24.09.2009.

assignment week 01

THE ETERNAL RETURN


The Mobius strip:

 

The Mobius strip consists of a one-sided surface with only one boundary component and is demonstrated by a single continuous curve. One of its main properties is that of being non-orientable.

 

In order to get the idea of how the continuous surface works, one can imagine a racetrack, where the blue arrows are seen from above (they are visible from our point of view), and the red ones from below.
 

The Mobius strip is also Chiral, meaning its figure is not identical to its mirror image.

In the past, the notion of something constantly recreating itself could already be found in the Ouroboros, an ancient symbol represented by a serpent or a dragon biting or swallowing its own tale. The strong symbology here evidently refers to the cyclical nature of things.

Furthermore, the Klein bottle:

In mathematics, the Klein bottle is a certain non-orientable surface with no distinct "inner" and "outer" sides. Unlike the Mobius strip, the Klein bottle has absolutely no boundary.

Key words relating to the theme:

-    Orientability
-    Boundary
-    Topology
-    Manifold
-    Cyclicality
 

Examples in architecture:
 

www.moma.org/collection/object.php

Max Reinhardt Haus project, Berlin, Germany (Peter Eisenman)

www.archdaily.com/33238/national-library-in-astana-kazakhstan-big/

 National Library project, Astana, Kazakhstan (BIG architects)

Interesting properties and understanding:

I believe the possibility of visiting a surface, by traveling it entirely in one direction and coming back to the starting point is fascinating. In this “eternal cycle” one can reflect on what ground one stands, as one can literally be above or below the strip and still be in the same space. The example of the Mobius strip developed into the Klein bottle is also something curious, as it is a space that has neither proper inside nor outside, the limits are not determined.

Even if there are complex mathematical explanations behind these geometric elements, I believe one can focus on the outstanding visual parameters that define them. In other words, I think there’s no need to be a mathematician to study these forms, the principle can be studied as a concept.