Spidron

:"This article discusses the plane geometric figure; for the science-fiction character see Spidron (character)."

In geometry, a spidron is a continuous flat geometric figure composed entirely of triangles, where, for every pair of joining triangles, each has a leg of the other as one of its legs, and neither has any point inside the interior of the other. A deformed spidron is a "not" a spidron, but rather a three-dimensional figure sharing the other properties of a specific spidron, as if that spidron were drawn on paper, cut out in a single piece, and folded along a number of legs.

It was first modelled in 1979 by Dániel Erdély, as a homework presented to Ernő Rubik, for Rubik's design class, at the Hungarian University of Arts and Design (now: Moholy-Nagy University of Art and Design). Also Dániel Erdély gave the name Spidron to it, when he discovered it in the early 70s. [cite web|url=http://www.sciencenews.org/articles/20061021/bob11.asp|title=Swirling Seas, Crystal Balls|publisher=ScienceNews.org|accessdate=2007-02-14]

The spidrons can appear in almost infinite number of versions, and the different formations make possible the development of a great variety of plane, spatial and mobile applications. These developments are suitable to perform aesthetic and practical functions that are defined in advance by the consciously selected arrangements of all the possible characteristics of symmetry. The spidron system is under the protection of several know-how and industrial pattern patents. It was awarded a gold medal at the exhibition Genius Europe in 2005. It has been presented in a number of art magazines, conferences and international exhibitions. During the last two years it has also appeared, in several versions, as a public area work. Since Spidron-system is the personal work by Dániel Erdély but in the development of the individual formations he worked together with several Hungarian, Dutch, Canadian and American colleagues, the exhibition is a collective product in a sense, several works and developments are a result of an international team-work. Dániel Erdély has been developing the spidron system for 28 years – without any institutional background, but with the help of selfless and enthusiastic friends and acquaintances: scientists, artists, craftsmen and interested individuals. It was in 1979 that he made the first relief of spidrons, for a class of Ernő Rubik's. At present there is an international research team at work on the Spidron project, the development and research of spidrons. Erdély’s geometric system invention called Spindron is a true mathematical and interdisciplinary world-novelty, which promises a multitude of new opportunities in the field of contemporary fine art as well. His work has achieved a great success at several international forums of both mathematics and art, e.g. at universities and in artistic associations.

The most important appearances of the Spidron system

1998 12th International Congress of Crystal Growth, Jerusalem

1999 Mathematical Research Institute of the Hungarian Academy of Sciences (MTA) – co-organized by the Symmetry Society

1999 Ernst Museum, World Conference of Science, Ars (Dis)Symmetrica ’99

1999 Symmetry Symposium – Szeged Division of MTA

2000 Intuition, Innovation, Invention – Scientific and technological inventions and artistic innovations, Art Hall, Budapest

2003 Symmetry Exhibition, Millenáris Park

2003 Presentation - Graduate School of Human and Environmental Studies, Kyoto University, Sakyo-Ku, Kyoto 606-8501

2003 MathForum Philadelphia, Internet magazine of Mathematics

2004 Computer, algebraic and dynamic geometric system in mathematical education, Pollack Mihály Technical College of Pécs University of Sciences (PTE)

2004. Ars and Mathesis, Baarn, Holland, presentation and exhibition

2004 Ars and Mathesis, Spidron quartet postcad series together with Rinus Roelofs

2004 Genius Europe - Invention Exhibition

2005 A selection of folding; a publication by Pollák Mihály College, Pécs

2005 Passages, Bos van Tytsjerk, Spidrohedron sculpture exhibition, Holland

2005 Exhibition and presentation, New York, Bond 7 Studio-gallery

2005 BRIDGES conference, Banff, Canada (see the article in the conference volume)

2005 Spidrons - One-man exhibition in exhibition hall Budapest Kiállítóterem (5 Szabad sajtó Road, Budapest, 1056)

2005 Spidron composition - Plastic work installed in the lounge of Jövő Háza

2006 7g4g (Gathering for Gardner), Atlanta

2006 Hungarian Cultural Institute, New York,

2006 London, BRIDGES (see the article in the conference volume)

2006 Spidron-plastic installed in the lounge of the building of the directorate of National Rehabilitation Institute

2006 Presentation - Pécs – Cultural Capital of Europe, a lecture held in the Cultural Center

2007 Pécs, one-man exhibition and lecture in the Közelítés Gallery (Király Street)

2007 Moscow, Rossupack – lecture and workshop; the guest of honour at the world expo of wrapping technology

2007 San Sebastian, Spain, an exhibition related to the conference BRIDGES

Prizes for the Spidron project:

