29 may. 2011

The number Pi

π (sometimes written pi) is a mathematical constant whose value is the ratio of any circle's circumference to its diameter; this is the same value as the ratio of a circle's area to the square of its radius. π is approximately equal to 3.14159 in the usual decimal positional notation. 
Many ecuations from mathematics, science and engineering involve π, which makes it one of the most important mathematical constants. π is an irrational number, which means that its value cannot be expressed exactly as a fraction (m/n, where m and n are integers). Consequently, its decimal representation never ends or repeats. π is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics.
Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.
Probably because of the simplicity of its definition, the concept of π has become entrenched in popular culture to a degree far greater than almost any other mathematical construct. It is, perhaps, the most common ground between mathematicians and non-mathematicians. Reports on the latest, most-precise calculation of π are common news items. The current record for the decimal expansion of π, if verified, stands at 5 trillion digits. 
The Greek letter π was first adopted for the number as an abbreviation of the Greek word for perimeter, or as an abbreviation for "periphery/diameter", by William Jones in 1706. The constant is also known as Archimedes' Constant, after Archimedes of Syracuse who provided an approximation of the number, although this name for the constant is uncommon in modern English-speaking contexts.

"There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to  ...  3.14159, etc. = π ..." William Jones.
  
The decimal representation of π truncated to 50 decimal places is:
π = 3.14159265358979323846264338327950288419716939937510...
Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of the decimal representation of π, no simple base-10 pattern in the digits has ever been found:

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

An estimate of Pi accurate to 1120 decimal digits was obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the most accurate estimate of Pi before electronic computers came into use. 
Many schools around the world observe Pi Day (March 14, from 3.14).

On November 7, 2005, alternative musician Kate Bush released the album Aerial. The album contains the song "Pi" whose lyrics consist principally of Bush singing the digits of π to music, beginning with "3.14".
In Carl Sagan's novel Contact, π played a key role in the story. The novel suggested that there was a message buried deep within the digits of π placed there by the creator of the universe. This part of the story was omitted from the film adaptation of the novel.

Some films and TV series deals with the number Pi as a part of the mysteries that involved the plot too.


8 comentarios:

  1. Should I ask?...

    Ok, let`s go: Why are you talking about pi? ;-)

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  2. haha, no no, It's a freak entrance but it doesn't matter. I don't know why I've written this...I only have to say that the number Pi it's a number that was involved in many "things" like: plots of several books, part of many ecuations.... you know very well (especially the last statment =oP). Haha, I was talking yesterday with a friend when I said: "I´m writting an entrance...it's about something you have in one of your t-shirts..." and He said as answer: "I have a Homer Simpson and Lost t-shirts....but I always want to have a Pi t-shirt...ey! you can write about the Pi number!" and I answered:"It's the last thing you said I´m writting on my blog ¬¬ haha, you're right"
    Kisses Deivid ;)

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  3. It has no sense at all XD (As this strange comment exchange in perfect English doodoo)

    One thing I love is, when people asks for a number between 0 and 10... I usually answer "pi" ^^

    But... your story is even more strange, if possible.

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  4. Haha, when people ask me for a number between 0 and 10 I usually say 8 or 2 because I don't like odd numbers, haha, It's strange... I know =oP. But now, I know that if I ask you for a number, You will think in the number "pi", therefore I will be right ;). It isn't a secret anymore =oD.

    By the way, the strage stories rules =o).

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  5. When I watch a TV series, I always wait for the 3rd season and the episode number 14, so I can say "yeah! it's the pi-episode!!" :D

    And yes, the number pi has the same rights as the rest of the numbers, so I agree with David.

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  6. Haha, yes yes, the number pi has the same rigths as the rest, I know, but when someone says "think in a number between 0 and 10" people usually think in an integer and not in a decimal number that's all, nevertheless, from now I'll think about the possible of choosing a decimal number when I've to guess a number that person was thinking about.

    P.S.: The pi-episode....it's a great name ;).

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  7. Pi-episode XD Brilliant ^^

    By the way, Zuich, you won't be able to predict which is my number. I sometimes say "pi/2", "2*pi" (or similar)

    But, that's true, you'll be closer than the others if you guess "pi + sthg"

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  8. Haha, as you said: "I´ll be closer than the others"; the sthg is a small factor that do the differents ;)

    P.S.: Now you can guess the number I supose I'll think looking for an even number =oD, haha I must be more predictable than you.

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