21. Re: Changing The Value Of Pi Re changing the value of pi. Date Fri Jan 7 091411 2000 Posted By Dan Berger,Faculty Chemistry/Science, Bluffton College Area of science Physics http://www.madsci.org/posts/archives/jan2000/947264282.Ph.r.html

MadSci Network : Physics Re: changing the value of pi Date: Fri Jan 7 09:14:11 2000 Posted By: Dan Berger, Faculty Chemistry/Science, Bluffton College Area of science: Physics ID: 946538700.Ph Message: i realize its somewhat silly to consider, but a science fiction novel once referred to changing the value of pi in *a* universe. what explicit effects would this have on the world as we know it? thanks for all your help! steve Steve, you have it exactly backwards. p (Pi) is a ratio - the circumference of a circle divided by its diameter - defined by the geometric properties of the universe one inhabits. In a "flat" or Euclidean universe - named for Euclid of Alexandria , who wrote the Element s , the definitive geometry text for thousands of years - parallel lines never meet or diverge. In such a universe the value of p is 3.14159... (or approximately 3 ). The universe we live in is Euclidean on most scales, in fact on almost every scale we can measure; at the very largest scales it may be non-Euclidean Actually, General Relativity says that the presence of matter curves space, so that any local area of space will be non-Euclidean, even if only a little. But if the total curving effect of matter cancels out, the universe as a whole can be Euclidean. This is equivalent to saying that "the density of the universe is one," just enough to stop the universal expansion at infinite time. For more, see

22. Changing The Value Of Pi Subject changing the value of pi. Date Thu Dec 30 012500 1999 Posted by StevenLagerstrom Grade level undergrad School Drew University http://www.madsci.org/posts/archives/jan2000/947264282.Ph.q.html

MadSci Network : Physics Subject: changing the value of pi Date: Thu Dec 30 01:25:00 1999 Posted by Steven Lagerstrom Grade level: undergrad School: Drew University City: No city entered. State/Province: NJ Country: USA Area of science: Physics ID: 946538700.Ph Message: i realize its somewhat silly to consider, but a science fiction novel once referred to changing the value of pi in *a* universe. what explicit effects would this have on the world as we know it? thanks for all your help! steve Re: changing the value of pi Current Queue Current Queue for Physics Physics archives Try the links in the MadSci Library for more information on Physics MadSci Home Information Search ... Join Us! MadSci Network, webadmin@www.madsci.org

23. Urban Legends Reference Pages: Religion (Alabama's Slice Of Pi) Did the state legislature of Alabama redefine the value of pi according to She said, As far as I am concerned, the value of pi is only a theory, http://www.snopes.com/religion/pi.htm

Alabama's Slice of Pi Claim: Responding to pressure from religious groups, Alabama's state legislature redefined the value of pi from to 3 in order to bring it in line with Biblical precepts. Status: False. Example: [Collected on the Internet, 1998] introduced without fanfare by Leonard Lee Lawson (R, Crossville), and rapidly gained support after a letter-writing campaign by members of the Solomon Society, a traditional values group. Governor Guy Hunt says he will sign it into law on Wednesday. The law took the state's engineering community by surprise. "It would have been nice if they had consulted with someone who actually uses pi," said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, pi is a Greek letter that signifies the ratio of the circumference of a circle to its diameter. It is often used by engineers to calculate missile trajectories. Prof. Kim Johanson, a mathematician from University of Alabama, said that pi is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that pi is an irrational number, which means that it has an infinite number of digits after the decimal point and can never be known exactly. Nevertheless, she said, pi is precisly defined by mathematics to be "3.14159, plus as many more digits as you have time to calculate". "I think that it is the mathematicians that are being irrational, and it is time for them to admit it," said Lawson. "The Bible very clearly says in

24. Pi In The Bible? So the author of this passage may not have known the exact value of pi, He then puts this value into his formula and gets a value for pi of 3.143. http://www.uwgb.edu/dutchs/pseudosc/pibible.htm