2004 Genius Budapest – inventors' gold medal;

2007 Knight's Cross Order of Merit of the Republic of Hungary

The stages in the history of Spidron:

The history of the spidron goes back to 1979, when as a student of Ernő Rubik's at Hungarian Academy of Applied Arts, I created the first swirling relief for the theory of form class. Rubik's evaluation was: "I've never seen a thing like that!" Ten years later I managed to compile a closed, spatial shell-structure of one of the components, the six-armed spidron-nest. In 1994 I met Cristiana Grigorescu, a Romanian optical crystal physicist, who did her best to persuade me to present my idea at the 12th International Congress of Crystal Growth in Jerusalem. Since then I have received invitations on end in Hungary. The most important lectures I held were the presentation at MTA's Szeged Division and the lecture at the Mathematical Research Institute (now called Rényi Institute) at the request of Symmetry Foundation. The year 2000 saw the widely appreciated exhibition in the Art Hall, titled "Intuition, Innovation, Invention", which was initiated by László Beke, created by scientists, artists and inventors. Here the spidron system played a space filling role. Then the interest in the spidron seemed to be flagging for a while, except for some scientific news coverages – but it proved to be the silence before storms; after 2000 the interest burst out again. The break-through was due to Dr Lajos Szilassi's work, who managed to provide a mathematical description of the spidron movements. Now, let's see the events between 2003 and 2006.

August 16-22, 2003."'Symmetry Festival and Ars(Dis)Symmetrica"' Budapest, Hotel Agro Lecture, exhibition and an article in the festival's publication: Spidron System http://www.conferences.hu/symmetry2003/festival-Pre.htmlhttp://www.matud.iif.hu/04jan/013.htmlInternational Symmetry Foundation

May 21-22, 2004Folding Selection Conference Pécs, PTE Pollack Mihály Technical College, a lecture on the geometry of the spidrons, co-held by Dr. Szilassi Lajos. The material of the event was published in a book, too. http://matserv.pmmf.hu/hajtas/

May 1- 4, 2004 Genius Europe EURÓPA International Expo of Inventions, Applied and Fine Arts HUNGEXPO Budapest Fair Center, "F" pavilion. Géniusz Budapest Prize.

October 1, 2004.Spidron II.A lecture at a session of Filozófiai Vitakör (Philosophical Discussion Circle), MÁFI Directorate's Conference Room

October 14, 2004 Spidron systemA lecture in the Geometry Department of technical university BME"The extraordinary characteristics of the triangle complex in the plane and in space"

October 14, 2004 OrnametriaErdős Renée Ház http://www.artportal.hu/aktualis/hirek/?hir=2004-10-12

October 23, 2004Minimal - 4th Arnolfini Autumn Festivalexhibition and lecture http://www.arnolfini.hu

November 26, 2004 Ars & Mathesis Baarn, Holland. A lecture held at the invitation of the Ars & Mathesis Foundation http://www.arsetmathesis.nl/

December 19, 2004Sacra Geometria 2B Art Galleryhttp://www.pipacs.hu/2b/

February 23, 2005Spidron geometryDemonstration lesson in Lauder school

March 10, 2005 SuliNovaThe presentation of the spidrons for the educational development program SuliNova. ELTE Department of Mathematics.

June 25 – September 5, 2005 PassagesBos van Ypeiy, Holland. Open air sculpture exhibition near Leeuwarden, together with 11 other artists. The premiere of the Spidrohedron sculpture. Master joiner: István Sági. http://www.vijversburg.nl/activiteiten.php?vid=75&an=2http://www.tietjerk.nl/ypey/passages/passages-officiele-opening24-6-05.html

June 29, 2005Spidron New York, workshop exhibition and presentation in Louise McCagg's studio

June 31 – August 3, 2005BridgesBanff Centre, Alberta, Canada

August 8, 2005The first big-size spidron painting, acryll and canvas; I made it together with John Hiigli in New York.

