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3D mirror inverted numbers

  1. Dec 15, 2008 #1
    Rules: Compress to single digits to reveal ratio pattern.
    The line is to be followed - 1,2,4,8,7,5 and back to 1. Each number being added to itself.The other line is the invisible nines.

    Control Dial:
    l_c3f47ea9e1d1a916eaaed031c830e96e.gif l_65e6efff0c4bcfa40322126945a4191f.gif

    2-D Skin (ignore the +&-)

    3-D Torus

    Have fun! :smile:
    Last edited: Dec 15, 2008
  2. jcsd
  3. Dec 15, 2008 #2
    Let's see. In the first image, the solid lines join powers of 2 (since the number is duplicated on each step). So the image illustrates that a power of 2 cannot be congruent to a multiple of 3 (mod 9), which is something that can be proved by observing that, if 2^n is congruent to r (mod 9), then 9 divides 2^n - r; and since 3 divides 9, then 3 must divide 2^x - r. If 3 divided r it would have to divide 2^x as well, which is false, so 3 cannot divide r.

    In the second image you used a different concept; this time not duplicating each number, but adding always the initial number; thus each row represents the multiples of the initial number (mod 9), if you care to replace 9 by 0.

    As for the pattern in the third image, or how it ended on the surface of a torus, I'm lost.
  4. Dec 15, 2008 #3
    l_64b2d589aee0062e7d0561bd6c338ba4.gif l_3e9ff2dc779235f290707c8cc2c1bc55.png
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