Pi in the Bible? Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay First-time Visitors: Please visit . Use "Back" to return here. A Note to Visitors I will respond to questions and comments as time permits, but if you want to take issue with any position expressed here, you first have to answer this question: What evidence would it take to prove your beliefs wrong? I simply will not reply to challenges that do not address this question. Refutability is one of the classic determinants of whether a theory can be called scientific. Moreover, I have found it to be a great general-purpose cut-through-the-crap question to determine whether somebody is interested in serious intellectual inquiry or just playing mind games. Note, by the way, that I am assuming the burden of proof here - all you have to do is commit to a criterion for testing. It's easy to criticize science for being "closed-minded". Are you open-minded enough to consider whether your ideas might be wrong? One of the most famous mathematical statements in the Bible is in I Kings 7:23-26, describing a large cauldron, or "molten sea" in the Temple of Solomon:

25. Indiana Bill Sets The Value Of Pi To 3 If we pass this bill which establishes a new and correct value for pi , the author The bill implies four different values for pi and one for sqrt(2), http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node18.html

Next: Fields Medal Up: Human Interest Previous: Human Interest Indiana bill sets the value of pi to 3 The bill House Bill No. 246, Indiana State Legislature, 1897 , reportedly set the value of pi to an incorrect rational approximation. The following is the text of the bill: HOUSE BILL NO. 246 "A bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the legislature of 1897. "Section 1. Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle's area is entirely wrong, as it represents the circles area one and one-fifths times the area of a square whose perimeter is equal to the circumference of the circle. This is because one-fifth of the diameter fils to be represented four times in the circle's circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can, in like manner make the square's area to appear one fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle's circumference.

26. Science And Technology/Computers/accurate Value Of Pi Most accurate value of pi As continuation of a longrunning project, YasumasaKanada of the University of Tokyo has calculated the number pi to http://www.guinnessworldrecords.com/content_pages/record.asp?recordid=47055&Reg=

27. Sci.math FAQ: Indiana Bill Sets Value Of Pi To 3 246, Indiana State Legislature, 1897, reportedly set the value of pi to an incorrect The bill implies four different values for pi and one for sqrt(2), http://faqs.jmas.co.jp/FAQs/sci-math-faq/indianabill

sci.math FAQ: Indiana Bill sets value of Pi to 3 Path: news.jmag.net news.jmas.co.jp !nf9.iij.ad.jp!nr1.iij.ad.jp! news.iij.ad.jp news.qtnet.ad.jp !news1.mex.ad.jp!news0-mex-ad-jp!giga-nspixp2!newsfeed1.dti.ad.jp! news-out.cwix.com !newsfeed.cwix.com!torn!watserv3.uwaterloo.ca!undergrad.math.uwaterloo.ca!neumann.uwaterloo.ca!alopez-o From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Newsgroups: sci.math, news.answers daisy.uwaterloo.ca Summary: Part 10 of 31, New version Originator: alopez-o@neumann.uwaterloo.ca Originator: alopez-o@daisy.uwaterloo.ca Xref: news.jmag.net news.answers sci.answers:148 http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick Last updated: Sat Feb 19 00:01:05 2000

28. NOVA | Infinite Secrets | Approximating Pi | PBS The value of pi lies between those two lengths. By doubling the number of sidesof the hexagon to a 12sided polygon, then a 24-sided polygon, http://www.pbs.org/wgbh/nova/archimedes/pi.html

Approximating Pi Infinite Secrets homepage [an error occurred while processing this directive] The interactive version of this feature requires Flash, a free software plug-in. Install Flash , or go to the non-interactive version Contemplating Infinity Philosophically, the concept remains a mind-bender. Working with Infinity Mathematicians have become increasingly comfortable with the concept. Great Surviving Manuscripts Ancient documents offer a tantalizing glimpse of lost cultures. The Archimedes Palimpsest Follow the 1,000-year-long journey of the Archimedes manuscript. Approximating Pi See Archimedes' geometrical approach to estimating pi. Around 250 B.C., the Greek mathematician Archimedes calculated the ratio of a circle's circumference to its diameter. A precise determination of pi, as we know this ratio today, had long been of interest to the ancient Greeks, who strove for precise mathematical proportions in their architecture, music, and other art forms. In Archimedes' day, close approximations of pi had been known for over 1,000 years. An Egyptian document dated to 1650 B.C., for example, gives a value of 4 (8/9) , or 3.1605. Archimedes' value, however, was not only more accurate, it was the first theoretical, rather than measured, calculation of pi.

