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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Stephen Wolfram did Not Think About Different Deformations of the Living Material Without Extra Material

At least in his book, Published in 2002 and spread worldwide since then.
After I contacted his Company, Wolfram Research Ins., which is the developer of the famous software, Mathematica, I informed them about my new invention in 2009. This is the SpHidron deformation, based on my own 30 years long research of Spidrons. You can see examples of this new kind of deformation below in this page.


This series of possible deformations does not contain my SpHidron deformation.

He and his company did not want to publish anything about Spidrons, saying there is no scientific publication about the topic, what is actually not true, as we with my colleagues, The Spidron Team published several papers in the Proceedings of the World Conference on Art and Math - BRIDGES, and we published a paper with Mr. Lajos Szilassi in the Publication of the University of Pecs and Karlsruhe in 2004:

There was published my website also in the MathForum in 2004:http://mathforum.org/electronic.newsletter/mf.intnews9.51.html

After more mail we changed, Mr. Eric Weisstein erased the only link to my old webpage, disappearing all informations from their web portal, while he and his colleagues are publishing different articles close to my investigations. I decided to go to Atlanta, to talk personally with Mr. Stephen Wolfram. I asked him to give me some minutes to clarify the situation on the first day I arrived to the Gathering for Gardner 9, where he was an invited speaker. He said, ok, but until the last day he did not came to me, in spite I was always around in this small space of the Conference, and the garden party we were invited together to Tom Rodges house. On the last day I asked a nice man to give to Stephen my business card, and tell him that it is my note on the back of the little card. I wrote to Stephen asking his pardon for my rude manner when I wrote to his colleagues after asking them to actualize my spidron links. They did not, but I reacted it too angrily, so I thought it is the best to ask Mr. Wolfram excuse. After returning home I tried to send again the paper on spidrons and I got a mail from the company, saying that they can not open the pdf file. At that moment I sent the file to the gentleman who helped me to contact Stephen in Atlanta, asking him to forward my file to the Wolfram Research. Till then I have no reaction from them, only I had to experience, that my old link also disappeared.

More SpHidron Creatures & Sketches After G4G9


Complex SpHidron deformation around vortexes on different intersecting planes


Deformations around th origo of 3 2-dimensional planes


Sketch on the transfer of the SpHidron deformation at the edge of the intersecting planes


Nicely deforming planar disc around four logarithmic SpHidron arms


Mathematical theoretical remarks on the even an simultenous Sphidron deformations

Wed, Apr 14, 2010  Permanent link

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Newest Creatures of the SpHidron World

Surface is laying on some logarithmic spiral arms. 20 of it can fill the surface of the Sphere, like in the case of a icosahedron. But - to be honest - I don't believe in sphere, as they are simply doubled toruses. Torus has axis just like my creature has.




Inside of this shape is 1/20 of the volume of a "sphere". But this "sphere" does not have an absolute size.




First trial to make a Sphidronized Octahedron




First trial to make a Sphidronized Icosahedron




First trial to make a Sphidronized Octahedron




Dual Creature of the SpH World

Thu, Apr 1, 2010  Permanent link

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Pythagorean Theorem in the Third Dimension

I guess I have found the only possible 3D deformation of the Euclidean plane which - regarding of the 9 vertices of the basic shapes of the Pythagorean Theorem, like the triangle and the squares - is preserving the validity of the theorem. The triangle in the 2D plane is rotating and shrinking, but its proportions and angles don't change. I tried to make some drawings to demonstrate this interesting swirling deformation below.


This picture shows how to make SpHidron deformation from the classical Spidron deformation


The arms of the Sphidron disc are rotating around themselves. The longer distance from the center increases the measure of the rotation. Here the change of the rotation is continuous while in the case of Spidrons it is discrete.


In between every pair of twirled arms must be another arm which like the twirled ones remains in one plane but it isn't not rotating around itself - like an axis - during this deformation.




The spiral arms one by one remain on their own plane, but these planes on which they lie on can be lifted up and pushed down alternately. This way you can make more and more dense surfaces in the same volume.




To make this deformation possible, you have to change your previous imaginations on the plane. It is a little more complicated, as the elements of the plane are not points with no dimension, but they do have dimensions, what make possible their rotation and sliding. While two of the neighboring "spoints" remain neighbors, the rest of them can be changed. Just like in the case of a simple pearl-string where every bounce has only and maximum two permanent neighbors.



Copyright 2009 -2010
Drawings by D Erdely, computer visualization by Janos Erdos

Mon, Mar 15, 2010  Permanent link

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Visualisation of the Hungarian Pavilion at the 12. Venice Biennale of Architecture 2010

Design of the pavilion is a result of Dániel Erdély and The Spidron Team

It is not the winner!, It is the looser application!
Please don't let me misunderstood!




