 00:38, 15 March 2014 (UTC)
Current entries in the antiquity India section give a feel that those calculators were off the mark where as Aryabhata and Madhava approximated Pi value to 5 and 11 digits accuracy. Infact, Aryabhata's work has been included in Polygon Approximation in a below section where it does not belong-I did not get any reference of his using a polygon method to calculate Pi value to 5 digit accuracy. I feel, Including Aryabhata and Madhava's works subsequently is also chronological otherwise, antiquity section itself is misleading?. Madhava's work gets a mention in Infinite series but does not stress on his value to pi value approximation. He was never in competition with any Persian mathematician. the language used does not sound neutral. Also, I feel, Wikipedia should revert all BC/AD to BCE and ACE. That can be another discussion. — Preceding unsigned comment added by Sudhee26 ( talk • contribs) 21:44, 9 June 2014 (UTC)
In section 1.5, in Approximate Value, a few lines are missing numbers.
It's minor.. But, I just wondered, given the international reach of Wikipedia (and of π!), whether that should read "Greek fonts" or something. From the "Name" section:
69.201.175.80 ( talk) 21:15, 22 July 2014 (UTC)
If under the section "Approximate Value" the first 100 decimal digits are defined as: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679, then the leading 3 is not considered a decimal digit. In this case, under the section "Polygon approximation era", the sentence: "With a correct value for its seven first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." should be replaced with "With a correct value for its six first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." — Preceding unsigned comment added by 65.201.161.119 ( talk) 15:31, 15 April 2014 (UTC)
I find the following from Boyer at [ [6]]
>However, Tsu Ch'ung-chih went even further in his calculations, for he gave 3.1415927 as an "excess" value and 3.1415926 as a "deficit value." 7< with notes 6 See the excellent article on Liu Hui, written by Ho Peng-Yoke, to appear in the forthcoming volumes of the Dictionary of Scientific Biography. 1 [presumably 7] See the article cited in footnote 6. There seems to be some confusion in the citation of this value by Mikami, op. cit., p. 50, by Smith, op. cit., II, 309, and Hofmann, op. cit., I, 76.
This strikes me as badly written for Tsu Ch'ung-chih would presumably not have expresed himself in the decimal system. However I am not in a position to consult the source. If anyone is it might constitute a worthwhile addition to the article. Sceptic1954 ( talk) 17:13, 2 September 2014 (UTC)
There's a very blatant error in this article. Proponents of Tau want it to replace 2 pi, not pi/2. This has to be corrected. — Preceding unsigned comment added by 2601:4:3780:5B:B166:F5D6:3AA5:71A3 ( talk) 03:50, 2 October 2014 (UTC)
I remember 31415926535 by heart , now I search for that number (to long, but if I could) using http://pi.nersc.gov/ binary search engine in Pi
Then I will use this new Pi part to search again (when we have powerful enough machines) for event longer number.
How big the number representing starting point will be ?
Bigger than googleplex ?
KrisK 68.199.112.146 ( talk) 01:15, 25 November 2014 (UTC)
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Please include in external links: Mnemonics to remember Pi https://www.mnemonic-device.com/arithmetic/pi/may-i-have-a-large-container-of-coffee/
regards, Pjotr
Pjotrw ( talk) 12:47, 3 January 2015 (UTC)
This talk section's content appears not to engage the purpose of this talk page, which is to improve the accompanying
WP article. I've downsized its content, to reduce the distraction it causes from this talk page's purpose.
--
Jerzy•
t
07:18, 21 February 2015 (UTC)
So my Question is. If you mirror Pi I mean if you take the digital Version of Pi and use the not operator. What kind of Number would you have then ? Also a transcendence Number ? What kind of Geometric Figure you can discern from this digit ? — Preceding
unsigned comment added by
87.122.187.198 (
talk)
20:59, 16 May 2014 (UTC)
So my Question is. If you take the digital Version of Pi and use the not Operator. What kind of Number would you have then? Also a transcendence Number ? What kind of Figure can you discern of this digit ? — Preceding unsigned comment added by 87.122.187.198 ( talk) 21:03, 16 May 2014 (UTC)
So my Question is. If you take the digital Version of Pi and use the not Operator. What kind of Number would you have then. Also a transcendence Number ? What kind of Figure can you discern from this digit ? — Preceding unsigned comment added by 87.122.187.198 ( talk) 21:06, 16 May 2014 (UTC)
Happy Ultimate Pi Day (3-14-15)! Timo 3 13:33, 14 March 2015 (UTC)
Pi can also be described by ~ 22/7 - 1/800 - 1/70,000 - 1/5,000,000 Pi² = ~ 9.87 - 1/2500 V pi = ~ 16/9 - 1/200 — Preceding unsigned comment added by 84.80.54.162 ( talk) 19:07, 14 March 2015 (UTC)
Maybe a better solution to this issue would be to have disambiguation pages for 3.141 etc?
