Talk:Perfect ruler

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 Field: Discrete mathematics

There are multiple definitions of "Perfect ruler". One is Peter Luschny's definition, part of which requires the ruler to measure up to its entire length (be complete) and has no requirement for distances to be unique. Another definition is at PlanetMath, which requires the distances to be unique, but not necessarily complete. However, the process for verifying the example given makes no mention of the uniqueness requirement, even though the example meets it. As a result, I believe that my edits are more appropriate for the "sparse ruler" page and I am changing this page back. Wnmyers (talk) 06:28, 16 December 2013 (UTC)

connection to Golomb rulers[edit]

Is this notion any different than that of a perfect Golomb ruler? I may be being dense, but it seems like they describe the same thing. Cyrapas (talk) 23:26, 18 June 2015 (UTC)

A perfect ruler can measure all distances up to a certain length, sometimes more than one way. A Golomb ruler must have all lengths different, but does not require that all lengths are present. {0, 1, 2, 6, 9} would be a 9-perfect ruler because it can measure all distances up to 9, but it is not a Golomb ruler because it can measure length 1 twice. {0, 2, 5} is a Golomb ruler (but not an optimal one) because all lengths are different, even though it cannot measure length 1. Only 4 rulers are both, with the longest 6 only units long. I have noticed that some people use different definitions than are described in Wikipedia, though. Wnmyers (talk) 03:05, 6 July 2015 (UTC)