Member 1870
46 entries
199121 views

 RSS
Contributor to project:
Polytopia
daniel erdely (M, 64)
Budapest, HU
Immortal since Aug 13, 2008
Uplinks: 0, Generation 3

Spidron Main page
Spidron presentation 1
Spidron presentation 2
Spidron article
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.
  • Affiliated
  •  /  
  • Invited
  •  /  
  • Descended
  • edanet’s favorites
    From whiskey
    Buckminster Fuller
    From Autotelic
    Klein Bottles
    From erdos
    Fractal maze
    From erdos
    Spidron Pattern Genetics
    From erdos
    Experiments With...
    Recently commented on
    From edanet
    SpHidron can deform plane...
    From erdos
    Experiments With...
    From edanet
    Looks Hyperbolic, But it...
    From Irek Kielczyk
    Mirage #02
    From Irek Kielczyk
    Mirage #05
    edanet’s project
    Polytopia
    The human species is rapidly and indisputably moving towards the technological singularity. The cadence of the flow of information and innovation in...
    Now playing SpaceCollective
    Where forward thinking terrestrials share ideas and information about the state of the species, their planet and the universe, living the lives of science fiction. Introduction
    Featuring Powers of Ten by Charles and Ray Eames, based on an idea by Kees Boeke.
    Tue, Aug 12, 2014  Permanent link

      RSS for this post
      Promote
      
      Add to favorites
    Create synapse
     
    FIRST PERFORMACE OF A NEW GEOMETRIC FENOMENA

    Today succed to realize my concept in a series of drawings. How can we deform a planar sqquare to a torus without edges and torsion! I think it is a really new type of deformation what is NOT mentioned before. It is one of the extra cases what Gauss' Curvature Theorem haven't described ever before.
    Tue, Aug 12, 2014  Permanent link

      RSS for this post
      Promote (2)
      
      Add to favorites
    Create synapse
     



    A catalog piece, especially if one is writing it for one’s own catalog, allows too much freedom for the author. In many cases, the text is a formulation of thoughts that only serve to underline messages already communicated by the exhibition or the works once more, and needlessly. I would like to avoid that mistake and so I only make use of this opportunity in order to realize two distinct objectives.
    The first one is to document, as far as possible, the development of the Spidron as innovation, as it pertains to names, to persons. The second is to settle a long-standing debt by finally defining what I/we understand the Spidron to be. I attempted to complete the first task in the text and images of the thirty-two pages of this brochure.
    I shall attempt the second one below.
    The real source of the Spidron is an old family name that has been changed, the name ‘Spitzer’. I have not revealed this before and instead offered the words ‘spider’ and ‘spiral’ as an explanation. The ‘-on’ at the end of the word follows Greek nouns, where a many-sided plain figure and a geometric body are called a polygon and a polyhedron.
    Is the Spidron a polygon? As I often say, a Spidron arm is a spiraling formation constructed from a sequence of two kinds of triangles (usually isosceles ones). It is not possible to specify the number of its vertices or sides. Its area and circumference can be determined in the limit, but no matter how large or small a piece of it we take, it can always be extended by additional triangles. As professor of quantum logic Gyula Fáy put it, the Spidron is a process. It is a procedure in which, like the tower of Babel, the building of Spidrons can be continued as long as we want. The starting point can be set arbitrarily. The ratios of angles and lengths are the crucial aspects. Those ratios are constant and ever-present in the Spidron formations. The Spidron-arm cannot be finished, but it can be given a starting point with a clever trick: I can pick one triangle and declare that it will be the first and largest one. In order to prevent the addition of an even larger one, I can reflect the entire spiral formation across the base of that triangle. If it is a central reflection, I get the form we initially called the Spidron. If it is a mirror reflection, we get a figure like a pair of horns, which we have called the Hornflake. Various versions of those two figures fill the world of Spidrons. Those Spidron arms can be used to construct extraordinary shapes in the plane and in space. Our research ranges from plane tilings and regular and semi-regular solids through saddle surfaces and to the investigation of special, aperiodic tilings and quasi-crystals.
    But the process induced by the subject of our shared thinking—which happens to be the Spidron, this time—in various human communities is at least as interesting. It generates action groups, provokes arguments and often results in striking scientific and aesthetic qualities.
    It was particularly astonishing for many people that it can be used to create structures with an entirely novel kind of movement.
    The Spidron has defined a position. I hope that sooner or later, through processes of their own, others will also be able to occupy that position.
    At last, others may also achieve their rightful positions.
    Sun, Mar 10, 2013  Permanent link

      RSS for this post
      Promote
      
      Add to favorites
    Create synapse
     
    Have you ever seen similar, before?
    Wed, Aug 22, 2012  Permanent link

      RSS for this post
      Promote (1)
      
      Add to favorites
    Create synapse
     
    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

    Good Luck!