-- [[
User:Edokter]] {{
talk}}
11:39, 15 March 2015 (UTC)At the time of writing, paragraph 3 begins "Although ancient civilizations needed the value of π to be computed accurately for practical reasons, it was not calculated to more than seven digits, using geometrical techniques, in Chinese mathematics and to about five in Indian mathematics in the 5th century CE." This sentence clearly needs to be rewritten but I am unable to correctly do this myself. Please could someone more knowledgable of the subject oblige? Many thanks. MikeEagling ( talk) 11:32, 14 March 2015 (UTC)
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Archive 10 | Archive 11 | Archive 12 | Archive 13 | Archive 14 | Archive 15 | → | Archive 17 |
To whomever add the 3rd series ("Another that converges even more rapidly is the arcsine series" ) into the "Rate of Convergence" section. I don't think a 3rd series is needed to demonstrate the convergence principle: there are hundreds of series for pi; it takes only 2 to illustrate the point to lay readers. Why stop at 3? why not 4? 5? But, in any case, that 3rd series needs a citation or it should be removed. -- Noleander ( talk) 03:00, 8 January 2013 (UTC)
There is currently an RfC underway at User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant) over whether to have a full Wikipedia article about tau. (You may want to read through it if you haven't already.) Among other new sightings of tau listed there is that the UC San Diego math department has begun teaching tau in one of its Calculus courses. There's plenty of other evidence, but when an accredited math department at a major university has begun using tau instead of pi in one of its courses, you can no longer claim tau is just "popular culture". I'm not asking for tau to be given more lines in the pi article. Just that it be moved to a more appropriate section. -- Joseph Lindenberg ( talk) 23:16, 28 February 2013 (UTC)
They're also teaching tau in some courses at Queen Mary University of London. I haven't had time to sift through their website yet and determine the full extent of it, though. -- Joseph Lindenberg ( talk) 22:13, 1 March 2013 (UTC)
Tau is a very silly choice for 2π anyway. Just look at it, it's more like half a π, or like a π with one leg missing, so it would have been a good choice for π/2 or perhaps π/3, but 2π? No, definitely not. - DVdm ( talk) 14:16, 3 March 2013 (UTC)
I removed a "who" tag. A sentence that says "proponents" and then has two references by different people is perfectly clear about "who" is making the claims: the people being referenced.
However, I am mildly troubled by labeling people who write or say anything in favor of τ as "proponents". I find it too dualistic; I don't see an need to divide people into "proponents" and "opponents" when actual opinions will be more nuanced. — Carl ( CBM · talk) 13:44, 12 March 2013 (UTC)
Implying that there is only a link between pies and pi puns because of the shape of a pie is ridiculous as pies come in any such shape they are made in, and plenty are not circular. Whether a pie is baked round or square, it's almost certainly the name association that leads people to make jokes regarding the two, not the shape. Most people aren't so mathematically enthused as to make the effort to make a math-enthusiast-only-audience joke. — Preceding unsigned comment added by 121.215.129.230 ( talk) 09:08, 14 March 2013 (UTC)
This is actually pretty good. (Not tau propaganda, though it does mention tau at one point.) www.youtube.com/watch?v=wCEhvenbfYM -- Joseph Lindenberg ( talk) 10:27, 15 March 2013 (UTC)
It really is a new MIT tradition. They've announced that again this year, admissions decisions for the fall freshman class will be posted online on Pi Day (3/14) at Tau Time (6:28pm). For anyone who missed it last year, here is a link to the formal proclamation, written in official MIT crayon: mitadmissions.org/blogs/entry/i-have-smashing-news -- Joseph Lindenberg ( talk) 02:53, 8 March 2013 (UTC)
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Samiwala78652 ( talk) 17:50, 19 March 2013 (UTC)mention that 22/7 is a rational number which is a approximation of pi and pi by itself is a irrational number.If you divide 22/7 you will get 3.1428571 and then it will just keep on repeating.Also because of pi we can do solve many math problems like area of circle,cone,cylinder,many geometrical figures volumes,etc.
www.youtube.com/watch?v=nnZk_YuIYkA (This is apparently a follow-up to www.youtube.com/watch?v=G2lFfH6Rknk, in case you haven't seen that video. It includes an actual serious teacher's lecture starting about 5 minutes in.)-- Joseph Lindenberg ( talk) 22:13, 20 March 2013 (UTC)
sin 18=1÷(1+sqrt5) and in radian asin(1÷(1+sqrt5))=π÷10 Twentythreethousand ( talk) 21:10, 28 February 2013 (UTC)
the difference from 180 to 18 is 162 as for pi to pi/10=162*1radian,why is this not correct? Twentythreethousand ( talk) 22:31, 23 March 2013 (UTC)
Take any rational or irrational numbers under 180,divide those numbers by 180 and take the sine of those digits in radian mode or by the use of Taylor series.Invert the sine in degree mode and divide the numbers that were divided by 180 using the answers that were given by Taylor series or in radian mode reverted to degree mode(the dividend), and you obtain pi. — Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 20:40, 28 February 2013 (UTC)
Twentythreethousand ( talk) 22:38, 27 March 2013 (UTC)
Editors (both from [3], meat puppets?) appear to be trying to recreate Tau_(2π) contrary to prior discussions. Can some others keep an eye? IRWolfie- ( talk) 23:59, 11 March 2013 (UTC)
Is there anything controversial about the following removed sentence? "Salman Khan, named in Time's 2012 annual list of the 100 most influential people in the world,[149] advocated the use of τ before π in one of his educational videos at Khan Academy.[150]" – St.nerol ( talk) 01:47, 12 March 2013 (UTC)
The John Machin method is inaccurate past the 16th digit. See WolframAlpha. -- 72.219.142.167 ( talk) 20:29, 6 April 2013 (UTC)