October 12, 2005SpidronOne-man exhibition in the exhibition hall Budapest Kiállítóterem. "The history of the development of the spidron system from 1979 to date" http://www.szinhaz.hu/edan/SpidronGallery/opened by: Professor Borisz Szántó, privatdocent

October 12, 2005Spidrons Workbook - Spidronok MunkafüzetA bilingual, 16-page-long publication, which presents the basic constructional rules of the spidron, its plane- and space-filling versions, as well as the way it can be moved and other characteristics through exercises.http://www.szinhaz.hu/edan/SpidronWorkBook/The preface to the 16 page catalogue was written by Dr László Beke, director of MTA Art History Research Institute. The diagrams were made by me and Rinus Roelofs.

November 11-12, 2005Varga Tamás Methodology Days A lecture in the English-language sectionSpidrons http://www.sulinet.hu/tart/fcikk/Kcs/0/28595/1

December 2, 2005 –January 3, 2006. Spidron exhibitionin the Vályi Péter Vocational School, Tamási http://valyip-tamasi.uw.hu/e107_plugins/coppermine_menu/thumbnails.php?album=11The exhibition was opened by art writer Zsuzsa Dárdai.

December 16, 2005SpidronplasticBudapest, the lounge of Jövő Háza: in the entrance hall of the Millennáris Park there is a hanging spidronplastic of a 4.5 m diameter. http://www.szinhaz.hu/edan/Millenaris/Architect: István Tenke. Master joiner: István Sági.

January 6-11, 2006Spidron 0 International Spidron Meeting in Wijk van Aalburgban (Holland), where we surveyed the most recent findings about the spidron, compared our ideas and outlined the tasks for the coming period.http://www.spidron.hu/spidron0.htmlParticipants: Amina Allen, Dániel Erdély, Simon Erdély, Marc Pelletier, Rinus Roelofs and Walt van Ballegooijen

March 16-19, 20067th Gathering for GardnerAtlanta, USA, Hotel Ritz-Carlton

March 16-19, 2006TRIANGLEHungarian Cultural Institute, New York "Extruding Art from a Flexible Space-Filling Structure"Presentation and exhibition of the latest spidron models. http://www.gimagine.com/gimagine/HCC/2006/2006-03-21-Spidron-Daniel_Erdely/default.htmJazz drummer Imre Kőszegi provided the musical background for the projection.

April 19, 2006Spanyolnátha Művészeti Hálóterem http://www.spanyolnatha.hu/http://www.spanyolnatha.hu/sp/index.htmlEditor-in-chief: Tibor Vass

May 4, 2006Spidron exhibition in the Bárka TheatreThe Bárka Theatre celebrated my 50th birthday by displaying the exhibition titled Spidron, which was preceded by a play of Mrožek. Its title was The Party. http://www.theatrefestival.hu/index.php?id=1266&cid=14765The exhibition was opened by composer Béla Faragó.

May 10 – June 30, 2006SupreMADIsmMoscow. International geometrical artistic and constructivist exhibition and symposium. A part of the event series where I presented the latest versions of the Spidron. http://www.gyoriszalon.hu/hetnap/index.php?t=MADI3.htmlThe event series was organized by the Moscow Hungarian Cultural Center, the Museum of Modern Art and the MADI Foundation.

July, 2006 ORNAMETRIA II. Erdős Renée Ház – the exhibition was opened by Dr László Beke.

August 4-7, 2006BridgesLondon, Institute of Education Bridges between Mathematics and Art and Music. Here were the latest results of the Spidron research presented.http://www.lkl.ac.uk/bridges/programme.htmlhttp://www.sckans.edu/~bridges/

August 19, 2006SpidronreliefBig-size spidronplastic made of wood, National Rehabilitation Institute, Budakeszi http://www.szinhaz.hu/edan/rehab/Interior desigjer: István Szenes, master joiner: István Sági.