29. NOVA Online | Teachers | Classroom Activity | Infinite Secrets | PBS (The actual value of pi to four decimal places is 3.1415.) Pi is an infinitedecimal; its value is currently known to more than 1 trillion decimal places. http://www.pbs.org/wgbh/nova/teachers/activities/3010_archimed.html

Back to Teachers Home Infinite Secrets Classroom Activity Materials Procedure Activity Answer Standards ... Print this Teacher's Guide (PDF, 4 pages) Objective To duplicate the method Archimedes used to estimate the value of pi. copy of the "Archimedes' Recipe for Pi" student handout ( PDF or HTML paper pencil compass ruler calculator Tell students that they will be exploring Archimedes' method for estimating the value of pi, a mathematical constant that is the ratio of a circle's circumference (the distance around a circle) to its diameter (the distance across a circle through its center). The Greek symbol for pi is pi. Organize students into groups. Provide copies of the "Archimedes' Recipe for Pi" student handout and other materials to each group. Define some terms for students: perimeter, circumference, radius, diameter, and area. (See Activity Answer for more information.) Demonstrate how to draw polygons that are inscribed in a circle and circumscribed around a circle: Draw a circle on the blackboard. Use a ruler to draw four lines that divide the circle into eight equal parts, extending the lines beyond the boundary of the circle.

30. Biblical Value Of Pi The value of p (pi) is known to be equal to the circumference of a circle dividedby its diameter,. The aforementioned scripture states that the molten sea http://www.learnthebible.org/molten_sea_value_of_pi.htm

Biblical Value of Pi Solomon and the Molten Sea here that the scripture is not exact, what other passages also contain words that cannot be received with complete accuracy? Let us examine the passage more carefully. First, the Bible says that the molten sea was “ten cubits from brim to brim.” This logically would be from the very edge of the rim on one side to the very farthest point on the opposite side. Second, the same verse declares that “a line of thirty cubits did compass it round about.” What is the antecedent of “it?” Clearly it is the molten sea mentioned previously in the verse; therefore, the “line of 30 cubits” compasses the sea, or the liquid contained in the vessel Taken exactly as described, the measurement appears to be the inner diameter of the basin the distance around the sea. When we realize that this molten sea has a thickness associated with it, the 10 cubits from brim to brim becomes the outer diameter, while the 30-cubit measurement describes the inner circumference. Since the diameter is obtained by simply dividing the circumference by (pi), the inner diameter can be calculated as 9.549 cubits. Additionally, the thickness of the vessel is found by taking half of the difference between the inner and outer diameter. Using the inner diameter just calculated and the given outer diameter of 10 cubits, the thickness is 0.225 or approximately 4 inches.

31. Ancient Chinese Technology - A Refined Value Of Pi Thus, they could try to find a value for pi, since the circle s area was found by Archimedes used a 96sided polygon, and decided that pi had a value http://library.thinkquest.org/23062/pi.html

A Refined Value of Pi The irrational number pi can be computed to an infinite number of decimal places. It expresses the ratio of the circumference of a circle to its diameter, a relationship which cannot be framed in terms of whole numbers. (Pi is needed to compute the area of a circle or volume of a sphere.) The value of pi was computed by Archimedes to three decimal places, and by Ptolemy to four decimal places. But after that, for 1450 years, no greater accuracy was achieved in the Western world. The Chinese, however, made great strides forward in computing pi. One way in which the ancient mathematicians tried to approach an accurate value for pi was to inscribe polygons with more and more sides to them inside circles, so that the areas of the polygons(which could be computed) would more and more closely approach the area of the circle. Thus, they could try to find a value for pi, since the circle's area was found by using the formula containing it. (They could measure the diameter, and squeeze a polygon whose area they knew into the circle; the only unknown number would be pi, which could then be calculated.) Archimedes used a 96-sided polygon, and decided that pi had a value between 3.142 and 3.140. The Chinese tried to sneak up on pi in the same fashion, but they were better at it. Liu Hui in the third century

32. Pi Experiments If n=infinity then you get the most accurate value of pi. The value of pi isthen between n sin(Pi/n) and n tan(Pi/n). n sin(Pi/n) Pi n tan(Pi/n). http://www.hypercomplex.org/pi.htm

