Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    [​IMG] [​IMG]

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?