The Intersection

Fun With π

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Over at Correlations, I’m having fun with π:

Just think: patterns exist that establish themselves out of disorder. So could it be that a higher order of some kind constructed a universe ascribing to specified geometrical axioms that result in early trajectories forward? And what if these single points of origin determine not only where we came from, but where we are headed?

Comments

  1. #1 Alan Kellogg
    December 27, 2007

    Trouble is, pi is only an approximation. We have forgotten that decimals are not the only valid way to write a fraction.

    Let me explain. Pi as a decimal is only an approximation. The value of pi in the real world is related to the size of the circle being measured. A circle 20 cm in diameter will have an exact value of pi different than a circle 30 cm in diameter. The difference will be exceedingly small, but it will be there. At our scale 3.14 works well enough. But at greater scales that small difference can mean the difference between life and death.

    Decimals have their limitations and should only be used when they are appropriate and provide accuracy. Expressing one third as 0.333333 ad infinitum does not provide accuracy. So if the ratio between a circle’s diameter and circumfrence comes out to be three and seven fifty-firsts, then that’s the ratio.

    Death to the decimal dorks, promote proper fraction use!

    (I do have a psychosis, and your point is?)

  2. #2 Lassi Hippeläinen
    December 27, 2007

    Stick to decimal. The binary Pi is seriously evil…
    http://www.netfunny.com/rhf/jokes/01/Jun/pi.html

  3. #3 Lance
    December 27, 2007

    Alan Kellogg,

    You seem to be confused about pi. Pi is an irrational number and therefor by definition can never be represented by a ratio of two integers. This was proven in 1761 by Johann Heinrich Lambert.

    A decimal representation of pi should always be followed by three dots as in 3.1416…

    Also you say, “A circle 20 cm in diameter will have an exact value of pi different than a circle 30 cm in diameter.” This is incorrect. Pi is always “exactly” the same number, just as the integer 2 or pi’s fellow irrational number “e” are invariant.

    Perhaps you meant to say that limits of measurement will result in “calculated approximations of pi” that differ by an amount dependent on the precision and accuracy of the instruments used, not to mention the circle being measured.

    Sorry if this seems pedantic but as a physicist and university math instructor I felt it was important to be clear on this subject. Pi, e and c (the speed of light in a vacuum) are perhaps the most important “numbers” in the universe.

  4. #4 Fred Bortz
    December 27, 2007

    Actually, pi is not merely irrational, it’s transcendental — though I have forgotten the distinction between the terms. All transcendental numbers are irrational, but not all irrational numbers are transcendental.

    Irrationally engaging in non-transcendental meditation and some rational medication has yielded this serious silliness.

    Someone rescue me please, and our just desserts will be … PI!

  5. #5 Todd Sayre
    December 27, 2007

    A decimal representation of pi should always be followed by three dots as in 3.1416…

    Sorry if this seems pedantic but, as a pedant and web developer, a decimal representation of pi should always be followed by a horizontal ellipsis as in 3.1416… (3.1416…) when using HTML or anywhere sophisticated typesetting is available.

  6. #6 Lance
    December 27, 2007

    Todd,

    Hehe. Yes you are correct. My math skills are somewhat better than my computer skills. And I see that I rounded the last number which would also be incorrect before the horizontal elipsis!

    Fred,

    Yeah, I think it is transcendental as well, but I couldn’t recite the proof or its author.

  7. #7 Lassi Hippeläinen
    December 28, 2007

    A transcendental number can’t be the solution of a polynomial equation whose coefficients are rational numbers.

    Pi is transcendental, as first proven by Ferdinand von Lindemann in 1882. The immediate consequence is that circles can’t be squared using a ruler and a compass.

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