    Sun, Aug 15, 2010  Permanent link

      RSS for this post
      Promote (1)
      
      Add to favorites
    Create synapse
     
    About spidrondeformation:


    1. it is not a folding in a traditional sense, as there is no stage when I folded the paper all across the paper surface.



    With my friend the perpetuum mobile Walt van Ballegooijen


    2. I folded the traditional honeycomb accordion spidron net in 1979 edge by edge, vertex by vertex, that is why it took so much time, and needed so big trust to go on. Only in the last stage it became clear that the paper can be folded this way.



    Hard work of the Spidron Team


    3. In case of spidrons, it has an extra unique property: I did not want to fold the triangles by their edges but I tried to rotate them along axes which were pointed from the middlepoints of their base (which remained always on the baseplane) toward the center of the nests. The level of freedom of the whole system allowed to get rigid triangles at the end.



    One of the reliefs


    4. I know, it is strange for most of the mathematicians to hear, that the center of the spidronnest are closed, But I can prove it. I am sorry but for it I need personal meeting or I can write it only in Hungarian, because it is not so easy.



    Special transformation of the nest


    5. There is an extraordinary property of the spidron deformation: at a certain stage the monotone rotation of edges results two different, but equivalently possible rotation at the neighbouring - coresponding - edge. This property leads me to very strange idea about the 2D plane. The reversibility of the 3D movement during the monoton change - rotation - of one of the edges means that this movement is not a real 3D movement, only similar to it. To be extreme: I think the Spidron deformation proves that the 3D Euclidean space does not exist at all. All what we experience is only an embedding physical "space" in which the deformations of a 2D object takes place.



    Dodecaspidron


    6. The stage where this extraordinary property appears is a very unique stage. The equations are divided into two equivalently valid equations, so that the last undivided value of the "f", what is the angle between the edge - of the second ring's from outside of a nest's periphery - and the baseplane - is 35,26˘. It does not look a specific number, but if we measure the angle between the adjacent edges on the same (second) ring we find that this angle is exactly 90°! After this stage the angle is decreasing to 30°, inspite of continuing the rotation of the outer edge monotonously from 0° to 60°.



    Sphidronised spacefillers (42 new shapes)


    7. I described more (very many) consequences of this interesting deformation, but - I think - it is enough for now.



    Sphidron rings

    8. More Archimedean - and other different - reliefs can be fold from a flat 2D paper.




    Timaean Serie - Sphidrondisc


    9. I started to work with sphidrons (spidron with a "h" in between "p" and "i" - what means spherical or bent, twisted spidrons), which has more freedom and this investigation leads me to the description of a new type of geometry, where the points of the plane are little spheres, which can rotate, roll and slide on each other making possible infinite incredible deformations. To preserve the measure of the sphidrons I introduced logarithmic and perpendicularly swirling deformations. We can say that the spidron and its movement is the "sceleton movement" of the smoother and slider (does this word exist?) sphidron movements. I work on this project with a young Hungarian student, called Janos Erdos.

    Conclusion:

    Spidron deformation is not a traditional way of folding, and its unexpected properties allows us to think over the "facts" what we have learned about the 3D Euclidean space.

    I found references of these ideas in lower dimensional topology, quantum gravity and other fields of mathematics and physics as crystallography and quasy-crystal theory. Most of them were mentioned by Hungarian scientists like

    Mr. Peter Hamburger, professor of Indiana, Purdue University, author of the book: Set theory - with A. Hajnal

    Janos Hajdu from Koln, author of the book: Introduction to the Theory of Integer Quantum Hall Effect, he was the student and personal colleague of Mr. Werner Heisenberg, and

    Janos Polonyi, from Theoretical Physics Laboratory, Louis Pasteur University, Strasbourg, France

    Emil Molnar - the professor of Budapest University of Technology and Economics
    and

    Andras Nemethi from Renyi Mathematical Institute, Hungary

    ... but as the main actor of the Spidron Story I have to mention

    Mr. Lajos Szilassi who was the first to describe this very complex and new kind of deformation. I attach the link of his terrific paper which made the spidron movement a mathematical fact:

    you can dowload it from here:
    http://www.zentralblatt-math.org/matheduc/en/search/?q=au:Szilassi%2C%20L*


    I have to thank the results of the spidron project to a lot of persons, you can find their names on our websites.


    www.spidron.hu
    www.spidron.hu/spidronised-spacefillers
    www.spacecollective.org/edanet


    ...etc.


    best regards,
    daniel e
    Sun, Aug 23, 2009  Permanent link

      RSS for this post
      Promote
      
      Add to favorites (1)
    Create synapse
     
    You can see some strange and suspicious information about the events I took part in Albany, New York, USA recently. I have a chance to meet again Mouse soon. Any remark, advice is very welcome.

