When the prestigious architectural firm Foster + Partners wanted to display a Möbius strip in the entrance of their corporate library, they called Geometrica. What a fun project — and quite a departure from the long span domes we build around the world.

The Möbius strip is one of the most famous surfaces known to mathematicians, largely because it changes a seemingly ordinary construct into something extraordinary! Young math students might be introduced to the basic concept as an arts and crafts project:

• Cut a paper strip

• Half-twist the strip 180 degrees

• Join (tape or glue) the ends of the strip together to form a loop

• Voila — a Möbius strip is born!

* ** Graphic of a Möbius strip The actual product under construction*

Interestingly, the strip seems to have no beginning or end. Try as we might to define a surface normal at a point, it is impossible to extend the definition to the whole surface.

Our 12 foot creation was a bit more complex. Geometrica employee Jorge Parada and representative Jerry Forrest built a single closed continuous curve with a twist, but did so from a geometrical network of metal tubes constructed as a one-sided, one-edged, non-orientable surface. The tubular members were designed by a computer program, manufactured at our facilities in Mexico, barcoded and then shipped to London to be assembled on site at the Foster + Partners library. Then our metal Möbius strip was displayed for all to enjoy.

*Fully assembled and ready to be displayed*

Origins of the Möbius Strip

The Möbius Strip was named in honor of German mathematician August Ferdinand Möbius, who discovered it in September of 1858 as he studied polyhedra. As a side note, apparently fellow mathematician Johann Benedict Listing had documented the concept a few months prior, but Möbius, for whatever reason, received "top billing" — and the world has called it the Möbius strip ever since. The Möbius strip is also referred to as a Moebius loop or Mobius band (with various spellings and with or without the German umlaut).

There are a wide variety of geometric versions of the Möbius strip depending on the size and shape of the surface used. Some versions can be smoothly modeled in Euclidean space, while others cannot. The Geometrica version was round, but any closed rectangle with length L and width W could be glued to itself after reversing the orientation. Often the configuration is a figure 8. In fact, people tend to confuse the Möbius strip with the infinity symbol, which resembles a "lazy 8."

* Infinity symbol Example of a Möbius band configured to an "8"*

For Geometry Enthusiasts

Geometrica is a global designer and installer of geodesic domes. Our engineers and architects rely on geometric principals to achieve the long spans necessary to cover raw materials in the mining, cement, power and fertilizer sectors. We use also geometry to achieve stunning architectural projects such as retail centers, houses of worship and airports. In fact, Freedome® technology has revolutionized dome design by providing barrier-free space on any topography, slope or climate — up to 300m. That's longer than three football fields!

For those who are curious, please visit our geometry page to see the structural shapes inherent in our building systems.

The question is, "What can Geometrica design for you?" To learn more, please inquire below.