Pi experiments Home Members Fractals Quaternions ... Links Your browser doesn't support Java, please upgrade your browser or enable Java In July 2000 I had a strange geometrical dream in which I could see a circle circumscribing a regular polygon. The number of sides of the polygon was increasing so much that after a while it actually became the circle itself. At that point I woke up quite intreagued and drew what I had just seen on a piece of paper so I would remember it when I wake up in the morning. The next evening it occured to me that this simple visual experience was a way to calculate the value of Pi. Basically the concept was that if there is a link between the perimeter of a circle an Pi then there also was a link between the perimeter of a regular polygon with an infinite number of sides and Pi. The same concept can also be applied using the area of a circle and the area of a regular polygon instead of using their perimeter. I started with the perimeter method. If you draw a circle of radius r circumscribing a regular polygon of n sides the perimeter of the polygon is 2n r sin(Pi/n). If n=infinity then you get the most accurate value of Pi.

33. Ivars Peterson's MathLand isolated digits of pi, the computation of the value of pi to a record 4.3 billion of bright stars across the sky to approximate the value of pi. http://www.maa.org/mathland/mathland_3_11.html

Search MAA Online MAA Home Ivars Peterson's MathLand March 11, 1996 A Passion for Pi I consider myself a loyal member of the Ancient and Honorable Society of Pi Watchers. During the last year, I've written about the discovery of an algorithm for calculating individual, isolated digits of pi, the computation of the value of pi to a record 4.3 billion decimal digits (now up to 6.4 billion digits), and the use of the distribution of bright stars across the sky to approximate the value of pi. Representing the ratio of a circle's circumference to its diameter, pi turns up in an astonishing number of settings. So, when I received a press release a few weeks ago about a new mnemonic device for remembering the first 167 digits of pi, I was naturally intrigued. Some of you may be familiar with the sentence: How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics! The number of letters in each word represents successive digits of pi: 3.14159265358979. Over the years, pi enthusiasts have created mnemonic devices for encoding pi in just about any language you can imagine from ancient Greek to modern Icelandic. These sentences, poems, miniature dramas, comic episodes, and so forth reflect not only the digits of pi but also the considerable ingenuity of their authors. Even going beyond the 31st decimal digit requires invoking some new rule such as using 10-letter words to encode the zeros of pi. The news release I had received came from Alexander Volokh, a writer and amateur mathematician in Los Angeles. The memory aid described in his announcement involved the use of many sentences, with the end of each sentence representing a zero.

34. Bible Wrong About Pi the bible is wrong about the quoted dimensions and the inferred value of pi . Therefore, at one point or another the right circumference value may http://www.unm.edu/~humanism/bible-pi.html

Why the bible is wrong about PI The best way to get things started is to look at one of the verses in question. Perhaps the most familiar passage is 1 Kings 7:23 which, in the King James Version states, "And [Solomon] made a molten sea, ten cubits from the one brim to the other: it was round all about , and his height was five cubits: and a line of thirty cubits did compass it round about". In this particular case, the statement, "it was round all about" and the fact that only a single diameter is quoted, both are strong evidence that the intended object was circular or of constant diameter. 2 Chronicles 4:2 goes further and states that the object was "round in compass" and that a line of 30 cubits " did compass it round about". Both of these passages suggest that the measurement being made was of the diameter of the object and it's circumference. In that case, it turns out that according a little know theorem due to Barbier , all constant diameter shapes must have the same perimeter which is Pi*Diameter. Therefore it is manifestly not possible for any constant diameter shape to have the dimensions of Pi. More commonly one finds arguments such as the approximation apology. In this version they seem to forget the fact that rounding off is a form of error. Therefore, it doesn't work well for inerrantists to suggest that the bible is introducing round off errors into their calculations. One naturally wonders which other numbers in the bible may be approximations. For example, is 666 the mark of the beast or should we just round it to 700 :)?

