Impulsive Arts

The Mobius: Strips and Sculptures

The Mobius strip, at its simplest, may be modeled by taking a flat strip of paper and giving it a half twist before joining the ends.  The resulting structure has many intriguing properties, most notably the fact that it has only one surface and one edge.   A variety of fascinating hollow structures may be generated from the notion of a non-orientable surface, and metal crochet offers a versatile construction method. 

The properties of the mobius and its derived structures make it a natural symbol for the unity of all things and the illusory nature of duality.  It has also been used to represent concepts such as rebirth, and the cycles of continuous change and renewal in the natural world.

My own Cocoon pendant in silver, gold, and amber:

 

I was intrigued by the idea of combining a symbol of One-ness with a form that is intrinsically sheltering and nurturing.

Further resources:

Mathematics of the Moebius strip and related structures such as the Cross-cap and the Klein bottle.

The Moebiustorus - a fabulous sculpture by Rinus Roelofs - the rest of the gallery is also well worth a look.

Battered Moonlight - a sculpture by George Hart.

M.C. Escher's famous Ants woodcut.

Hyperbolic Space

Though easily modelled in crochet and knitting as a steadily increasing ruffle, hyperbolic space was a radical discovery that challenged the old Euclidean notions of linearity.  In hyperbolic space, multiple "straight" lines may pass through a given point without intersecting, a feat not possible in Euclidean geometry and with fascinating implications for the understanding of the structure of our universe.

In biology, examples of hyperbolic planes abound, including ruffled lettuces and, in the ocean reef environment, sea slugs, nudibranches and flatworms.  This pattern of growth is a very efficient way to create maximal surface area in a limited space.

My own Orchid, crocheted in fine silver:

Further reading on hyperbolic space:

From the Institute for Figuring: a very readable introduction to the subject, with lots of illustrations and interesting links:   http://theiff.org/oexhibits/oe1.html  Particularly intriguing is their gallery of crochet models, especially the coral reef project.

The application of hyperbolic symmetry to tiling patterns, particularly favored by the famous Dutch artist, M.C. Escher:  http://www.sciencenews.org/articles/20001223/bob8.asp

Hyperbolic tile patterns by Jos Leys:  http://www.josleys.com/show_gallery.php?galid=262

A discussion of the influence of non-Euclidean geometry on modern art: http://math.mohawkcollege.ca/ocma/conf05/Post_Conf05/john_Modern_%20Art.pdf