Please review WP:NOTFORUM as articles talk pages are not a place to discuss new ideas that are not based on reliable sources. Johnuniq ( talk) 07:02, 12 April 2013 (UTC) |
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1. Any point in 2-dimension or 3-dimension is not a point, unless below described exceptions Consider the points below: .... Which of the above is a point – fourth dot or fifth dot (so small, that it can not be seen with the naked eye)? If we enlarge the fourth point and the fifth point with a lens or a microscope, we will see it as big as probably the first dot, if not bigger. Thus, the fourth and fifth points are spheres (or something else) and they are not points. However small and accurately we describe the position of the point, it will still have a left, right, above and below to it, besides the sides / diagonals. The position of a point can be defined only if the coordinates are in multiples of 1 or other exceptions below. Also, it will not be possible to represent the point diagrammatically, even if all its coordinates are in multiples of 1. If we put a point in that coordinate, then, some part of the point will be above the coordinate, some part below and so on. Even here, it is only a hypothetical point and any attempted representation of the point will only be an approximation, with the spreading across of the minute point (when enlarged through a lens, as described above). Exclusions: The fact of the matter is that there is no point in 2-D or 3-D, excluding certain exceptions. Let us take 2-D for starters. If we have coordinates of (1, 2), then 1 and 2 being whole numbers, this will exactly represent a point in 2-D with respect to origin i.e. (0,0). A point with the coordinates in 2-D of (3.23, 4.69) cannot be a point. This is because, 0.23 lies between 0 and 1 or between 0.22 and 0.24. What it means is that if it is not in multiples of 1 or an equally divided proportion of 1 and its multiples, then it cannot be a point. If we take 1m as the length of a line, then the line can be divided into exactly equal and measurable parts only by 2, 5 and multiples and powers and other combination of products and powers of these two numbers; of parts. This is so, because 1 cannot be divided into exactly 3 equal parts; nor 6; nor 7; nor 9. But, it can be divided into 2, 4, 5, 8 equal parts. It can also be divided into 1000 equal parts or 25 equal parts. This is so because; the division of 1 by the other numbers does not have a finite number of decimal places. So, how much ever precision we go to, we can never represent any point accurately, with the other decimal representations. So, (1, 1.1) can be represented for a point and similarly, (1, 1.25) can also be represented. But not (1, 1.35). 2. Any line is not a line; except the hypothetical line measuring in length as above Consider below lines (assume of varying widths): ________ ________ ________ ________ Similar to a point, a line, too, cannot be represented as a line. For, which of the above 4 lines is a line and which are combination of multiple parallel lines? Same as above, if we expand the third and fourth (so small, that it is not visible to the naked eye) lines under a microscope, we will see it as big, if not bigger that the first line. Obviously, the first one is not a line and similarly, other 3 are also not lines. Any straight line drawn is as good as a rectangular thin rod (or something else), as we will have points on the line, which will be like other geometrical objects like sphere, etc. So, a straight line is only a hypothetical line, joining two points that can be defined as above. In reality, it would not exist. When it comes to the length of a line, again, it has to be as described in the previous point (point no. 1). Otherwise, it will have a range of length. Let us see how? If we have a length of a line of 1 m, then it is exactly measurable. However, if we have the length of a line which is not in multiples of 1 or multiples of parts of 1 divisible by any combination product / power of 2 and 5; then, it is never a line. In those cases (e.g. 2.53 m), the line is not a line, it is a function of numbers, whose size falls between 2.5 m and 2.625 m (which are multiples of 1 + numeric multiples of equally divisible parts of 1 i.e. divisible by 4 and multiples of 8 and hence exactly measurable). Thus, any line is hypothetical, like points. And any two points in space (even if defined as per point no.1) will never be able to form a line, unless the length of the line joining the two points (shortest distance between the two points) is as described in this section. And, if they don’t follow this principle, then the distance between the two points can never be measured accurately. 3. A circle can have diameters only as defined above in point no.2 Any line (even if hypothetical) will have a measurable and constant length, only if the previously stated conditions hold for the length of the line. Thus, this holds for even the diameter of a circle. Thus, any diameter other than of length as described in point no. 2 is neither measurable, nor constant. And, if the diameter is neither constant nor measurable, then, it cannot form a perfect circle. Thus, you can have a diameter of 1 m or 1.5 m; but not a diameter of 1.59 m. Or maybe, you can also have a diameter of 1.59 (= 1 + ½ +1/25 + 1/20); which the mathematicians should ascertain. In this case, by rotating the diametrical line by 360 degrees, we will get a circle – or we thought so! Let see more surprise below. 