Whether we call it a Strip, Band or Loop, in simple terms & in our 3-dimensional world, the Möbius strip is a figure that can be built by attaching the ends of a strip of paper (or metal, etc.) together after giving one end an odd number of half twists. In strictest Topological sense, any 3-Dimensional ‘Möbius Loops’, such as those built by Daniel Salisbury, are an approximation of the theoretical Möbius Loop which by definition has no thickness.

The Möbius Loop has two distinct qualities

1) The quality of having only one single surface. Any odd number of half twists will render a form which has only one surface.

2) The quality of being non-orientable, which in simplest terms means it has no inherent up or down, inside or outside.

Excavations in the Marche region of Italy unearthed evidence that the ancient Romans were familiar with the idea of the one sided band. 

Aion mosaic ca. 200–250 C.E.

A dramatic example, known as the Aion mosaic, was excavated at the site of an ancient Roman era villa just outside of the modern town of Sassoferrato. Featured are Aion (Uranus), the young man standing within the circle of the Zodiac, and Tellus Mater (Terra, Mother Earth), sitting in the right corner with the four seasons.  In Roman symbolism of the time, Aion’s association with the Zodiac and the Seasons implies the eternally cyclical & uninterrupted return of events and things.

The Möbius Strip, as we know it, emerged in the 1850’s from the realm of theoretical mathematics now known as Topology.  The idea of the Strip was discovered almost simultaneously by two German mathematicians in 1858. August F. Möbius for whom the band is named, and Johann B. Listing, who coined the term Topology, each conceived of the band in their studies of surfaces, apparently without knowledge of one another’s work.

Swiss artist Max Bill (1908-1994) was a pioneer in sculpting Möbius strips. Starting in the 1930s, he created a variety of "endless ribbons" out of paper, metal, granite, and other materials. Initially unaware of the mathematical history, he believed he had invented a completely new shape.

Perhaps the most well known expressions of the Möbius band were produced by the famous Dutch artist M.C. Escher in the early 1960s. Two of Escher’s best known prints graphically represent the Möbius band and its enigmatic quality of endless single-sidedness.

Max Bill ‘Endless Ribbon’ 1953

Today, we see the Möbius band’s inherent idea of endless connected cycles in the ubiquitous modern recycling symbols.

Scholarly description, study and definitions of the Möbius Strip are found in various Topological treatises. For the technically minded, a concise and deep dive into the mathematics can be found here: