Celtic Möbius strip by Paul Bielaczyc

Celtic Möbius

by Paul Bielaczyc

Colored Pencil and Ink, 21" x 13".

In this image by Paul Bielaczyc we see joining of aspects of artist's life. As he says Celtic knots surround him in his job, M.C. Escher who has always bee inspiring in his art and the Möbius strip as intriguing mathematical form.

Staircase knot

This strange composition of staircase reminds Möbius strip, but unlike Möbius strip this figure has two sides. So someone, who will try to rise this stairs, will continue rising infinitely returning to the starting point.

The sculpture also reminds one of the famous Escher's images "Knots". One of the them you can see below. This knot is also not a Möbius strip, because it has four sides.

Snow sculptures from Breckenridge

Lately, we published snow sculpture by Bathsheba Grossman which was represented at Breckenridge snow sculpture contest. Here some other mathematical snow sculptures represented at Breckenridge in other years.

Knot divided (2005)

This is a triply twisted Moebius band. There is a self-referential beauty in our sculpture: If one forms a Moebius band by twisting a belt through three half-turns (instead of just one), then the band's edge forms a trefoil knot.

Whirled White Web (2003)

This sculpture is a 3-fold symmetrical whirl of twisted and stretched saddle shapes. Such saddles occur naturally in soap films that are spanning warped wire frames; such "minimal surfaces" are nature's way of creating strength in delicate structures. Our sculpture uses these natural ideas to create an intricate network of ribs and internal spaces suspended from a web of three mutually interwoven double loops.

Turning a Snowball Inside Out (2004)

In the 1960s, mathematicians showed how to turn a sphere inside out. To do this, the surface must pass through itself, but no tears or creases are allowed to form at any point. This design is an artistic interpretation of the halfway point of such a sphere-everting process, where the surface displays half of its outside, shown as a solid form, as well as half of its inside, rendered as a transparent grid.

Here we see a snail shell but it's also a representation of fractal twisting to it's center.

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This article was created by materials of
http://www.cs.berkeley.edu/~sequin/SCULPTS/sculpts.html

Möbius strip

Möbius strip a surface with only one side and only one boundary. It was first described in 1858 by German mathematician August Ferdinand Möbius and co-discovered by Johann Benedict Listing in the same year.

The most known illustration of the surface was created by M.C. Escher in his lithograph "Möbius band II" where read ants crawl by the Möbius strip.

Also it frequently being used in logos. The most famous is international symbol of recycling.