Spidrons

First, here's the incredibly boring eye-gouging Kill-me-now-Lord Wikipedia version (I present a cooler and better version following) :

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 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.^[1]

The spidrons can appear in a very large 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.

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

References

1. ^ "Swirling Seas, Crystal Balls". ScienceNews.org. Archived from the original on February 28, 2007. http://web.archive.org/web/20070228210951/http://www.sciencenews.org/articles/20061021/bob11.asp. Retrieved 2007-02-14. 

External links

• Spidron Main page
• [1]
• Spidron Geometric Systems
• New Developments
• The Pécs Exhibition on Spidron homepage
• Peterson, Ivars (Oct. 21 2006). "Swirling Seas, Crystal Balls" (^{[dead link]}). Science News (Society for Science &#38) 170 (17): 266. doi:10.2307/4017499. JSTOR 10.2307/4017499. Archived from the original on February 28, 2007. http://web.archive.org/web/20070228210951/http://www.sciencenews.org/articles/20061021/bob11.asp. Retrieved 2006-10-21. 

Retrieved from "http://en.wikipedia.org/wiki/Spidron"

Categories: Geometric shapes

Here is the much more fun version by Clifford A. Pickover in "The Math Book" :


     Journalist Ivars Peterson writes of Spidrons, "A field of triangles crumples and twists into a wavy crystalline sea. A crystal ball sprouts spiraling, labyrinthine passages. Faceted bricks stack snugly into a tidy compact structure. Underlying each of these objects is a remarkable geometric shape made up of a sequence of triangles - a spiral polygon that resembles a seahorse's tail."


     In 1979, graphic artist Daniel Erdely created an example of the Spidron system, as a part of his homework for Erno Rubik's theory of form class at the Budapest University of Art and Design. Erdely had experimented with earlier versions of this work as early as 1975.


     To create a Spidron, draw an equilateral triangle, and then draw lines from the three corners of the triangle to a point at its center, creating three identical isosceles triangles. Next, draw a reflection of one of these isosceles triangles so that it juts from the side of the original triangle. Create a new, smaller equilateral triangle, using one of the two short sides of the jutting isosceles triangle as a base. By repeating the procedure, you'll create a spiraling triangulated structure that gets increasingly small. Finally, you can erase the original equilateral triangle, and join two of the triangulated structures along the long side of the largest isosceles triangle to create the seahorse shape.


The Spidron's significance arises from it's remarkable spatial properties, including its ability to form various space-filling polyhedra and tiling patterns. If we crawl like an ant along the deeper regions of the seahorse's tail, we find that the area of any equilateral triangle equals the sum of the areas of all the smaller triangles. The infinite collection of smaller triangles could all be crammed into such an equilateral triangle without overlap. When crinkled in just the right manner, Spidrons provide an infinite reservoir for magnificent 3-D sculptures. 


Possible practical examples of Spidrons include acoustic tiles and shock absorbers for machinery.


finis

MathMUSEments: Articles for Kids about Math in Everyday Life, written by Ivars Peterson for Muse magazine

Daniel Erdély holds a complex polyhedron constructed from spidrons. Photo by Regina Márkus.