wahoo I know all about the number e, it's totally sweet

This is a discussion on wahoo I know all about the number e, it's totally sweet within the A Brief History of Cprogramming.com forums, part of the Community Boards category; my math teacher (I'm doing a summer math thing) showed me a little bit about e. He said e is ...

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    wahoo I know all about the number e, it's totally sweet

    my math teacher (I'm doing a summer math thing) showed me a little bit about e. He said e is the best number in the universe because it models everything in our universe from population growth to motion. I also found out that e is the limit to the function:

    f(x) = (1+(1/x))^x

    and I have no clue how to use this but I sure feel a lot smarter and better aboutmyself and probably wont' become an alcoholic for another week or so.

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    The number e is used a lot. In electrical engineering we use the number e for example for making calculations with signals easier. A signal can be described as the sum of sines and cosines, and a certain man called Leonhard Euler came with:

    e^(j x) = cos x + j sin x

    This formula makes it a lot easier to do calculations. The number j is the imaginary number. Mathematicians use i, technicians use j, since they use i usually for the amperage.

    If you're interested in math and strange numbers, you might like to visit mathworld:
    http://mathworld.wolfram.com/e.html
    http://mathworld.wolfram.com/i.html
    http://mathworld.wolfram.com/EulerFormula.html

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    Toaster Zach L.'s Avatar
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    Indeedy... Euler's famous equation (the five fundamental 'numbers' and equality, and a particular solution to what Shiro said):

    e^(i * pi) + 1 = 0
    The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.

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    Rad gcn_zelda's Avatar
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    right... Don't confuse me. I'm only in Algebra II/Trig

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    Crazy Fool Perspective's Avatar
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    e is also the base of the natural log [ln(x)] and has some good calculus properties that make integration really easy.

    e also appears twice in the word "hehe"

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    Pursuing knowledge confuted's Avatar
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    Perfect time to start learning calculus gcn_zelda.

    Anyway

    e^x dy/dx = e^x
    Away.

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    PC Fixer-Upper Waldo2k2's Avatar
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    logarithms have always been my favorite part of math, i've always had a knack for solving them
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    e is also the base of the natural log [ln(x)] and has some good calculus properties that make integration really easy.
    e^x is the derivative of e^x right?

    Shiro that's cool stuff, my math teacher actually somewhat touched upon what you were saying somewhat

    does anyone here know how to calculate any number raised to the one half power (square roots)

    I want to write my own square root function to see if i can make it faster, I found an inverse square root function written by carmack but it wasn't accurate enough or something

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    Pursuing knowledge confuted's Avatar
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    Originally posted by Silvercord
    e^x is the derivative of e^x right?
    Yes
    Away.

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    is that what this means:
    e^x dy/dx = e^x
    I don't understand the whole dy/dx part what does that mean?

    EDIT: im trying to read at that first site you posted shiro, that's really really heavy stuff
    Last edited by Silvercord; 08-17-2003 at 05:27 PM.

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    Crazy Fool Perspective's Avatar
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    > e^x is the derivative of e^x right?

    yes and..

    S e^x dx == e^x

    or more formally

    S e^(ax) dx == a*e^x

    ( where S is the integral sign )

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    sweet! I have no clue what you are talking about!

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    Toaster Zach L.'s Avatar
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    You can use Newton-Raphson to find the roots of (well-behaved) functions quickly (such as: x^2 - n, where n is the number to find the square root of).

    Basically, it goes as follows:

    x[i+1] = x[i] - f(x[i]) / f'(x[i])
    x[0] is an initial guess, basically

    You can find other methods in "Numerical Recipes in C" which is available free online (nr.org, I think ... easy to find with google anyways).

    dy/dx is the derivate of y with respect to x... confuted's equation might be easier to read as:

    d[e^x]/dx = e^x

    Cheers
    The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.

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    Originally posted by Zach L.
    Indeedy... Euler's famous equation (the five fundamental 'numbers' and equality, and a particular solution to what Shiro said):

    e^(i * pi) + 1 = 0
    Yea, a lot of people regard that as his "famous" equation although he had so many great equations. I like the one you posted because it uses, imo, the five most important numbers in mathematics.

    Silvercord:
    Wait until you get to Differential Equations, you will be real good friends with e.
    "...the results are undefined, and we all know what "undefined" means: it means it works during development, it works during testing, and it blows up in your most important customers' faces." --Scott Meyers

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    Pursuing knowledge confuted's Avatar
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    In my experience, when you get to Diff. Eq., you and e will grow to hate each other
    Away.

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