35. PI Powers And Power Roots Calculator Use our default value for PI or enter your value of pi; then click on Calculate.Both the powers and power roots values are calculated to 18 digits. http://www.csgnetwork.com/pipowerrootpowercalc.html

PI Powers And Power Roots Calculator This calculator requires the use of Javascript enabled and capable browsers. This calculator is designed to give the powers and power roots of PI . In certain cases, as is the case with mainframes and minicomputers, our calculations of the powers' roots are very close approximations. Use our default value for PI or enter your value of PI; then click on Calculate. Both the powers and power roots values are calculated to 18 digits. You may click on Clear Values to do another. Other flavors of PI include: Historical Computation Of Pi Table Pi Calculator Multiply And Divide By PI Piece Of Pi PI Powers And Power Roots Required Data Entry The value of PI Enter A Power Value Calculated Results Calculated Power Root Calculated Power Default Value For PI This Calculation's Value For PI Version 1.1.9 For Automotive Calculators, Converters and Tables For Aviation Calculators, Converters and Tables For Communications Calculators, Converters and Tables For Computer Calculators, Converters and Tables ... For Weather Calculators, Converters and Tables Of Special Interest HOME SITE MAP E-MAIL US MS WMP7 MS IE ABOUT CSG APPLE - MAC HEADLINES AUTO RACING ... WEB BIZ

36. FamilyFun: Learning Projects: Teaching Kids The Value Of Pi Teach your children about science, art and history with projects the whole familycan enjoy. http://familyfun.go.com/parenting/learn/activities/feature/famf010302_teach/famf

Browse site by Classic Themes Barnyard Pals Cars and Trucks Fairy-Tale Princesses Pirates Under the Sea Search FamilyFun Tools My Great Idea Parent Problem Solver Field Guide to Parenting ... Solutions A to Z The Value of Pi of 10 This project, courtesy of Jayne Fountain-Miller, a science instructor at Ohio's East Canton Middle School, is a perfect example of hands-on learning: kids measure a variety of circles in the real worldtires, flower pots, hula hoopsand do calculations that show how pi never changes. No matter what size a circle is, it's always about three times longer around than it is across. PROJECT: To measure different circles and determine the value of pi (the Greek word for circumference) GOAL: To show that the value of pi constant and not dependent on size AGES: 11 to 13 MATERIALS: STEP 1 Each child should mark off four columns on a piece of paper. Label them "Object", "Circumference" (C), "Diameter" (d), and the last "C/d = ?". STEP 2 Without explaining what you expect them to find, turn the kids loose outdoors or indoors to look for as many circles as they can. They should stick with circles they can wrap a measuring tape arounda picture of a circle won't work, for example, because the measurements will be too imprecise. STEP 3 Instruct the kids to carefully measure the distance around the circle (the circumference) and the distance across the circle (the diameter). Make sure they write down each number and translate any fractions into decimals (23 1/4 = 23.25; 12 5/8 = 12.625, etc.). Tell them to divide the circumference by the diameter and record the result. Repeat the process for a number of different circles.

37. Pi And The Great Pyramid So, when they say that the Great Pyramid exhibits the value pi, to many decimal Any fool can figure that the value of pi is a little greater than 3, http://www.jimloy.com/pseudo/pyramid.htm

Return to my Pseudoscience pages Go to my home page Pi and the Great Pyramid People seem to think that it is amazing that dimensions of the Great Pyramid might be related to pi. Evidence of ancient astronauts? In (pi) , I said this: I hear that the dimensions of the Great Pyramid (of Khufu, also known as Cheops) show that the ancient Egyptians knew the value of pi. Those people who measure the dimensions of pyramids claim tremendous accuracy, much more accuracy than the rough exterior of a pyramid warrants. So, when they say that the Great Pyramid exhibits the value pi, to many decimal places, a person should be skeptical. But, it is also not very remarkable that the ancient Egyptians might have used pi in this pyramid. It seems that the base (much of it is missing) of the pyramid is within a few inches of being square, and is just a few minutes of arc from being aligned with true north, very accurate indeed. By the way, there are many pyramids, and each has a different slope. So, the Great Pyramid is the only one with just those dimensions and ratios (one of Seneferu's pyramids is close). There is also evidence that the ancient Egyptians preferred a steeper slope than that of the Great Pyramid, but had to settle for shallower slopes, to keep the pyramids from collapsing. The ancient Egyptians seem to have sometimes used a value of 22/7 (3.142857 . . .) for pi. There is also evidence that they estimated the area of a circle with a square with a side that is 8/9 the size of the circle's diameter. This gives a value of pi of 3.16049382716 . . .