4. The circumference of a circle can never be determined Assume that the diameter of a circle is 1 m. Then the circumference of the circle = π x d = π. The circumference of a circle is nothing but a straight line of same length as the circumference, turned into a circle. Thus, the length of the line representing the circumference is π, in this case. However, π is not a number that can be represented in any of the manner mentioned in the previous point nos. 2 and 3. That is, it is not a finite number, which can measure a line accurately and precisely. It is represented by an infinite series. So, definitely, it cannot be a measurable and constant length, as should define a line or the length of the circumference of this circle. Thus, if we were to split the circle at any point and then stretch the two ends to form a line, then, if the length of this line is π or any multiples thereof, then it is definitely not going to be measurable or constant or finite. Anything finite (circumference of a circle) cannot be represented by and infinite number / series. Although π is termed to be a constant; since it does not follow the above rules, it is not a measurable constant for a line; and, hence for the circumference. Thus, there are two options: a. Either π x d is not the circumference of a circle or b. The circumference of a circle can never be determined accurately, despite an accurate and measurable diameter. And a circle can be formed only by a measurable diameter, as described above. E.g. 1/3 meters can never be the diameter of a circle, as it is not finite. Likewise, 1/6 or 1/7 or 1/9 meters also cannot be the diameter of a circle, as the resulting fractional number is not finite and the length of the line is not an exact equal divisor of 1. In case (a), mathematicians have to determine the new circumference of a circle, if it is exactly measurable from point to point. In case (b), what it means is that the so calculated circumference of the circle is either less or more than the point to same point distance traversed through the circumference of the circle. What this means is that, a circle as defined generally as traversing from one point to the same point around a 360 degree arc, around a center, with the same diameter, is never possible in reality to draw. Thus, we always draw somewhat lesser or somewhat more of a circle. In other words, a circle can only be defined as an infinite loop, with no beginning or no end, with every point in the circle being exactly the same distance from a central point. Of course, the distance of each point from the center should follow the above description of a proper line (point nos. 2 and 3). Conclusion: It is thus, for the mathematicians to define the exact laws and review formulaes again. For, this article can sound the death knell for the most vouched for and most wowed constant π! I am sure the above theories will apply to all geometrical figures, their lengths, their circumferences, their areas, their volumes and so on. -- Annienaras ( talk) 14:48, 11 April 2013 (UTC)
Why PI x D cannot represent the circumference of a circle? Gentlemen, I accept your comments; however, please look at the below logic, which explains my rationale better:
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I don't think I've ever seen Π used for the circle constant, ever. It's production, just about always, isn't it? Twin Bird ( talk) 18:16, 24 April 2013 (UTC)
I think Simple Harmonic Motion rates a mention. Pi crops up whenever we are discussing things that oscillate or wobble. — Preceding unsigned comment added by Paul Murray ( talk • contribs) 05:14, 1 May 2013 (UTC)
The actual method of approximation for pi with 96 gons within a circle of 1 diameter is sin(180/96)*96=3.141031950890509638111352....,correct to 3 digits to the decimal places. Twentythreethousand ( talk) 20:18, 11 May 2013 (UTC)
We propose here to set up and run, on a spreadsheet, the calculation of Pi using the idea of Archimedes to inscribe in a circle the regular polygon with 6 sides (regular hexagon), then (by halving the central angles) one with 12 sides, then 24, 48 and 96 sides, calculating for this a perimeter equal to: " three times the diameter plus a certain portion of it that is smaller than a seventh and largest of 10/71 of the same diameter " which is the approximate value of Pi suggested by Archimedes.
Draw a circle of unit diameter and inscribe in it the regular hexagon. Divide by half the angle AOB through OC, then the angle AOC through OE and continue indefinitely, resulting in the succession of regular polygons of 12, 24, 48, ... etc.. sides, inscribed in the circumference, which associate with positive integers n (n = 1 is associated with the hexagon, n = 2 with the dodecagon, etc..).
The arrow CD of the arc AB, denoted by f, is:
CD = OB-(OB2-DB2)1/2 cioè:
f1 = r-(r2-(l1/2)2)1/2
where r is the radius of the circle and l1 the side of the hexagon (r = l1 = 0,5). It has, in general:
fn = r-(r2-(ln/2)2)1/2
and the lengths of the sides of the polygons are calculated in succession:
ln+1 = (fn2+(ln/2)2)1/2
Entering formulas in a spreadsheet, as shown in figure (Inserting formulas):
you get the table (Calculation):
The last column of the table contains the succession of values of pn, the perimeter of the regular polygon of n sides inscribed in the circle of unit diameter. By induction will be lim pn = Pi as n tends to infinity. — Preceding unsigned comment added by Ancora Luciano ( talk • contribs) 16:56, 24 May 2013 (UTC)
In theory, pi has to conclude. It is the ratio of a circles diameter to its circumference, and it has to be a rational number. — Preceding unsigned comment added by Dakoolst ( talk • contribs) 22:11, 28 May 2013 (UTC)
See User talk:Tazerdadog/Tau (Proposed mathematical constant) at the bottom. Chutznik ( talk) 19:26, 6 May 2013 (UTC)
{{
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: Unknown parameter |month=
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We need to find some way of finally resolving this issue. Martin Hogbin ( talk) 10:15, 11 May 2013 (UTC)
Certian Solutions to PI π the ration of diameter & parameter of a circle, square, hexagon, etc where the diameter is the max dameter measured thru the center of the 2- or 3=dimensional object was first published as part of a High School Project @ Golden Sr Hich, Golden Colorado(Golden Demons), in 1975. These Postulates, Theorems, etc were not independantly confirmed during the 9 wk-course which also contains solutions to √ square root and cube root of 2 necessary to get a euclidian solution to PI.
