Mark DowWed, Nov 11, 2009 By "transformed to rational by request", I think you mean "approximated by a rational by request", because your ruler needs to be "adjusted finely". I can finely adjust my Euclidean straight ruler in analogous fashion.

Also, a golden mean spiral is not special in this respect, aside from its relationship to the golden mean (ratio). The Pell sequence, sometimes called the silver sequence, is more directly related to the square root of two and so a Pell spiral would be a "natural" ruler. Any of the silver means can also be used.

I do like the idea. Is there a higher resolution graphic available?

Comment onRational Sphidron RulerMark DowWed, Nov 11, 2009By "transformed to rational by request", I think you mean "approximated by a rational by request", because your ruler needs to be "adjusted finely". I can finely adjust my Euclidean straight ruler in analogous fashion.

Also, a golden mean spiral is not special in this respect, aside from its relationship to the golden mean (ratio). The Pell sequence, sometimes called the silver sequence, is more directly related to the square root of two and so a Pell spiral would be a "natural" ruler. Any of the silver means can also be used.

I do like the idea. Is there a higher resolution graphic available?