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daniel erdely (M, 64)
Budapest, HU
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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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    New Spidron Geometry - ELEMENTS
    Expected results

    I made Euclide's elements with golden log spirals and it works. I think you know the most about it.
    Please help to communicate and solve the final parts of the work.
    It is a good feeling, especially the parallels postulate 5 are proved very elegantly, but I like all of them.
    You can try if you give me the credits: use metric golden log spirals and it's segments (it is the nicest!) instead of the concepts of fixed points and a "straight line" between them!

    The points A and B can be fixed, while the sequence of the golden log spiral can be moved rotated or chosen in different ways) keeping its measure. postulate 1 For example it is 1 inch.
    And the 1 inch section of the golden log spiral is (GLS) always similar to a part of an other GLS. postulate 2
    The point A can be the source of a finite long spiral or a segment of it.

    In case of postulate 3 where Euclide determined point and "distance", we could use "sequence" or "half-spiral" which can have different shape.
    Half spiral is where A is a source, and whole spiral is a spiral where both A and B are sources and the spiral arms are meeting exactly in halfway of them. This theory was based on my spidrons and the newest spHidrons!



    All the lines are the same length. the last two figures are: half logarithmic golden spiral and the whole one.




    All consequences derived from the new postulates are solving infinite more dimensional questions, paradoxes and anomalies. Including optical illusions and incommesurability.
    More philosophical results are on work on the last years. Fig by Jano Erdos

    About postulate 4 it is true that A does not have to be a source point, because the normal cross section of the two spiral is remaining normal while the whole shape (for example looking through a circular whole) is looking as a rotating or coming closer and closer to us, while the normal cross section does not change under any circumstances. And the parts to what the spiral arms are cutting the plane (or a circle) are always equal.

    If the spirals are whole spirals (A and B are sources) the parallel sections of the third SPline will never meet (only!!!) in the infinity while they are crossing each other several times. In case of an equilateral triangle's A, B and C points (where C is the center of the space [circle, universe, horizon] they do meet and exactly ONLY one time and only in the infinity! postulate 5 any spidronised regular polygon can be made this way with uncrossing arms.

    So it seems to me that it the total merge of the Euclidean, spherical and Bolyai (and who knows which else? May be Emil Molnar knows it better!) geometries in one system.












    Nautilus snail is not a golden log spiral. John Sharp's remark.

    Details of the SpELEMENTS are on note papers. I'll publish it soon.


    www.spidron.hu
    www.spidron.hu/spidronised_spacefillers
    www.spacecollective.org/edanet


    Erdély Dániel
    + 36 70 514 8885
    www.spidron.hu

    Sun, Nov 1, 2009  Permanent link

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    nagash     Sun, Nov 1, 2009  Permanent link
    SpHidrons??
    Please explain what is it : )
    edanet     Sun, Nov 1, 2009  Permanent link
    Istvan Lenart's Questions and my answers

    I have a long note handwritten about my system what gives answer to most of these questions below.

    1. In your system, do points exist?

    2. In your system, do some quivalent of straight line exist? If so, are they spidrons?

    3. Parts of the spidrons: do they correspond to segments or half-lines, that is, rays?

    4. How many straight line-equivalents go through a point?

    5. What elements of your system does the parallel postulate refer to?


    Briefly (not finalized answers, but prompt):

    1. New concept of geometrical point: Rotating and can be approach only never can be reached. More like a spinning Black Hole.

    2. Straight infinite line In SPG is equivalent of a whole spidron with two infinite arm. If only one of the arms is finite, it is a half line, and if both, it is a segment.

    3. No, more in 2.

    4. It is a nice result, but quite comlicated to imagine. The answer is infinite many halflines and/or if it is a whole line, the middle of it can be seen as a "point" of crossection. Other parts also can be a place of a section-point like the one which cuts the whole spidron into two parts, related to each other like the golden section. Both parts are infinite but the measure of the two spiral are relating as Golden section.

    5. postulate 5 - any spidronised regular polygon can be made this way with uncrossing arms. Conjecture: Only the regular polygons have sides what don't cross each other only in A or B once, i.e. at their "end".
    Interesting: Parallel SpLines has 0 or even crossings!
    edanet     Sun, Nov 1, 2009  Permanent link
    SpHidrons are curved spidrons. Spidrons are the skeletons of them.
     
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