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daniel erdely (M, 64)
Budapest, HU
Immortal since Aug 13, 2008
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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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    Looks Hyperbolic, But it is The Real Plane
    Dear Friends,

    You may ask about my magic hyperbolic 0 curvature disc. How come?
    It looks really hyperbolic, because the surface itself is curling, but these waves are created by exact rules.
    They are logarithmic golden spirals. Some of them are horizontal and the rest are perpendicular to them, preserving the horizontal spirals as axes. The axis itself is rotating (further from the center, the rotation is increasing!) so , not the "material" of the disc is changing expanding or suffering torsion, but ONLY the AXIS is changing!

    This is the essence of the Sphidron deformation!

    The ridges at the circumference are showing up from "material" of what? It comes from an evenly developing "material" around the whole circumference. It means that the disc itself is only a representation of a larger disc. There is no measure of it. This way the change what you can experience as curling the surface is simply a wider part of the same surface. It is the proof of the characteristic of the plane. We have to accept that the plane is not plane, and the line is not a line, as well as the point is not a point. Those definitions of Euclides are good for learning, but they are not corresponding to the reality. Not at all. But try to use logarithmic golden spirals instead of compass and ruler. Everything will be fine, and you don't meet any irrational relation anymore. This is the button we need on each computer: Spidronise! End on all plans and drawings all data will get a common divisor.

    I tried! The Pythagorean Theorem is remaining truth is spite of sphidron deformation. Regarding only the vertices of the three squares around the right angle triangle, it preserves the angles and the ratios, for sure, while the figure is rotating and shrinkind as a whole! It is the result of the "planar" logarithmic golden curves on which the points of the original triangle are laying and running simultaneously.You must be smart, but it works after a while. I can show how.

    Have a look, here:
    http://spacecollective.org/edanet/5719/Pythagorean-Theorem-in-the-Third-Dimension

    Excuse me for my poor English!

    Best Regards
    Daniel



    Picture by Janos Erdos


    And here we are with my brother, Gyuri (on the left), 30 years before.
    He just finished his military service what was obligatory in that times.

    Good Luck!


    Sun, Aug 15, 2010  Permanent link

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    michaelerule     Mon, Aug 30, 2010  Permanent link
    I am having trouble understanding your math.

    The best hint I am getting is that you say that the Pythagorean theorem is preserved on this surface. Can you tell me more about that ?


    Is that the same notion as "conformal" or something else entirely ?

    ... I should learn more topology, I suppose.
    edanet     Mon, Aug 30, 2010  Permanent link
    Thank you for your remark. I can only ask you to help me to express myself much better.
    Please go into the details! Ask questions etc...

    daniel
     
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