    What is going on here?????? WOWWW!!!!!!!!!!!!!!!!!!

    The system (us) does not allow me to upload my files. Could you help me? I'd send to any of you the files,asking to upload them!

    THANK YOU!!!!

    I hate THIS KIND of CONTROLLED Societies!
    It was enough for 50 years in my life!!!

    Help me to get rid of this kind on MANIPULATION NOW!!!
    Thanx again, Friends.
    Hugs

    Daniel
    Mon, Jul 13, 2009  Permanent link

      RSS for this post
      Promote
      
      Add to favorites
    Create synapse
     
    Scientific Sensation

    As you can see, four touching sphere's sphidronized polygon 'side' can be unrolled into planar surfaces if we cut them into thin and spirally rotated ligamental bows. The result will be four planar surfaces. The same four planar surfaces i.e. fractal-sided polygons can create a simple sphere if we join them by their sides instead of their middlepoints. The spherical twisted sphidronnests are the solutions of the ancient problem of the metrically correct mapping. The picture below is made by mathematical algorithms, which were created by Janos Erdős. He was listening my ideas and succeed to transform the narrative into mathematical expressions. The result is a "3D" picture. In this way the 3 kinds of expression could be presented in one process: Narrative, mathematics and picture. Surprisingly the final consequence of this "3D" fenomena is that the 3rd dimension IS NOT an Euclidean Dimension. It is something else, what we can suspect as a trauma of perception of the fetus, who cam out from the total safety of mother's womb and water of life. As the baby is delivered the shock of gravitation causes a trauma of perception and makes the change of brain. The eye start to see double and sees something what have never existed: the third dimension. The real physical content of the "3D" or we can say: the third dimension is a 'simple property" of the embedding physical space. The GRAVITATION.
    In a word: The real structure of the so called space is the following: Two-dimensional Euclidean plane in an "n-dimensional" embedding physical "space". The first physical dimension we can experience is the gravitation. Yes, we are residents of a flatland. Everybody is folded like an origami and the first shock after birth causes the illusion of the third dimension, which - in reality the Gravity itself. All other dimension can be real, including the 3rd 4th or the time itself, but they are only embedding physical ones. If you don't believe us, please look after the anomalies in wolfram's pages, especially the http://mathworld.wolfram.com/  ! An example: the Banach-Starsky paradox. Our - The Spidron Team's - theory implies answer to that problem too, among others.

    It is breathtaking that Ms Schelley Heath found the Sphidron sphere intuitively just recently. We found her extraordinary work on the web by chance:

    Celestial Cyclon on page:
    http://www.redbubble.com/people/bundygal/art/641334-6-celestial-cyclone

    Look and enjoy. Maybe she was the first who described the mathematics of sphidrons. I don't know, but anyway she was the one who was able to demonstrate the other side of our development. The New Geometry,

    THE DEVELOPABLE SPHIDRON SPHERE

    I can hardly imagine that the perception of colors are the result of the trauma of birth, as the unity of the light can NOT BE taken apart. In darkness we see only the essence of the outer world. Normally we see everything in black and white like in our dream and in our fetal time.

    Is not it a fatal error? Or fetal?


    At least ;o){image 2}
    Sat, Jun 6, 2009  Permanent link

      RSS for this post
      Promote
      
      Add to favorites
    Create synapse
     
    In Jeffer R. Weeks book he presented a hyperbolic surface which can not be folded to the plane.
    After Pr. Lajos Szilassi proved, that the nest - made from flat triangles, we can be certain that the curved circular nest is also foldable from a plane sheet of paper. If it was thrue then it is easy to show the difference between hyperbolic, what he presented, in Shape of time and our developable surface. Our shape is foldable, because of the whirling shape of the sphidron. The vortex-like deformation is radially symmetrical. this kind of deformation is possible without stretching the surface.



    Mon, Mar 23, 2009  Permanent link

      RSS for this post
      Promote (1)
      
      Add to favorites
    Create synapse
     

    A path, also known as a rhumb line, which cuts a meridian on a given surface at any constant angle but a right angle. If the surface is a sphere, the loxodrome is a spherical spiral.
    The loxodrome is the path taken when a compass is kept pointing in a constant direction. It is a straight line on a Mercator projection or a logarithmic spiral on a polar projection (Steinhaus 1999, pp. 218-219). The loxodrome is not the shortest distance between two points on a sphere.

    Source: http://mathworld.wolfram.com/Loxodrome.html 
    Mon, Mar 9, 2009  Permanent link

      RSS for this post
      Promote
      
      Add to favorites
    Create synapse
     
          Cancel