Perfect and Optimal Rulers

Generating and counting.

• What is a perfect ruler? A short introduction.
In English, in German, in French and in Russian.

• The basic definitions: Rulers which are complete can have
nice properties like being length-maximal or marker-minimal.
A more formal description.

• Counting rulers: All checked values known.
Here is a table, some samples and the perfect ruler pyramid
and all optimal rulers with length <= 101.
New:
A list of all minimal prime number rulers.

• Generating rulers: Ruler hacking is hard!
A coder's starter kit in C#, a Sage worksheet and a
Maple worksheet. 'Rulez', a Java program for the fast
generation of perfect and optimal rulers.
'Kamm', an alternative program by Klaus Nagel in C,
here adapted to Java. A Fortran program by
Hugo Pfoertner for complete rulers.

• Wichmann rulers: A great idea to find big rulers.
Here used for searching optimal rulers with length > 1000.
A table and insights from a discussion on de.sci.mathematik.
Are optimal rulers Wichmann rulers? A conjecture.

• Fun! How to craft a perfect ruler by hand.
A Java applet by Klaus Nagel.

• References to the Online Encyclopedia of Integer Sequences, an overview.

Thanks to Hugo Pfoertner and Rainer Rosenthal for for many helpful and encouraging comments.

 Rational Trees Orbitals Eulerian Polynomials vonStaudt Primes Irregular Primes Generalized Binomial Bernoulli Confusion Partitions Stirling Zeta Polynomials Perfect Rulers Swinging Primes Clausen Numbers Hadamard Gamma History Factorial Permutation Trees Swiss Knife Swinging Factorial Worpitzky Triangle