38. The Ultimate Value Of PI Web site specialized in Internet and computerrelated news. Your source for thelatest news on the Internet. http://www.infosatellite.com/news/2004/07/p120704pi.html

sections Own Material Satellite e-mail this to a friend others Archive Contact Us Advertise Terms of Use/Privacy ... InfoSatellite.com / News The ultimate value of PI By Pedro Gomes InfoSatellite.com July 12, 2004 Well, let's get right to the point: Pi has 1.3511 trillion digits, according to a Japanese team of researchers at Tokyo University, led by Professor Yasumasa Kanada, that calculated the value for pi with a Hitachi supercomputer for over 500 hours in April. "Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception, and human interest as the number pi," said David Blatner, author of The Joy of Pi. "It is the ultimate limitless vista serving as inspiration to mathematicians the world over. With our world so rudely circumscribed, how are we to continue? What point is there in going on if even pi has a limit?" So let's get a lethal dose of some weird chemical substance and wait for death reading the Tokyo Telephone Directory (complete edition). Straight Dope has put the important questions: Who was the first person to realize the ratio of any circle's circumference to its diameter is constant? Who was the first person to realize the fundamental importance of this ratio in finding other quantities, such as areas and volumes? And finally, who was the first person to use the Greek letter p to designate this ratio? The answers, respectively, are "I don't know," "I'm not sure," and "It's complicated."

39. Pi Story The bill to change the value of pi to exactly three was introduced without She said, As far as I am concerned, the value of pi is only a theory, http://www.math.utah.edu/~cherk/Pi-story.html

Pi story HUNTSVILLE, Ala. NASA engineers and mathematicians in this high-tech city are stunned and infuriated after the Alabama state legistature narrowly passed a law yesterday redefining pi, a mathematical constant used in the aerospace industry. The bill to change the value of pi to exactly three was introduced without fanfare by Leonard Lee Lawson (R, Crossville), and rapidly gained support after a letter-writing campaign by members of the Solomon Society, a traditional values group. Governor Guy Hunt says he will sign it into law on Wednesday. The law took the state's engineering community by surprise. "It would have been nice if they had consulted with someone who actually uses pi," said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, pi is a Greek letter that signifies the ratio of the circumference of a circle to its diameter. It is often used by engineers to calculate missile trajectories. Prof. Kim Johanson, a mathematician from University of Alabama, said that pi is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that pi is an irrational number, which means that it has an infinite number of digits after the decimal point and can never be known exactly. Nevertheless, she said, pi is precisly defined by mathematics to be "3.14159, plus as many more digits as you have time to calculate". "I think that it is the mathematicians that are being irrational, and it is time for them to admit it," said Lawson. "The Bible very clearly says in I Kings 7:23 that the alter font of Solomon's Temple was ten cubits across and thirty cubits in diameter, and that it was round in compass."

40. What Is The History Of Pi? But what is that value, the value we call Pi? Archimedes, a wellknown Greekmathematician and The value of pi has been a fascination for centuries. http://wvwv.essortment.com/pimathematicsa_rjar.htm

What is the history of pi? Over the years, Pi has been calculated in many different ways by many different people. Examine some of the more famous methods of calculating Pi. People have known the ratio of the circumference of a circle to its diameter is a constant value since before recorded history. Even from the earliest records of Babylonian, Mesopotamian and Egyptian societies agree to this fact. The Bible references this several times. But what is that value, the value we call Pi? Archimedes, a well-known Greek mathematician and physicist from the 2nd Century B.C.E., is credited with the first theoretical calculations of Pi. Before that point, all values were derived from measurements. He inscribed and circumscribed regular polygons around a circle. He knew the area of the inner polygon was less than that of the circle and the area of the outer polygon was greater. Using a 96 sided polygon, Archimedes determined that 223/71 < Pi < 22/7. This was a very good approximation of Pi. This method of calculating Pi is called "squaring the circle." Many others including Ptolemy continued using Archimedes' method of calculating Pi to further refine its known value. Ludolph von Ceulen used this method with a 2^68-sided polygon to calculate Pi to 35 decimal places. For many years, Pi was called the Ludolphin, named after von Ceulen. Until the Renaissance hit Europe, Archimedes' method seems to be the sole method used to calculate Pi. With the advent of higher mathematics including calculus in the 17th Century, several mathematical formulas for Pi were derived. The most famous of these, Pi/4 = 1 - 1/3 + 1/5 -... , is generally credited to Gottfried Liebniz, but in actuality was first discovered by James Gregory. This calculation provides fairly accurate results but is very tedious...you have to calculate many terms before it starts approaching the value of Pi.

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