The solutions were dubbed Ken- where '-' is the actual abbreviation for solution invarious bases which then were used for various objects like sphere, cube, etc
Remote terminal to School of Mines computer
[Kenneth Maurice Rogers May 14, 2013 6:13PM] — Preceding unsigned comment added by 98.245.71.86 ( talk) 00:34, 15 May 2013 (UTC)
I removed two things from the tau section: (1) an illustration; and (2) a sentence about Albert Eagle. The illustration was a bit UNDUE, considering that tau is not used seriously, and an illustration is very suggestive - and also there is a lot of info about pi that is not in this article. The sentence about Eagle was perhaps okay, but was not supported by a cite (at least, I could find no mention of Eagle in the cites). -- Noleander ( talk) 11:51, 11 May 2013 (UTC)
It may be of interest to record that Oxford University hosted a day school (June 2013) on Tau and Pi. The proceedings are here. Robinwhitty ( talk) 21:52, 3 June 2013 (UTC)
somebody please add this:
The day after New Zealand legalised same-sex marriage, [1] a Catholic priest appeared on a television news show and drew parallels between legalising same-sex marriage and the 1897 attempt to regulate pi, saying pi – and heterosexual marriage – were both "pre-existing" realities that couldn't be changed. [2] 46.11.30.197 ( talk) 20:26, 6 June 2013 (UTC)
I found the reference to Euclidean and non-Euclidean geometry confusingly written, since the preceding definition of Pi, which it refers to, does not directly mention geometry at all. To parse the reference to EG / NEG, one has to already be familiar with the idea that generalized geometries can be defined, and that the notion of circle can be defined in such a way so as to generalize to any geometry. I do strongly believe that this should be fixed somehow, but I'm not particularly wedded to my own fix, so feel free to replace it if you think you have something better. Lewallen ( talk) 18:30, 7 June 2013 (UTC)
OK, I don't know what to think with Pi#cite_ref-153. Should I treat it as a notable source and start a real article on tau, should it be taken out because it is just another newspaper article on a subject which Wikipedia just can not handle, or, the third option, add to it with a counter journal article like http://digitaleditions.walsworthprintgroup.com/display_article.php?id=1013141 ? John W. Nicholson ( talk) 23:34, 14 June 2013 (UTC)
Added ref/source and will continue to do so in Electronics section. Many issues in this field NOT covered in physics. Please add references rather than just deleting whole section because of "unsourced"!! I will continue to add sources as I expand. Thanks. Pdecalculus ( talk) 01:14, 3 August 2013 (UTC)
The History section now has 9 subsections, which is a lot. The focus of most of those subsections is the quest for more digits. In the middle are subsections 4 and 5, which are not about the quest for more digits. Subsection 6 again resumes the quest for more digits, this time with modern computers. That seems like a natural point to break off a new major section, especially since all those additional digits are considered unnecessary for practical use. The modern quest for more digits is a different kind of pursuit, so much so that subsection 7 has to explain to the reader why they're still doing it. But mainly, I'm just looking for a natural breakpoint, and this seems like a good place to do it. -- Joseph Lindenberg ( talk) 07:28, 4 August 2013 (UTC)
It is astounding that the article only briefly mentions the Fourier transform (and doesn't mention Fourier series at all). These applications come from the fact that in harmonic analysis π appears naturally as an eigenvalue of the translation group (actually the Casimir eigenvalue—on the torus for Fourier series, Rn for the Fourier transform). The Fourier decomposition is then the spectral decomposition of (convolution with) a function. In my opinion, this is where π comes in nontrivially into most physical formulae. Sławomir Biały ( talk) 12:34, 4 August 2013 (UTC)
Please see the electronics discussion also. I added a section on electronics, and had intended to expand it, then add sections on molecular biology and physical chemistry, but an editor kept deleting with "already covered" (not true) as a strategic explanation for deletion, instead of contribution to the section or discussion of the bigger issue of balance.
My general problem with this article is the paucity of "use" coverage and the overbearing corpus of information on finding additional digits! Can we look at the whole article from a 30,000 foot view of balance? If you Google pi in electronics or physics, bio, chemistry, etc. you will find a real opportunity for Wiki to contribute here. I've checked 6 current texts in computational electronics alone, and there are over 33 pages of very important material on pi in that "use" (which probably should be called "applications") alone. This is a subset of the broader, and changing, field of pure vs. applied math, which of course have converged. Instead of a 50/50 balance, the article relegates "use" to a small section, and one which seems the subject of a trend to compress and defeature rather than expand. I'm hoping we have an attitude of supporting STEM in addition to gleefully adding a bunch of pop culture facts that admittedly will help us win at trivia at our favorite pub (not a small benefit), but not ignore topics (like electronics) that themselves make this site itself possible.
