*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.A list of all minimal prime number rulers.

New:

**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.