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Math Help - Non-algebraic pattern - multiplication by 11 - decimology.

  1. #1
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    Non-algebraic pattern - multiplication by 11 - decimology.

    A new non-agebraic pattern I found for the field of Decimology. (Click me for decimology information)

    Take any number and multiply it by 11.
    Post(s) in this thread contain the math BBCode, for a full directory of this code, please click here.
    Example 23...

    2311 = 253.
    2+3 = 5
    stick the 5 inbetween the 2 and 3, the answer is: 253

    Example2:

    5311=583
    5+3 = 8
    583

    Example3:

    2611
    2+6=8
    286
    2611=286

    Example4:

    8911
    8+9=17
    number = 8(17)9 ... carry the 1 over.
    number = 9(7)9
    =979
    979=8911

    Example 5:

    12311
    2+3 = 5
    1+2 = 3
    1353


    This works with all number, however large or complex.
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  2. #2
    Senior Member roninpro's Avatar
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    What exactly do you mean by "non-algebraic pattern"? The reason why your pattern works isn't very amazing - it just comes straight out of the way we multiply numbers.

    Suppose abc is a three-digit number, with digits a,b,c. Then, abc\cdot 11=abc\cdot(10+1)=10\cdot abc+abc=abc0+abc. But then, adding these up, we have a[b+a][c+b]c, which is the pattern you describe (after carrying over, if necessary).
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  3. #3
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    Ah! cool, I didn't think of it that way, originally I thought this pattern had no algebra involved, but it was based purely off the numbers involved int he equation. It's still pretty neat to me though.
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  4. #4
    Senior Member roninpro's Avatar
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    I think that I see what you mean. In that case, you might be interested in this: Look-and-say sequence - Wikipedia, the free encyclopedia. There are actually some interesting results involved with this type of pattern.
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  5. #5
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    AH! Cool! I remember doing things like that in grade-school, nice to see that it is something real ahhaha... Thanks!
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  6. #6
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by orange gold View Post
    Decimology, the study of all patterns in mathematics, specifically non-algebraic patterns, and the solving of an equation using only the numbers found in that equation.
    Decimology.com/forums/forum.php
    Dude... what's a non-algebraic pattern?
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  7. #7
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    Quote Originally Posted by Bruno J. View Post
    Dude... what's a non-algebraic pattern?
    This: http://www.mathhelpforum.com/math-he...gy-168811.html
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  8. #8
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by orange gold View Post
    I'm not asking for an example, as you claim to have supplied one already. How do you define such a thing?
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  9. #9
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    Oh! My idea for a non-algebraic pattern was a pattern for a math operation, number sequence, equation, etc. that used methods unknown to algebra to solve it. Example: Taking the sum of all the digits in a number wouldn't be algebraic.
    if "x" equaled the sum of all the digits in the number "n" and (n = 361) than x would equal 3+6+1 or "10"
    Now the idea would be to incorporate this into a pattern for something like division of a specific number so that you could solve the problem without having to do any algebra harder than something like addition.
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  10. #10
    MHF Contributor Bruno J.'s Avatar
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    Quote Originally Posted by orange gold View Post
    Oh! My idea for a non-algebraic pattern was a pattern for a math operation, number sequence, equation, etc. that used methods unknown to algebra to solve it. Example: Taking the sum of all the digits in a number wouldn't be algebraic.
    if "x" equaled the sum of all the digits in the number "n" and (n = 361) than x would equal 3+6+1 or "10"
    Now the idea would be to incorporate this into a pattern for something like division of a specific number so that you could solve the problem without having to do any algebra harder than something like addition.
    With all due respect, this is very vague. Taking the sum of the digits is certainly not "unknown to algebra"...
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