Whoever had the idea to add "outside mathematics" had a good idea. That would be the section I'd add apps in chem, bio, physics, electronics, as "outside" probably is intended to mean "outside pure math." I mean, some of the examples of algorithms in the article get beyond math (AND their intended topic of adding digits) and into computational complexity; unless you want to lump the whole field (big O etc.) under "discrete math" (meaning, all the material relevant to IT that high schools no longer teach in the US), or regroup that under an outside math topic of "computing," which it actually is. The distinction is subtle: as soon as I start using pi, even in a compiler equation in Scheme, to produce a model of a molecule, I've transitioned "into" rather than outside of math!! — Preceding unsigned comment added by Pdecalculus ( talk • contribs) 15:36, 4 August 2013 (UTC)
I'm happy to put in the work to expand applications in chemistry, biology, physics and electronics if anyone thinks that this would be of value, but with a busy semester of teaching coming up I don't want to do so just to have global deletion if there is no agreement on the need in GENERAL for expanded applications (forget the specifics, they can be built). Pdecalculus ( talk) 13:55, 4 August 2013 (UTC)
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In the fourth paragraph of the introduction, I suggest changing "ubiquitous nature" to "ubiquity". "Nature" means "birth", and so should only be used to describe an inborn characteristic of something living -- or at least metaphorically alive -- and even then only when a suitable noun for the characteristic can't be found. 66.108.3.12 ( talk) 00:33, 19 August 2013 (UTC)
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template.. I'll note that the Oxford American Dictionary includes among its definitions of nature "the basic or inherent features of something, esp. when seen as characteristic of it" and includes the example "helping them to realize the nature of their problems", which is roughly analogous to the usage here.
Rivertorch (
talk)
19:58, 19 August 2013 (UTC)Not sure where to post this. Can't seem to find history or a discussion page. Article used to say, as I recall, that 39 digits of pi were enough to calculate the circumference of the universe to the width of an atom. That's about right. Now it says 39 digits is enough to calculate the volume of the universe to within the volume of an atom. I believe that is incorrect, notwithstanding a reference to a source. My calculation says it takes 113. (FWIW, I have a MA in math, so I know how to figure.) Details of my calculation are in Yahoo Answers at http://answers.yahoo.com/question/index?qid=20130918143934AA8vutk . I'm reluctant to change this myself since this is a featured article. Here's a video confirming that 39 digits applies to circumference, (it would not also apply to volume): http://gizmodo.com/5985858/how-many-digits-of-pi-do-you-really-need. — Preceding unsigned comment added by Freond ( talk • contribs) 02:15, 19 September 2013 (UTC)
I think the current history section focuses too much on historical approximations of π whereas the adoption of the symbol π for the particular ratio of periphery to diameter of a circle is only scratched on briefly at the end. In my view, the history section should discuss in more detail how historical sources particularly before 1706 actually formulated the geometrical relationships between perimeter/volume on the one hand and side length/diameter/radius on the other. For example, it might be misleading to interpret historic clay tablets as implying a value for the ratio of perimeter to diameter if they actually describe for example the ratio perimeter to radius or area to side length of some polygon. How about subdividing the history section in two subsections, where the first discusses the development of the particular ratio perimeter to diameter as circle constant, including historical notation, and the second discusses the development of numerical approximations for π? Isheden ( talk) 20:50, 26 September 2013 (UTC)
On looking at the "Page length (in bytes) 89,180" I was wondering if pi is too big and needs to be split? -- John W. Nicholson ( talk) 00:21, 28 September 2013 (UTC)
In the section titled: "Motivations for Computing Pi", you cite Arndt & Haenel who state that 39 digits of Pi are necessary in order to calculate the volume of the known universe to an accurracy of the volume of one hydrogen atom. Being suspicious of this number,I found their book, and they report this number without comment or proof. They cite another paper by other authors, and I have to admit that I did not researtch this paper. Instead, I and a colleague calculated this quantity ourselves, and we determined that 111 or 112 digits are required. I am cutting and pasting our analysis. What do you think?
OOOPS! This page does not support "Equation Editor" in Microsoft Word. This is my very first time I have ever commented on a Wikipedia page, and, as you can tell, I'm not that good at it yet. Is there some way I can attach a Word document? In any event, our procedure was to calculate the volume of the universe twice: Once using an exact expression for Pi, and the second: using (π-δ) where δ is the error one would need in their approximation of Pi to get the required error in the calculation of the volume of the universe. Subtract these two expressions for the volume, this difference in volumes is then set equal to the volume of a hydrogen atom. Solving for δ yields a value of approximately 5 times 10 to the negative 111.
What do you think?
Bob Michaud 74.78.5.64 ( talk) 13:09, 3 November 2013 (UTC)
Really? The 'circular shape of a pie' makes it a frequent subject of pi puns? Not, uhm, I don't know, the fact that it is a homophone? Small detail, but if you're going to make a caption to a picture, at least have it make sense. 92.109.161.68 ( talk) 17:38, 5 October 2013 (UTC)
Pi day (March 14) is also the birth date of Albert Einstein. Josh-Levin@ieee.org ( talk) 03:03, 11 November 2013 (UTC)
i wonder why pi even existed? — Preceding unsigned comment added by 108.45.142.191 ( talk) 01:13, 11 November 2013 (UTC)
Assuming that the hypotenuse of the right angle triangle equals to 180^2+180^2=64800 and sqrt 64800 equals 180*81*(sqrt 2 /81) then it is without no doubt that pi have a hypotenuse as well that is equal to pi^2+pi^2 where the sqrt of the result equals pi*81*(sqrt 2/81) therefore pi can be squared. 74.12.28.38 ( talk) 00:55, 28 January 2014 (UTC)
The article's sub-section entitled Infinite series contains the following:
This is several years before John Machin's improved algorithmic variations on that series. The subsequent sub-section entitled Rate of convergence indicates that:
The implication of the second statement on the first statement is that Abraham Sharp evaluated the first 50,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 terms. The world's fastest computer would take a lot more than trillions of years to directly evaluate that many terms, so Sharp as he was, I claim there's a contradiction. The second claim is easily verified "manually" by basic error bounding in Numerical Analysis, therefore the pre-Machin-like efforts of Abraham Sharp did not use the Gregory-Leibniz series to directly produce 71 decimal digits of π (or if he did, he hasn't finished yet; he won't have even really got going yet).
