A Symbol for Global Circulation

The recycling symbol consisting of three bent arrows is found on bottles, cartons and packaging of all kinds. It originated in 1970 when the Chicago-based Container Corporation of America (CCA) held a competition for the design of a symbol suitable for printing on cartons, to encourage recycling and re-use of packaging materials.

Recycling-Symbol-2Verions

Original (Moebius) and a variation (3-twist) of the universal recycling symbol.

The competition for art and design students across America was arranged in conjunction with the first Earth Day, 1970. There were over 500 entries and the winner was Gary Anderson, a senior at UCLA. He designed the symbol in the form of a Möbius band, a one-sided surface formed when a strip of paper is twisted once before the ends are joined.

The Möbius band has the curious property of having only one surface and one edge. It is possible to move from any point on the surface to any other point without crossing the edge. The surface was discovered independently by August Möbius and Johann Listing in the same year, 1858. This topological object was discussed in an earlier post on this site: Building Möbius Bands.

The symbol has helped the acceleration of recycling, greatly contributing to limiting damage to the planet. Anderson’s original design was modified by Bill Lloyd, PR Manager of CCA, who rotated it to have an apex at the top, revealing the outline of a tree within the negative space of the symbol, a nice environmental touch. It was then adopted for general use. The symbol is not under trademark and is in the public domain.

Variants

Recycling-Symbol-Column

It is a surprising fact that there are two versions of the symbol in common use (see figure). One has the form of a Möbius band, the other the form of a thrice-twisted band. The latter corresponds to joining the ends of a paper strip having twisted it three times. Like the Möbius band, it is a one-sided surface with single edge, but the edge is now knotted into the form of a trefoil knot (the edge of the Möbius band is equivalent to a circle, sometimes called the unknot).

Anderson’s original design had two of the arrows folding over themselves and one under. One over-fold and one under-fold can “cancel”, leaving a single twist, as in a Möbius band. However, most symbols appearing today have three folds in the same sense, corresponding to a band with three twists. It would seem likely that the alternative form was produced by a lazy draftsman who drew a single bent circle, made two more copies and arranged them in a triangle.

Chirality

The symbol usually has the arrows circulating in a clockwise sense. But this is not universal. The Möbius band has two chiral forms that are topologically distinct: they are mirror images of each other, effectively left-handed and right-handed.

Recycling-Symbol-Mirror-Images

In an interview with Penny Jones (1999), Gary Anderson said “The figure was designed as a Möbius strip to symbolize continuity within a finite entity. I used the arrows to give directionality to the symbol.” Anderson was unperturbed by the plethora of variants of the symbol, and happy that it has found such widespread use and value.

Sources

Lynch, Peter, 2017: Building Möbius Bands. That’s Maths Blogpost.

Penny Jones and Jerry Powell, 1999: Gary Anderson has been found. Resource Recycling, May 1999. PDF. 

Long, C., 1996: Möbius or almost Möbius. Coll. Math. J., 27, 277.

Peterson, I, 2003, Recycling Topology. Science News, April 22, 2003. Link


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