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| montecristo0612 Quote | Reply | | Archimedes, First Discoverer of Pi posted on: 8/26/2002 3:37:40 AM (NOTE: The above information was gleaned from an article in The New Yorker magazine, March 2, 1992, called "Profiles: The Mountains of Pi") Did u know that Archimedes was the first mathematician to discover the value of pi up to 10000 digits!!! Notes on Pi: Pi is the most famous ratio in mathematics, and is one of the most ancient numbers known to humanity. Pi is approximately 3.14 - the number of times that a circle's diameter will fit around the circle. Pi goes on forever, and can't be calculated to perfect precision: 3.1415926535897932384626433832795028841971693993751.... This is known as the decimal expansion of pi. No apparent pattern emerges in the succession of digits - a predestined yet unfathomable code. They do not repeat periodically, seemingly to pop up by blind chance, lacking any perceivable order, rule, reason, or design - "random" integers, ad infinitum. In 1991, the Chudnovsky brothers in New York, using their computer, m zero, calculated pi to two billion two hundred sixty million three hundred twenty one thousand three hundred sixty three digits (2,260,321,363). They halted the program that summer. Pi has had various names through the ages, and all of them are either words or abstract symbols, since pi is a number that can't be shown completely and exactly in any finite form of representation. Pi is a transcendental number. A transcendental number is a number but can't be expressed in any finite series of either arithmetical or algebraic operations. Pi slips away from all rational methods to locate it. It is indescribable and can't be found. Ferdinand Lindemann, a German mathematician, proved the transcendence of pi in 1882. Pi possibly first entered human consciousness in Egypt. The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 BCE by a scribe named Ahmes. He began scroll with the words: "The Entrance Into the Knowledge of All Existing Things" and remarks in passing that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which is composed of various mathematical problems and their solutions, the area of a circle is found using a rough sort of pi. Around 200 BCE, Archimedes of Syracuse found that pi is somewhere about 3.14 (in fractions, Greeks did not have decimals). Knowledge of pi then bogged down until the 17th century. Pi was then called the Ludolphian number, after Ludolph van Ceulen, a German mathematician. The first person to use the Greek letter for the number was William Jones, an English mathematician, who coined it in 1706. Physicists have noted the ubiquity of pi in nature. Pi is obvious in the disks of the moon and the sun. The double helix of DNA revolves around pi. Pi hides in the rainbow, and sits in the pupil of the eye, and when a raindrop falls into water pi emerges in the spreading rings. Pi can be found in waves and ripples and spectra of all kinds, and therefore pi occurs in colours and music. Pi has lately turned up in superstrings. Pi occurs naturally in tables of death, in what is known as a Gaussian distribution of deaths in a population; that is, when a person dies, the event "feels" pi. It is one of the great mysteries why nature seems to know mathematics. Math rules!!!  |
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montecristo0612
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Re: Archimedes, First Discoverer of Pi
replied on: 8/26/2002 3:38:26 AM In addition to my first post: According to some sources, the famous pi, which we only know as 3.141592, and has range of 22/7< pi < 223/71, its approx. in 100 digits, is: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196 Math rules!!!
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tranquilium
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Re: Archimedes, First Discoverer of Pi
replied on: 8/26/2002 4:17:31 AM I have a book on Archimedes and apparently he was the first person to get PI correct to 3 decimal places. He went beyond this but was the first to event get it that accurate 
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montecristo0612
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Re: Archimedes, First Discoverer of Pi
replied on: 8/27/2002 2:31:37 AM Just a query, What else is described on your book about Archimedes? I'm fascinated with your post.