Both of the article's statements are cited to a source, but the former is a book I cannot afford, and the latter requires a paid subscription I do not have.
On a related but almost pedantic matter, mathematicians are usually not interested in the number of correct digits in an approximation. The resultant error of an approximation is much more important, and these metrics are not the same thing. As an example of the difference, I have a wonderful approximation for 1. It is the sum of the series of terms where the nth term is defined to be 10^(-3(n-1)) - 10^(-3n). After just three terms, the approximation is 0.999999999 with an error of very nearly one part in a billion. But the number of correct decimal digits is zero, and will stay that way no matter how many terms are taken.
With thanks from
ChrisJBenson (
talk)
06:32, 11 January 2014 (UTC).
I removed the claim that "pi" is a Latin word. It isn't in any normal sense -- goodness knows what it says on page xi of the Greek grammar, but perhaps just something to generate the same confusion with the Latin alphabet. I think it is much more accessible to say "spelled out". I will change the Lede version as well: I confused myself into thinking (and wrote) -- "Romanized" is at least an accurate description -- but it isn't. The Romanization of π is 'p'; while 'pi' is its name. Imaginatorium ( talk) 08:54, 17 January 2014 (UTC)
In reviewing some of the more esoteric errors in the later sections over the last six months, I had missed a basic mathematical error featured quite prominently in the lead section. Since edit 563172535 on 6 July 2013 at 16:31 by Giraffedata, the third sentence of this article stated that no fraction can be exactly equal to π (the exact wording was: "no fraction can be its exact value"). A full rigourous proof (disproof) of this needs only one counteraxample. Here's a fraction that is exactly equal to π:
I've already reverted the text in the article. This is here just in case a proof was required. With thanks from ChrisJBenson ( talk) 07:43, 11 January 2014 (UTC)
I'm not too keen on the current version of the lead. There is a dangling sentence about approximation by rational numbers that for some reason is on a separate line. I think this should be put back into the preceding paragraph somewhere. (But that might just be me: I personally don't like extremely short paragraphs.) Sławomir Biały ( talk) 12:01, 22 January 2014 (UTC)
Divide numbers (whole number,irrational or rational )below 180 by 180 or digits in the middle of 180 and 360 or 360 and 540 all multiple of 180 ,and take sin of the result in radian mode or by the use of Taylor series then change it to degree mode and take the inverte sin from the resutlt in radian mode and you obtain digits of pi by choosing the number that was divided by 180 or 360 and 540....etc. example of a fraction 355/113(a fraction from the article). 355/360=0.98611111111111111111111111111111..... in radian=0.83388586828323059431360578387878.... in degree=56.500004797622844197953735997243....*2(because 360 is a multiple of 180)=113.00000959524568839590747199449... therefore 355/113=3.141592........
355/113.00000959524568839590747199449...=pi
70.55.23.230 ( talk) 19:18, 27 January 2014 (UTC)
The pi/tau controversy makes an appearance at xkcd: "Pi vs. Tau". — Loadmaster ( talk) 20:51, 12 December 2013 (UTC)
With respect to Tau=Pi/2 as proposed by Albert Eagle, the transformation of a unity length line to a two-dimensional semi-circular arc might serve as the defining example. Cerian Knight ( talk) 18:41, 17 February 2014 (UTC)
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Please change the following text: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of tencubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value.
To this: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of ten cubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value. Rabbi Eliyahu of Vilna (The Vilna Gaon) wrote in his commentary on the Bible that the correct reading of the Biblical text indicates to apply a factor of 111/106 which results in 1.04716981 to the approximate π value of 3. This means that the value of π used in the construction of the ceremonial pool was actually 1.04716981 X 3 which equals 3.14150943. It is accurate to the 4th decimal point. This factor is derived from the extraneous word "koh" (קוה) written in the original Hebrew of 1 Kings 7:23. It is to be pronounced however "ko" (קו). Similarly, in 2 Chronicles 4:2, the original Hebrew is actually written "ko" (קו). The Hebrew letters also have numerical values. (קוה) has a value of 111 and (קו) has a numerical value of 106. 108.2.9.169 ( talk) 16:42, 2 March 2014 (UTC)
With reference to Ludolph van Ceulen, "pi" was for a period of roughly 200 years often called the Ludolphine number&Ludolphsche Zahl, from his death in 1610 into the 19th century.
at present, the history section does not explicitly name this fairly important naming practice (to the extent that previous namings ARE important!), and a single sentence or so, for example along the line: "For about 200 years, pi was occasionally referred to as the Ludolphine number, in honour of Ludolph van Ceulen, who calculated pi correctly to 35 digits in the 16th century". Or something like that. Arildnordby ( talk) 00:38, 15 March 2014 (UTC)
Current entries in the antiquity India section give a feel that those calculators were off the mark where as Aryabhata and Madhava approximated Pi value to 5 and 11 digits accuracy. Infact, Aryabhata's work has been included in Polygon Approximation in a below section where it does not belong-I did not get any reference of his using a polygon method to calculate Pi value to 5 digit accuracy. I feel, Including Aryabhata and Madhava's works subsequently is also chronological otherwise, antiquity section itself is misleading?. Madhava's work gets a mention in Infinite series but does not stress on his value to pi value approximation. He was never in competition with any Persian mathematician. the language used does not sound neutral. Also, I feel, Wikipedia should revert all BC/AD to BCE and ACE. That can be another discussion. — Preceding unsigned comment added by Sudhee26 ( talk • contribs) 21:44, 9 June 2014 (UTC)
In section 1.5, in Approximate Value, a few lines are missing numbers.
