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daniel erdely (M, 64)
Budapest, HU
Immortal since Aug 13, 2008
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Spidron Space-fillers
My main goal is to present the Spidron project we develop with my friends for years. it is a system of triangles with extraordinary properties in space and time.
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    Rational Sphidron Ruler
    Make it simple!
    Make the irrational rational!


    All Rational Shidron Rulers are made of two similar spiral arms.



    The irrational distances, like sqrt2 or Pi can be transformed to rational ones as requested.
    All you need to perform this magic is a Golden Logarithmic Sphidron Ruler for this operation.
    As by Fibonacci numbers - by increasing the numbers of subsections - you can finely approach the Golden Mean, you can divide any sequence of the spiral to as many parts as you like to approach it. If you have a Golden Logarithmic spiral, you can slide any sequence of this spiral to any "point" of it from which you can approach the A and/or B as precisely as you like by smaller and smaller golden sequences.


    With the Rational Sphidron Ruler you can make any distance rational.
    Special thanx to Kathy Pedro, Lisboa

    Sun, Nov 8, 2009  Permanent link

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    Mark Dow     Wed, Nov 11, 2009  Permanent link
    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?
    edanet     Wed, Nov 11, 2009  Permanent link
    Hi Mark. Thank you for your remark. It is very useful. I corrected some typos and changed the text of the picture, though I did not touch the basic text, to leave your remark valid.
    I think the curiosity of this ruler is, that - in a way you can decide how long distance you would like to measure in advance. Naturally it is not logical to mix the measures randomly, only "rationally" to make measures, calculations and production (for example in architecture) easier.
    My e-mail: edan@spidron.hu. I send you higher resolution picture if you write me yours.
    Best Regards
    Daniel
     
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