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.