Tell me something cool

Discussion in 'Physics & Math' started by Euler is my Hero, Dec 26, 2005.

  1. Euler is my Hero Math Addict Registered Senior Member

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    Tell me something about math that's cool.
     
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  3. Mosheh Thezion Registered Senior Member

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    You dont need math to sit around and think about stuff and draw conceptual images and concepts down and analysis them theoretically...

    but... if and when you wish to apply any such science to actual things...
    then you need math... to determine your parameters...
    otherwise... there is little hope of getting it to work... (work right!)

    -MT
     
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  5. Euler is my Hero Math Addict Registered Senior Member

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    huh?? I'm just looking for my next math fix, that's all. I find so much about math to be amazingly cool. I'm just wondering what mathematical stuff other people find particularly interesting.
     
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  7. Mosheh Thezion Registered Senior Member

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    derivatives.. and functions.
    -MT
     
  8. Euler is my Hero Math Addict Registered Senior Member

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    Thanks, Mosheh. Your post has enlightened me into the fascinating world of 10th grade calculus. I was talking something more like...how Gauss, at age 15, pretty much conjectured THE Prime Number Theory, correctly stating an asymptotic forumula for the distributino of prime numbers. Cool shit like that.
     
  9. Mosheh Thezion Registered Senior Member

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    if you know so much.. why are you asking?

    why dont you telll us what is cool.

    -MT
     
  10. Euler is my Hero Math Addict Registered Senior Member

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    That last thing I'm trying to do is give the impression that I think I know "so much." I don't know the tiniest fraction of what there is to know out there in the math world alone, not to mention everything else. And I did tell you one example of what is cool, now it's your turn.
     
  11. BeavisAndButthead Registered Member

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    Euler...I asked my Algebra II teacher this question in 10th grade. You seem pretty smart, I hope you can get this, its relatively easy.

    | | <--- thats the distance you have.
    Cut that into half. And that into half. And that into half...infinitely. WHY does it add up to that distance?

    Another question. If you have a car at the starting point (beginning of that distance) traveling at some speed, how does it get to the end if you can cut up that distance infinitely? Wouldnt the pieces cut up be infinitely long? Use your knowledge of limits..dang, 12th grade Calculus again

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  12. Euler is my Hero Math Addict Registered Senior Member

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    I think this might have been one of Zeno's paradoxes actually but I'm no positive. I think he asked something like "how can you ever get from point A to point B if you go half way, then half way again, then half way again forever. This is basically what you're saying, right? Once calculus came along and the idea of a limit and an infinite series was invented, the paradox was explained. Consider the infinite summation 1/2^n from n=1 to infinity. This summation represents the situation you proposed, where the distance added keeps getting cut in half. Well this summation equals one, which would be the entire distance from A to B. But this summation goes to infinity, so how does that work in? Well in the case of the car, the ever-decreasing distances, which approach a limit one, take ever-decreasing amounts of time to travel, whose sum also approaches a limit of one. Basically as the distance of each segment approaches 0 so does the time to complete that segment, while the aggregate time and distance both approach one. Yeah?
     
  13. leopold Valued Senior Member

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    you want a challenge? explain human emotions with math
     
  14. DaleSpam TANSTAAFL Registered Senior Member

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    That is a challenge. Even though it may fail there I still think it is amazing how much math reflects reality in so many sciences (particularly physics). It seems weird since math, in general, is a purely logical construct and yet the world seems to be pretty well described by it. I don't know of any a-priori reason why the universe should be logical.

    -Dale
     
  15. Euler is my Hero Math Addict Registered Senior Member

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    Leopold, I really didn't mean for this thread to become a contest at all, just a place to share cool math stuff. But anyway, describing human emotions with math certainly isn't easy, but I for one believe that all human emotions (and human physiology in general) is completely chemical. Chemical interactions and properties are largely described mathematically, so in that sense you could say that human emotions are governed by math, at least in some respect.
     
  16. BeavisAndButthead Registered Member

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    Wow, that's pretty cool Euler. I didnt know I thought of a paradox that was already thought of. I have'nt even heard of that paradox, but I thought of it on my own, no prior knowledge. Hehe..I hope that means I'm a genius

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  17. D H Some other guy Valued Senior Member

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    Something about math that is cool: Paul Erdos.

    "A mathematician is a machine for turning coffee into theorems".
     
  18. TheAlphaWolf Registered Senior Member

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    yeah um... eh... fractals are cool *sheepish look of someone who doesn't know shit about math*
    lol... don't you just hate it that it's basially impossible to have an original thought anymore? Here one is thinking they're a genius for thinking up really complex things and you find out that someone a thousand years ago beat you to it. grr.
     
  19. BeavisAndButthead Registered Member

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    I concur, it angers me!!!
     
  20. Euler is my Hero Math Addict Registered Senior Member

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    Hell yes, AlphaWolf. Fractals are amazingly badass. The Mandelbrot Set is one of the more spectacular things, especially cuz it's defined so simply yet the set produced is so complex.
     
  21. TheAlphaWolf Registered Senior Member

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    *cough* riight...defined so simply...
     
  22. Euler is my Hero Math Addict Registered Senior Member

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    AlphaWolf, the Mandelbrot Set may seem intimidating but really it's not that daunting. In the complex plane (real axis horizontal, imaginary axis vertical) a point is inside the set if it converges under the iterative definition z(n+1)=z(n)^2+c; z(0)=0 where c is the point in the plane. This may seem complicated, but think of it like this: Take a point in the complex plane, say c=0 for simplicity. z(0)=0, z(1)=0^2+0=0, etc. No matter how many times you iterate this point it will not go to infinity (it converges). Therefore the point c=0 is in the Mandelbrot Set. You can do this for any point in the complex plane, say c=.25 + .2i where i is the square root of -1. z(0)=0, z(1)=0^2+c=.25 + .2i, z(2)=(.25 +.2i)^2+.25+.2i=.2725 + .3i. No matter how many times you iterate this number it never goes to infinity, so this point is also in the set. However, if you do this to the point c=.5, this point does go to infinity, so it's not in the set.

    Where the Mandelbrot Set really gets cool is when you add color to it. If you plot points OUTSIDE the set different colors depending on how quickly they tend to infinity, you get the amazing fractal patterns that made the Mandelbrot Set famous. If you have any questions let me know.
     
  23. water the sea Registered Senior Member

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    A good mathematician is lazy.

    Said my highschool math teacher. Because a good mathematician does the most in his head, and doesn't put much on paper, hence, he is externally lazy ...
    I think this is cool.
     

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