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Thread: Mathematics

  1. #1
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    Default Mathematics

    I recently became obsessed with mathematics. I lie awake at night, thinking of patterns. I have discovered the following things.

    1) Points. Points are pure positions.

    2) Lines. Lines trace relationships between points.

    3) Angles. Angles describe relationships between lines.

    That is as far as I've got. I am currently trying to figure out volume. I may be going insane.

  2. #2

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    Me too. Actually, I'm studying maths at the Open University. It's near the end of semester 1. Haven't got as far as volume yet.

    It's not the maths that's driving me insane, though, it's the Quantitative Research Methods module I'm also taking. I lie awake at night and think about questionnaire design. How demented is that?

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    That's where Russell and Whitehead went wrong - the fundamental basis of mathematics is not irreducible axioms but questionnaire design.

    Josef, if you have three vectors A, B, C delineating a parallelopiped (a cuboid which is allowed to be 'wonky'; the most general volumetric shape three vectors can define) then the volume is given by the magnitude of A . (B x C), where '.' is the scalar (or 'dot') product and 'x' is the vector (or 'cross') product. This seems like a reasonable place to start if you want to think about volume once you've got some idea of vectors and angles, maybe.

    Edit: there's a fairly decent diagram on the Wiki page I linked to...
    Last edited by Mr. Tea; 14-01-2009 at 04:37 PM.
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    Hold on. I have to plot this visually. I've discovered this is the only way I can understand it.

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    lines are infinitely long. wow.

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    and points, fuck, there's as many points between here and the sun as there are between these two full stops ..

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    massive massive book recommendation:

    mathematics and the imagination by edward kasner. it's from the 30s but it's spectacular.

    oooh here we go:
    http://books.google.co.uk/books?hl=e...um=5&ct=result

    since we're here... in that book it says something about terminating decimals, claiming everything we've been told in school maths is wrong - they don't terminate?

    i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence.

    not sure why this is lost in school though - because two results would be too confusing?

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    Quote Originally Posted by don_quixote View Post
    i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence.
    I'm not I get this: irrationals are the only non-terminating, non-repeating numbers by definition. Well actually the definiton is that they can't be written as the ratio of one finite integer to another, but it's trivial to show that this is equivalent to a non-terminating string of decimals.

    I derived the fundamental theory of calculus for one of my A-level students last night, which was pretty cool. Well, for differentiation anyway, integration will have to wait til next week.
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    Curves. Curves are very interesting. Also, wiggly lines. How the fuck do you analyze a wiggly line?

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    "since we're here... in that book it says something about terminating decimals, claiming everything we've been told in school maths is wrong - they don't terminate?
    i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence."
    I don't get what you're saying here? Recurring decimals don't terminate, they recur and any numbers which can't be written as a ratio (ie are irrational) are non-terminating and non-recurring.

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    Quote Originally Posted by josef k. View Post
    How the fuck do you analyze a wiggly line?
    It depends how it wiggles.

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    Quote Originally Posted by josef k. View Post
    Well that's just a wriggly line with no rhyme or reason - I thought you meant sine waves and stuff like that.

    Though you could still differentiate that curve, or integrate it, or express it as a Fourier series, or draw tangents to it at selected points...

    Edit: actually you couldn't, as it goes back on itself at a couple of points. You could still parameterise it as a trajectory or something, I dunno.
    Last edited by Mr. Tea; 15-01-2009 at 02:33 PM.
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    "It depends how it wiggles."
    And what you mean by analyze. I suspect that you mean find the function that generates it - which in the case of the line that you've just linked to would be, as Mr Tea says, rather hard and possibly pointless because any function that gave that line would be completely ad hoc. I guess you could find something that approximates it though if that's what you wanted.

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    I have put it in a cage... I am now examining it.

    PS - By analyze, I just mean figure out its relationship to other stuff. As in, wobbly lines exist. How do people understand them mathematically? What mathematical operations are performed on them in order to try and understand them? I don't really care about this particular line. But please don't tell it I said that.
    Last edited by josef k.; 15-01-2009 at 02:48 PM.

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