Mobius Strip

Infinity symbol and Mobius strip are synonym for each other. So starting with this post as tribute to my blog.The geometry of the Möbius band has great potential as an architectural form that is difficult to visualize and investigate without the aid of digital technologies. It is possible to develop a building that is a pure translation of the Möbius Band and it furthers a current trend in architectural forms being developed from mathematical concepts beyond mere inspiration. A Mobius strip is a non-orientable surface: you can build one with a strip of paper (twist the strip and glue end together to form a ring) and verify that it has only one side: it is not possible to paint it with two colors.

Mobius strip was named after the astronomer and mathematician August Ferdinand Möbius (1790-1868). He came up with his ‘strip’ in September 1858. Independently, German mathematician Johann Benedict Listing (1808-1882) devised the same object in July 1858. Perhaps we should be talking about the Listing strip instead of the Mobius strip.

A closely related ‘strange’ geometrical object is the Klein bottle. A Klein bottle can be produced by gluing two Möbius strips together along their edges; this cannot be done in ordinary three-dimensional Euclidean space without creating self-intersections.

Mobius Strip has always fascinated architects due its unique character. Lets see the actual execution of this concept.

The Klein Bottle House by McBride Charles Ryan Architects, located in Rye,Australia

We all know this gigantic and unique structure built in Beijing,China. Its a CCTV  buliding by Rem Koolhas and Ole Scheeren while Arup provided the  complex engineering design. It stands at 234 metres (768 ft) tall and has 51 floors.

The main building is not a traditional tower, but a continuous loop of six horizontal and vertical sections covering 4,100,000 square feet (381,000 m²) of floor space, creating an irregular grid on the building’s facade with an open center. The construction of the building is considered to be a structural challenge, especially because it is in a seismic zone. Because of its radical shape, it has acquired the nickname dà kùchǎ , meaning “big shorts”

For more details visit the link below.It will amaze you for sure.

http://beijingman.blogspot.com/2009/01/cctv-tower.html

The Möbius House by UN Studio, Het Gooi, Holland (1993-1998)

In 1993, a young couple commissioned the Dutch architect Ben Van Berkel to design “a house that would be acknowledged as a reference for the renovation of the architectural language”. It took the architect six years to fulfil his client creating a house based on Mobius Strip.

The scheme to convey these features was found in the Möbius band, a diagram studied by the astrologist and mathematician, August Ferdinand Möbius (1790-1868). By taking a rectangular strip of paper and marking its corners, A -superior- and B -inferior- in one side, and C -superior- and D -inferior- on the other, the Möbius band is constructed by twisting and joining corners A with D, and B with C. The result is a strip of twisted paper, joined to form a loop which produces a one-sided surface in a continuous curve. It is a figure-of-eight without left or right, beginning or end.

By taking a rectangular strip of paper and marking its corners, A -superior- and B -inferior- in one side, and C -superior- and D -inferior- on the other, the Möbius band is constructed by twisting and joining corners A with D, and B with C. The result is a strip of twisted paper, joined to form a loop which produces a one-sided surface in a continuous curve. It is a figure-of-eight without left or right, beginning or end.

In terms of architecture, Peter Eisenman pioneered the Möbius form by roughly translating it into the “Max Reinhardt Haus” building.He sliced the form at the ground, thus failing to achieve the visual continuity of the Möbius as a whole.

Glass Sculpture, San Fransisco

http://www.homebysunset.com/home_by_sunset/2008/11/glass-ceiling.html

Thus the Möbius Band has several interesting properties that can be interpreted into architecture. Some of them can be achieved spatially while others can be achieved in terms of form and structure. The infiniteness and paradox of the Möbius can be demonstrated in terms of an enclosure in which one would walk around and feel the spatial twist without having to walk upside down. The continuity, twist and visual dynamism can be generated in terms of form and space where a Möbius Band would split into a flat surface, on which one could walk, and a twisted Möbius surface that could be treated as a wall or a ceiling or even the floor at certain instances. Another unique property of the band that would be very interesting when expressed in architecture is the concept of transformation, the event of the inside
becoming the outside and vice versa. Considering these properties we proceeded to generate a series of variations of the Möbius Band and the Enclosure.