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Thread: World's biggest reduction gear - video

  1. #11
    Supporting Member Toolmaker51's Avatar
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    Quote Originally Posted by mklotz View Post
    A googol, ten raised to the power 100, is larger than the number of elementary particles in the universe so the fact that someone can construct a mechanical device that requires the use of the term in its description is really impressive.

    It's not that hard to construct computational examples that can exceed a googol of combinations or permutations but physical mechanisms are a whole other thing.

    Despite the stunning magnitude of the googol, there is an even bigger number, the googolplex, which is ten raised to the googol power; in math notation 10^(10^100). If you want a real shop challenge, design a mechanism that demonstrates a googolplex as this one does a googol. Good luck.
    K. If you help assemble.
    Yes, we all have favorite numbers..........
    Mine?





    Combination of shop door lock.

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  2. #12
    Supporting Member mklotz's Avatar
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    Beyond favorite numbers exists the exquisite world of beautiful relationships between mathematical quantities.

    Most folks with some education are aware of the so-called golden ratio, which is reputed to provide the most pleasing size of rectangles. It's value can be calculated by solving the equation...

    1/x = x-1

    to obtain x = [1 + sqrt(5)] / 2 = 1.61803...

    Also well known is the Fibonacci series. Starting with 0 , 1 each succeeding term is obtained as the sum of the previous two terms, e.g.

    0,1,1,2,3,5,8,13,21,34,55,89,144,233,377.......

    The series occurs in nature, manifesting itself in the layout of branches on plants and petals on flowers among other forms.

    Now, what is truly amazing is the fact that, if you take the ratio of adjacent terms in the Fibonnaci series, they will approach ever closer to the golden ratio...

    3/2 = 1.5
    5/3 = 1.67
    8/5 = 1.6
    13/8 = 1.625
    21/13 = 1.61538
    34/21 = 1.61905
    55/34 = 1.61765
    89/55 = 1.61818
    144/89 = 1.61798
    233/144 = 1.61806
    377/233 = 1.61803...

    If you've ever been puzzled hearing a mathematician describe something mathematical as "beautiful", this is the sort of thing they're talking about.
    ---
    Regards, Marv


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  4. #13
    Supporting Member Toolmaker51's Avatar
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    I so admire Mr. K's infinite ability of textually diagramming intricate subjects. Even more pleased his many decades dedicated to 'our side'. Talk about directing interest in serious topics, laid down comprehensibly......Evidence? Look at his contributions linked in his forum signature.

    Yes, admittedly I'm one of those with some [barely] education. The Fibonacci as a term was new to me, around the eighties or so, coming across 'their' divider/ mechanism/ tool. That an identifiable person realized it, then sat down to extract it; epic. We can visualize how either calculating OR device came first, to prove the other. Found myself wanting to illustrate that as "helping" to prove the other, but help is a weak term. It proves itself, in various ways.

    But visual factor was something I seemed to use regularly in photography, labeled "Rule of Thirds". Now while the ratios aren't exactly alike, nor any photo bugs running calculations, it makes itself known. Peer through the viewfinder, it tells you the ideal frame. The Golden Ratio, very prevalent with architecture, in use thousands of years. For some perhaps it's subliminal, but it's definitely not universal. Airy and Bessel come to mind, lol, different solutions to outwardly same physics.
    So yes, the math IS beautiful, unalterable, predictable, not unlike a mechanism; but the visual mystery more interesting.
    Same for music; one jumble of notes gives us chills, the same in different order, abominable. To another, the combination might reverse!
    Yet musical scales are a quite simple mathematical progression. And there are studies tying intelligence quotients to levels of intricacy preferred in music.
    All in all, good thing we are individuals, sharing that what we have in common.



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