User talk:SOFTowaha

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Speedy deletion nomination of Jeem Towaha
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JohnCD (talk) 14:34, 8 April 2010 (UTC)

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The first ten thousand digits of pi
3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 5082953311 6861727855 8890750983 8175463746 4939319255 0604009277 0167113900 9848824012 8583616035 6370766010 4710181942 9555961989 4676783744 9448255379 7747268471 0404753464 6208046684 2590694912 9331367702 8989152104 7521620569 6602405803 8150193511 2533824300 3558764024 7496473263 9141992726 0426992279 6782354781 6360093417 2164121992 4586315030 2861829745 5570674983 8505494588 5869269956 9092721079 7509302955 3211653449 8720275596 0236480665 4991198818 3479775356 6369807426 5425278625 5181841757 4672890977 7727938000 8164706001 6145249192 1732172147 7235014144 1973568548 1613611573 5255213347 5741849468 4385233239 0739414333 4547762416 8625189835 6948556209 9219222184 2725502542 5688767179 0494601653 4668049886 2723279178 6085784383 8279679766 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5256375678

In honor of Pi Day — 3.14.2011
I. A brief history of Pi

The mathematical constant we now know as Pi = 3.14159… has fascinated mathematicians for millennia. Archimedes of Syracuse (~250 BCE) rigorously showed that the area of a circle is Pi times the square of the radius. He then presented an approximation scheme, based on inscribed and circumscribed polygons, which enabled one to compute Pi to any desired accuracy. He himself found, with laborious and ingenious computation, that 3 10/71 < Pi < 3 1/7, so that 3.1408 < Pi < 3.1428.

in ancient times was indeed very difficult, until the discovery, in fifth century India, of our modern positional decimal arithmetic system with zero. It took nearly 1000 years for this system to be widely adopted in Europe, but when it did, mathematicians, armed with advances such as calculus, discovered countless new formulas and other facts involving Pi, and computed numerical values of Pi with great aplomb. Isaac Newton computed Pi to at least 15 digits, in the plague year 1666, although he sheepishly acknowledged “I am ashamed to tell you how many figures I carried these computations, having no other business at the time.”

Leonhard Euler (1707-1783), arguably the most prolific mathematician in history, discovered several new formulas for Pi, one of which later led German mathematician Bernhard Riemann (1826-1866) to present what is now known as the Riemann zeta function hypothesis, an unproven conjecture with rich connections to many fields of mathematics. The Clay Mathematics Institute in the U.S. has offered an award of $1,000,000 for a proof.

Carl Friedrich Gauss (1777-1855) discovered many interesting connections between Pi and applied mathematics and physics. Among these many discoveries was the essential idea of a clever computational technique, now known as the “fast Fourier transform,” which intimately involves Pi. This scheme is very heavily utilized in audio, video, microwave and data transmission applications. Cell phones typically include at least one special-purpose chip to perform this operation. Gauss also discovered some interesting facts regarding the “arithmetic-geometric mean”, which (see below) later led to a new algorithm for calculating Pi.

Some progress, but not a great deal, was made in computing Pi during this time. At the end of the Reformation in 1648, Pi had been calculated only to 35 digits; even by the end of World War II in 1945 it was known to only 527 digits. In 1948 ENIAC, the first digital computer, computed 2037 digits, and the race was on.

II. Pi in the computer age

In 1965, computer scientists rediscovered Gauss’ fast Fourier transform technique, and noted that among things it could be used to greatly accelerate many-digit multiplication operations. Also in 1965, Gordon E. Moore, one of the founders of Intel, noted that because of advances in silicon semiconductor technology, the number of transistors that could be placed on a single chip had roughly doubled each year since 1960, and, from what he could see, this trend was likely to continue for several more years. Much to the astonishment of everyone in the field, “Moore’s Law,” as this observation is now known, has continued unabated for more than 45 years, and no end is yet in sight. As a result, a present-day laptop computer has more computing power and memory storage than the world’s most powerful supercomputer of just 20 years ago, and present-day high-end supercomputers (which typically are highly parallel arrays of commodity components) are many thousands of times more powerful and capacious than today’s laptops.

