Perfect and Optimal Rulers
A judicious artist will use his eye,
but he will trust only to his rule.
Generating and counting perfect rulers.
- 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.
- Generating rulers: Ruler hacking is hard!
A coder's starter kit in C#, a
Sage worksheet and a
'Rulez', a Java program
for the fast
generation of perfect and optimal rulers.
an alternative program by Klaus Nagel in C,
to Java. A Fortran
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 for his helpful comments.
And to Rainer Rosenthal for many encouraging comments.