The newest item in the exhibition space is the Caduceus. It is a rotating attribute of Hermes' wand.

Animation can be seen:
http://www.youtube.com/watch?v=NobDdvmq9yI

The bent and twisted surface of the wings can be unfolded into the area between the spiraling tubes.


Entrance


Atrium


Exhibition Hall


Spidronized Archimedean Solids and SpHidron movement


Detail of the wall


Detail of the Main Hall

We are going to exhibit the Spidronized Archimedean Spidroballs,
http://spidron.hu/archispidron/

 http://spidron.hu/archispidron/deforming  and swirling Sphidron disks,
http://www.youtube.com/watch?v=a7hFn1ZDHHA

deforming reliefs,
http://www.youtube.com/watch?v=rvCBO9xChGA&NR=1

toys,
http://www.youtube.com/watch?v=xupWsbc4zhg&NR=1

tiles,
http://spidron.hu/sparchicards/

and 42 brand new space-fillers patented recently.
http://spidron.hu/spidronised_spacefillers/

You can see more animations here:
http://www.youtube.com/watch?v=lwrTVhtn0Pg
http://www.youtube.com/watch?v=RbNcXdnXrkc


Thank you for your kind attention.

Copyright 2010 Daniel Erdely and The Spidron Team

Sun, Feb 21, 2010  Permanent link

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Possible Unfolding of the Sphere

There is no point, no straight line, no circle, no sphere and no space in a manner how Euclide described them. There must be tiny elements, of which the plane is composed. These elements must have axes and radius to be able to slide and rotate around each other. If the particles -
i.e. atoms - of the material (what have been called "ideal plane" by Euclid) can rotate like a spiral string, the sphere can be unfold to the plane without any problem preserving its metrical measures along the string and the other distances and angles also can be calculated. The inner arms are the rotating string arms, it will be a half of the final sphere. They are becoming straight lines on the surface of the sphere. The outer parts of these "S"-like figures can be bent and twisted and creating another halfsphere on the top of the other one.



Enjoy this music:
http://www.youtube.com/watch?v=5T3FXFnoTzE&feature=quicklist&playnext=8&playnext_from=QL



The plane what bisects the sphere can be deformed similar way as it is shown on (partly) the figure above. The orange ribbons are showing the tangent planes with simultaneously equivalent Gaussian curvature.

Tue, Feb 16, 2010  Permanent link

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No Point - No Sphere - No Space

Misleading Euclidean Geometry can cause total chaos in the future of humanity. It is quite obvious that somebody or some superpowers in the past hide the secret of the true geometry. Maybe it was the knowledge what sunk with Atlantis. Descartes and Johann Heinrich Lambert had the last attempt to recover the ancient knowledge, but his colleagues killed his theories on swirling "space" and other structures. The Sphidron Geometry renewed his and his ancestors ideas and made clear that the universe is a discrete entity made of finite elements. No point exists, the spheres are tori (plural of torus) with axes and the space is only 2D in an embedding physical context.



you can see here some elements of the New Sphidronized Geometry without points and spheres.

we are looking for the polyhedra which have changing egdes meeting in its vertices and surfaces which can be applied on the surface of the torical spheres. Gauss knew very well, that Kant made a mistake saying that the three dimensional picture of the universe is an a priori knowledge of the mankind. Einstein, Bolyai and Riemann made the situation more difficult with more complex visions of reality, while the real life is a comprehensive, simple two dimensional phenomenon with some thickness. Everything can be unfold. We are looking for the surface which is a deformed disc on the paths of two or three logarithmic golden spirals. On this surface the Pythagorean theory might be surviving. It is the only surface what can be said really 3 dimensional, but this dimension is only a tricky shadow of the imagined one. The rest is only is a birth trauma of the fetus, who was confronted to the gravity after delivery.

How could a point rotate without a radius? How could a sphere rotate without an axis?
But Point with a radius is not a point anymore, and a sphere with only one axis is not a sphere anymore. They are only abstractions of limited human fantasy.

Sat, Nov 28, 2009  Permanent link

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42 New Spidronized Spacefillers are Patented in Hungary

Please visit our new site.

http://spidron.hu/spidronised_spacefillers/

I promise, you will be satisfied.
One of the most beautiful Spacefillers - multiplied.



FS-41 - This complex spacial model - just like the cube or any kind of brick, fills the space without any ovelappings and gaps.

Fri, Nov 20, 2009  Permanent link

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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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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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