A few years later, mathematicians Richard Brent (at the Australian National University) and Eugene Salamin independently discovered a way to compute Pi, based on some results by Gauss on the arithmetic-geometric mean and lovely classical ideas about elliptic integrals. This yielded a much faster scheme than the traditional calculus-based formulas for Pi — with each step, this new algorithm doubles the number of correct digits (provided that one is using computer arithmetic that is sufficiently accurate).

Armed with these new formulas, numerical techniques and rapidly growing computing power, scientists computed Pi to over one million digits in 1973, to over one billion digits in 1989, and then to over one trillion digits in 2009. The most recent computation (August 2010) was done by Alexander Yee and Shigeru Kondo, who computed five trillion digits of Pi. Remarkably, this was not done on a highly parallel supercomputer, but instead was performed on a conventional two-core Intel Xeon computer equipped with 96 Gbyte of main memory. They employed a remarkable sum formula for Pi due to David and Gregory Chudnovsky, and checked their results using variants of a new formula for Pi discovered in 1996 by Peter Borwein (Jonathan Borwein’s brother), Simon Plouffe and David Bailey. This new formula for Pi has the odd property that it permits one to calculate binary (base-2 or base-16) digits of Pi beginning at an arbitrary starting position, without needing to calculate any of the digits that came before. This scheme was itself employed in 2010 to calculate binary digits beginning at position two quadrillion (by the way, the two quadrillionth binary digit of Pi is a 0).

For Pi day 2011, the authors along with Andrew Mattingly and Glenn Wightwick of IBM Australia computed digits of various constants in various bases on an IBM blue Gene/P machine. The results include base-64 digits of ?? beginning at position 10 trillion, which in base-eight are: 60114505303236475724500005743262754530363052416350634. This suite of computations in total took roughly 1200 years of serial computing time (roughly 110 “rack days”).

It is amusing to note that as recently as 1961, Daniel Shanks, who himself calculated Pi to over 100,000 digits, declared that computing one billion digits would be “forever impossible.” This was achieved in 1989 by Yasumasa Kanada of Japan. And in 1989, noted British physicist Roger Penrose, in the first edition of his best-selling book The Emperor’s New Mind, declared that we likely will never know if a string of ten consecutive sevens occurs in the decimal expansion of Pi. This string was found just eight years later (1997), also by Kanada, beginning at position 22,869,046,249.

III. Why calculate digits of Pi?

Certainly there is no need for computing Pi to millions or billions of digits in practical scientific or engineering work. A value of Pi to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton. There are certain scientific calculations that require intermediate calculations to be performed to significantly higher precision than required for the final results, but it is doubtful than anyone will ever need more than a few hundred digits of Pi for such purposes. Values of Pi to several thousand digits are sometimes employed in “experimental” mathematics, but very few such computations require Pi to beyond 25,000 digits, and we are not aware of any requiring Pi to more than 10 million digits.

One practical application for computing digits of Pi is that these calculations are excellent tests of the integrity of computer hardware and software. If two separate computations of digits of Pi, say using different algorithms, are in agreement except perhaps for a few trailing digits at the end, then almost certainly both computers performed trillions of operations flawlessly. For example, in 1986, a Pi-calculating program that David Bailey wrote at NASA, using an algorithm due to Jonathan and Peter Borwein, detected some hardware problems in one of the original Cray-2 supercomputers that had escaped the manufacturer’s tests.

Along this same line, some improved techniques for computing the fast Fourier transform on modern computer systems had their roots in efforts to accelerate computations of Pi. These improved techniques are now very widely employed in scientific and engineering applications.

From a mathematical point of view, one historical motivation for computing Pi was to see if the digits of Pi repeat, thus disclosing that Pi is a simple ratio of two integers. But this question was laid to rest in the 1760s, when Lambert and later Legendre used the theory of continued fractions to prove that Pi cannot be written as the ratio of two integers. The more general question of whether Pi is the solution to an algebraic equation (to be specific, the root of a polynomial with integer coefficients) was laid to rest in 1882, when Lindemann proved that Pi is not of this class.