Articles, news bulletins and studies:

December 20, 2004.MathForum @ Drexel InternetNews http://mathforum.org/electronic.newsletter/mf.intnews9.51.html

November 15, 2005Válaszd a tudást! (Choose knowledge!)An interview with Dr Emil Molnár, leading professor of the Geometry Department, technical university BME, and Dániel Erdély. http://mtv.hu/cikk.php?id=73882Anchorman: Balázs Gaskó

Kikötő An interview and report

Kultúrház

2003/6. Old-New Hungarian Architecture – EpilogueSpidron systemThe diary of a geometrical adventure, i.e. the extraordinary characteristics of a triangle complex in the plane and space (plane filling, space filling, deformation) – an article by Dániel Erdély

SuliNet Dániel Erdély: On the Spidron systemhttp://www.sulinet.hu/tart/ncikk/Raf/0/8339/cikk_2.htm

January 24, 2005 Népszabadság: A cathedral of sticks and the infinity by Erzsébet Bogácsi http://www.pipacs.hu/2b/sajto30.html

June 25, 2005Passages – open air exhibition Bos van Ypeij, Holland exhibition, catalogue

October, 2005Comments to an exhibition A report on the exhibition in the Budapest Gallery, on the website of the SuliNet

October 22, 2005HVG: The puzzling spidron by Tamás Vajnahttp://hvg.hu/print/200542HVGFriss159.aspx

2005/44Élet és Tudomány: Being on a visit by Márta Kádár

October, 2005 Ponticulus Hungaricus: Object-history http://members.iif.hu/visontay/ponticulus/rovatok/hidverok/spidron1.html "'Proceedings of the BridgesRenaissance; Some Surprising New Properties of Spidrons"' by Dániel Erdély Banff Canada;

January, 2006Péter Mújdricza: Spidron chainsDániel Erdély's exhibition in the Budapest Gallery.Appeared in the XVII / 1 issue of Művészet

May, 2006 Ornametrics catalogueA publication by the Reneé Art Association – MTA Art History Research Institute, comprising the material of the symposium held about the exhibition

July – August, 2006 Ponticulus Hungaricus; SpidronNotes II. http://members.iif.hu/visontay/ponticulus/rovatok/hidverok/spidron_b.html

July, 2006 "'Proceedings of the Bridges, London – The Expanding Spidron Universe"'by Dániel Erdély & Marc Pelletier

October, 2006 Ivars Peterson: Swirling Seas, Crystal Balls Spirals of triangles crinkle into intricate structuresAn article in scientific magazine Science News on the Spindrons, on 2.5 pages and on the cover.

October 31, 2006What is the spindron good for?Népszabadság

November 3, 2006Dániel's invention became world-famousSzínes Magyarország

November 7, 2006Треугольные моря готовят инженерам спиральные достиженияMembrana – Russian language internet portal

November 17, 2006A world sensation whirling in spider webSzabad Föld – Tibor Borzák

December 10, 2006The magic spidron is a world attractionTamás Bodoky –internet daily Index

December 21, 2006Versatile SpidronFigyelő

December 28, 2006.The magic spidron, the special and new space filling entity, is a world attractionMagyar Hírlap

February, 2007The pattern is inside Kristóf Fenyvesi – Dániel Erdély; contemporary art magazine Balkon, 2007/1.

January, 2007SpidronsTony Philips; Math in Media - American Mathematical Society

February, 2007Spiraling TrianglesMUSE magazine, USA – Ivars Peterson

Many spidrons are designed to correspond to deformed spidrons that are also polyhedra.

References

External links

* [http://www.spidron.hu/ Spidron Main page]
* [http://www.szinhaz.hu/edan/SpidroNew/ Spidron Geometric Systems]
* [http://www.szinhaz.hu/edan/spidronatlanta/ New Developments]
* [http://spidron.hu/pecs/spidron_eng.html The Pécs Exhibition on Spidron homepage]
*cite journal| url=http://www.sciencenews.org/articles/20061021/bob11.asp| month=Oct. 21| year= 2006| volume= 170| issue= 17| pages= 266| title=Swirling Seas, Crystal Balls| first=Ivars| last= Peterson| journal=Science News| accessdate=2006-10-21| doi=10.2307/4017499| format=Dead link|date=May 2008