It's minor.. But, I just wondered, given the international reach of Wikipedia (and of π!), whether that should read "Greek fonts" or something. From the "Name" section:
69.201.175.80 ( talk) 21:15, 22 July 2014 (UTC)
If under the section "Approximate Value" the first 100 decimal digits are defined as: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679, then the leading 3 is not considered a decimal digit. In this case, under the section "Polygon approximation era", the sentence: "With a correct value for its seven first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." should be replaced with "With a correct value for its six first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." — Preceding unsigned comment added by 65.201.161.119 ( talk) 15:31, 15 April 2014 (UTC)
I find the following from Boyer at [ [6]]
>However, Tsu Ch'ung-chih went even further in his calculations, for he gave 3.1415927 as an "excess" value and 3.1415926 as a "deficit value." 7< with notes 6 See the excellent article on Liu Hui, written by Ho Peng-Yoke, to appear in the forthcoming volumes of the Dictionary of Scientific Biography. 1 [presumably 7] See the article cited in footnote 6. There seems to be some confusion in the citation of this value by Mikami, op. cit., p. 50, by Smith, op. cit., II, 309, and Hofmann, op. cit., I, 76.
This strikes me as badly written for Tsu Ch'ung-chih would presumably not have expresed himself in the decimal system. However I am not in a position to consult the source. If anyone is it might constitute a worthwhile addition to the article. Sceptic1954 ( talk) 17:13, 2 September 2014 (UTC)
There's a very blatant error in this article. Proponents of Tau want it to replace 2 pi, not pi/2. This has to be corrected. — Preceding unsigned comment added by 2601:4:3780:5B:B166:F5D6:3AA5:71A3 ( talk) 03:50, 2 October 2014 (UTC)
I remember 31415926535 by heart , now I search for that number (to long, but if I could) using http://pi.nersc.gov/ binary search engine in Pi
Then I will use this new Pi part to search again (when we have powerful enough machines) for event longer number.
How big the number representing starting point will be ?
Bigger than googleplex ?
KrisK 68.199.112.146 ( talk) 01:15, 25 November 2014 (UTC)
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Please include in external links: Mnemonics to remember Pi https://www.mnemonic-device.com/arithmetic/pi/may-i-have-a-large-container-of-coffee/
regards, Pjotr
Pjotrw ( talk) 12:47, 3 January 2015 (UTC)
This talk section's content appears not to engage the purpose of this talk page, which is to improve the accompanying
WP article. I've downsized its content, to reduce the distraction it causes from this talk page's purpose.
--
Jerzy•
t
07:18, 21 February 2015 (UTC)
So my Question is. If you mirror Pi I mean if you take the digital Version of Pi and use the not operator. What kind of Number would you have then ? Also a transcendence Number ? What kind of Geometric Figure you can discern from this digit ? — Preceding
unsigned comment added by
87.122.187.198 (
talk)
20:59, 16 May 2014 (UTC)
So my Question is. If you take the digital Version of Pi and use the not Operator. What kind of Number would you have then? Also a transcendence Number ? What kind of Figure can you discern of this digit ? — Preceding unsigned comment added by 87.122.187.198 ( talk) 21:03, 16 May 2014 (UTC)
So my Question is. If you take the digital Version of Pi and use the not Operator. What kind of Number would you have then. Also a transcendence Number ? What kind of Figure can you discern from this digit ? — Preceding unsigned comment added by 87.122.187.198 ( talk) 21:06, 16 May 2014 (UTC)
Happy Ultimate Pi Day (3-14-15)! Timo 3 13:33, 14 March 2015 (UTC)
Pi can also be described by ~ 22/7 - 1/800 - 1/70,000 - 1/5,000,000 Pi² = ~ 9.87 - 1/2500 V pi = ~ 16/9 - 1/200 — Preceding unsigned comment added by 84.80.54.162 ( talk) 19:07, 14 March 2015 (UTC)
Maybe a better solution to this issue would be to have disambiguation pages for 3.141 etc?
-- [[
User:Edokter]] {{
talk}}
11:39, 15 March 2015 (UTC)At the time of writing, paragraph 3 begins "Although ancient civilizations needed the value of π to be computed accurately for practical reasons, it was not calculated to more than seven digits, using geometrical techniques, in Chinese mathematics and to about five in Indian mathematics in the 5th century CE." This sentence clearly needs to be rewritten but I am unable to correctly do this myself. Please could someone more knowledgable of the subject oblige? Many thanks. MikeEagling ( talk) 11:32, 14 March 2015 (UTC)