Perfect ruler
From Wikipedia, the free encyclopedia
A perfect ruler of length n is a ruler with a subset of the integer markings 
that appear on a regular ruler. The defining criterion of this subset is that there exists an m such that any positive integer 
can be expressed uniquely as a difference k = ai − aj for some i,j. This is referred to as an m-perfect ruler.
A 4-perfect ruler of length 7 is given by {0,1,3,7}. To verify this, we need to show that every number 1,2,3,4 can be expressed as a difference of two numbers in the above set:
- 1 = 1 − 0
- 2 = 3 − 1
- 3 = 3 − 0
- 4 = 7 − 3
An optimal perfect ruler is one where for a fixed value of n the value of an is minimized.
[edit] See also
This article incorporates material from perfect ruler on PlanetMath, which is licensed under the GFDL.