There are many interesting mathematical questions that remain. In fact, we can prove shockingly little about either the digits of Pi or about its continued fraction. The most notable open question is probably this: Are the digits of Pi truly “random” in a statistical sense? This is more formally stated as the question of whether Pi is a “normal” number. A normal number is one whose digits in some number base (say base 10) have the property that the frequency of appearance of any finite-length string (say “4567”) tends to the expected frequency (1 in 10,000 in this case) as more and more digits are tabulated. It is widely believed that Pi has this property, not just for decimal digits but for all number bases. However, no one has been able to prove this assertion, and so mathematicians have analyzed large numbers of digits looking for any indication that this property might not hold, or for clues on how to rigorously analyze this question. A solid proof of this conjecture would yield, for instance, a provable source of pseudo-random numbers for computer-based statistical investigations. Until such a proof is in hand, it is always possible that a much longer calculation will indicate that Pi is not normal. Figure 4 shows how digit patterns in the fractions (22/7 and 223/71) jump out, while no such pattern is discernable in 100 digits of Pi (center).

But there is a more fundamental motivation for computing Pi, which should be familiar to anyone who has scaled a lofty mountain or competed in a major sporting event: “because it is there”– it is easily the most famous mathematical constants, and its properties have fascinated mathematicians and other scientists for millennia. Thus, as long as there are humans (and computers) we will doubtless witness ever-more impressive computations of Pi.

Happy birthday, Pi!

This material and much more can be followed up at The Life of Pi lecture for Pi Day 2011: JMB PiDay talk, a book chapter on Pi: JMB Pi chapter, an article on Pi in “The Conversation”: Conversation, and at David Bailey’s Pi Resources: DHB Pi site. Readers may also be amused by the following music set to the digits of Pi: Musical Pi.

Wikipedia talk:Articles for creation/Vernier Constant concern
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Your article submission Vernier Constant


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 * 1) Please submit your articles via this tool. Click 'log in' at the top-right and OAuth will take care the rest. You can also change the interface language at the top-right.
 * 2) Once you submit an article, the tool will add a template to the article and mark it as needing review by an organizer. You can check your progress using the tool, which includes how many accepted articles you have.
 * 3) Participants who achieve 4 accepted articles will receive a Wikipedia Asian Month postcard. You will receive another special postcard if you achieve 15 accepted articles. The Wikipedian with the highest number of accepted articles on the English Wikipedia will be honored as a "Wikipedia Asian Ambassador", and will receive a signed certificate and additional postcard.
 * 4) If you have any problems accessing or using the tool, you can submit your articles at this page next to your username.
 * 5) Wikipedia Asian Month is also held in other language Wikipedia and count independently. Check for language editions.
 * 6) If you have any question, you can take a look at our Q&A or post on the WAM talk page.

Wikipedia Asian Month 2017: Invitation to Participate


Hello! Last year, you signed up to participate in Wikipedia Asian Month (WAM) 2016 on the English Wikipedia. The event was an international success, with hundreds of editors creating thousands of articles on Asian topics across dozens of different language versions of Wikipedia.

I'd like to invite you to join us for Wikipedia Asian Month 2017, which once again lasts through the month of November. The goal is for users to create new articles on Asian-related content, each at least 3,000 bytes and 300 words in length. Editors who create at least four articles will receive a Wikipedia Asian Month postcard!

Also be sure to check out the Wikipedia Asian Art Month affiliate event - creating articles on Asian art topics can get you a Metropolitan Museum of Art postcard!

If you're interested, please sign up here for the English Wikipedia. If you are interested in also working on other language editions of Wikipedia, please visit the meta page to see other participating projects. If you have any questions, please visit our talk page.

Thank you!

- User:SuperHamster and User:Titodutta on behalf of The English Wikipedia WAM Team

This will be the last message you receive from the English Wikipedia WAM team for being a 2016 participant. If you sign up for WAM 2017, you will continue receiving periodic updates on the 2017 event.