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tranquilium
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Re: Re: Archimedes, First Discoverer of Pi
replied on: 8/27/2002 4:07:32 AM Here's the contents of the book. The Life of Archimedes? The law of the lever Center of gravity Big literary find in constantinople The mechanical method Two sums The parabola Floating bodies The spiral The sphere Archimedes traps PI It's just full of things which Archimedes played a big role in discovering. |
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HallsofIvy
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Re: Archimedes, First Discoverer of Pi
replied on: 8/31/2002 8:04:41 AM Montecristo0612, If "Around 200 BCE, Archimedes of Syracuse found that pi is somewhere about 3.14 (in fractions, Greeks did not have decimals).", why do you start the post by declaring that Archimedes "discoved thousands of decimal places"? Also, I think it is stretching a point to declare Archimedes was the "First Discoverer of Pi": MANY people had worked with and calculated different values for pi of different accuracies. (Yes, I agree that Archimedes was one of the greatest mathematicians in history and his work with pi was of great importance.) |
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herbert
Quote | Reply | This message was updated on 12/17/2003 3:31:30 PM by herbert |
Re: Archimedes, First Discoverer of Pi
replied on: 12/14/2003 8:12:06 AM Dear member ! I have to disappoint you. Archimedes NEVER described PI to more than 2 exact decimals. Unfortunately it is the case that by borrowing from others who borrowedd from others who never read the original papers disinformation is beeing created. I can only refer to HEIBERG´s edition of Archimedes works. It is a fact that not even the method of calculation of A. has been transferred to us. The simplest way would be to follow EULER and adopt his method for calcualting logarithms ( see his INTRODUCTIO IN ANALYSIN INFINITORUM volume 1 ) namely the repeated use of extracting square roots to the calculation of PI. But for that method one must be able to extract square roots efficiently and be using the decimal system. As far as I know the extraction of square roots with roman numbers or numbers in the greek notation at Archimedes time would have been an incredible task. Where Archimedes got his limits for PI from is unknown. So I can only recommend to be cautious and always to consult the original literature. Herbert |
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Harmke
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Re: Archimedes, First Discoverer of Pi
replied on: 3/29/2004 1:42:58 PM I got a question, why did they want Pi so precise? Couldn't they calculate everything they wanted with about three? Or was it more the sport of finding pi? |
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BobG
Quote | Reply | This message was updated on 3/30/2004 1:50:23 PM by BobG |
Archimedes, First Discoverer of Pi
replied on: 3/30/2004 1:24:01 PM The Greeks were just the first among the precursors of Western culture to discover the value of pi. And don't be too sure about how incredibly difficult a task it was before the modern Hindu decimal system. The Babylonians were able to calculate an extremely accurate value for pi, discovered the Pythagorean Theorem, and discovered a method for determining square roots by around 1900 BC and they used a sexigesimal numbering system (a dual base system with 60 as the primary base and 10 as the secondary base - in fact, they are the source of our degrees-minutes-seconds; hours-minutes-seconds). The Newton-Raphson iterative method for determining square roots (among other things) is surprisingly similar to the Babylonian method. Each step of the Newton-Raphson method corresponds to the result of every other step in the Babylonian method. The Newton-Raphson method is quite a bit more efficient (skipping every other step), but the Babylonian's method wasn't too shabby. Plus, don't get fooled by the accuracy of numbers in decimal format vs fractional format. 1/698 is the same number as 0.001432664756, so (using the above example) saying ancients had calculated a value accurate to 12 decimal places is a little misleading, even if technically accurate. By the way, montecristo, thanks for putting in a number so long that we have to keep scrolling our screen to see the right side of our posts. |
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HallsofIvy
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Re: Archimedes, First Discoverer of Pi
replied on: 9/30/2004 6:00:03 PM "I got a question, why did they want Pi so precise? Couldn't they calculate everything they wanted with about three? Or was it more the sport of finding pi?" No, three won't do it. Perhaps about 10 decimal places would give most calculations to the accuracy of measurement but not all. In any case, the interest in calculating pi to hundreds or thousands of decimal places is mostly a matter of testing the limits of computer hardware. |
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msmerchut
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Archimedes, First Discoverer of Pi
replied on: 12/28/2005 7:43:01 PM i'm wondering, because i cannot find any exact poll that shows this, which of Archimedes' disoveries is more often used, pi or the lever? |
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eanp
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Archimedes, First Discoverer of Pi
replied on: 1/11/2006 3:33:15 PM Hey. I wanna know a current investigation of the discoverers of Pi after Archimedes of Syracuse, of course, but I want to know who else has made a contribution and which it was. Similar to a time line |
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3.14159
Quote | Reply | This message was updated on 1/12/2006 2:41:28 PM by 3.14159 |
Archimedes, First Discoverer of Pi
replied on: 1/12/2006 2:39:15 PM quote: Read any book about pi. Pi: A Biography of the World's Most Mysterious Number is a good one. |
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Euler
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Archimedes, First Discoverer of Pi
replied on: 6/14/2006 1:14:19 AM Actually, Archimedes was not the first to discover pi, or to utilize its seemingly infinite capabilities. You should read "A History of Pi," by Petr Beckmann. |
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