It is easy to generalize number bracelets to moduli other than 10—at each step, add the two previous numbers and take the remainder of the result when divided by m. Here are some pretty pictures I made of the resulting bracelets for m ranging from 1 through 12. Click on any of them to get a larger version.

m = 1

m = 2

m = 3

m = 4

m = 5

m = 6

m = 7

m = 8

m = 9

m = 10

m = 11

m = 12

I used a little Haskell program to output descriptions of the graphs, and Graphviz to generate the images. I’d be happy to post the code if anyone is interested.

About Brent

Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
This entry was posted in arithmetic, fibonacci, iteration, pattern, pictures, sequences. Bookmark the permalink.

6 Responses to m-bracelets

  1. Jon Ingram says:

    Very pretty — thank you! I’d just decided to use number bracelets (in base 10) with my primary school maths club this week, and your other-bases pictures will tie in very well with the base-12 arithmetic session we had last week.

  2. Brent says:

    Jon: great! I hope your students enjoy the pictures. =)

  3. Uwe Hoffmann says:

    I want to see the code, thanks !

  4. Pingback: m-bracelets code « The Math Less Traveled

  5. Brent says:

    Uwe: the code is posted now, enjoy!

  6. Pingback: m-bracelets « sciencev

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