Remainder Graphs

Initializing live version

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

What is the remainder when some number is divided by another number, for example, 7? The result is called . You can find the answer quickly with the help of one of the graphs in this Demonstration.

[more]

For a number, say , select the desired modulus, then start at 0 and follow 9 blue arrows, 1 red arrow, 4 blue arrows, 1 red arrow, 0 blue arrows, 1 red arrow, then 6 blue arrows. If there is no red arrow, stay in place. Each digit specifies the number of blue arrows, then follow a single red arrow before moving on to the next digit. The number on your final landing place gives the remainder. In this example, .

[less]

Contributed by: Ed Pegg Jr (November 2015)
Open content licensed under CC BY-NC-SA

Details

Reference

[1] D. Wilson, "Divisibility by 7 Is a Walk on a Graph," Tanya Khovanova's Math Blog (blog, T. Khovanova, owner), (Aug 11, 2009) blog.tanyakhovanova.com/2009/08/divisibility-by-7-is-a-walk-on-a-graph-by-david-wilson.

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send