August 15, 2010

Recycling Arrows

The triangle of three bent arrows that signifies recycling is a fixture of the world in which we live. This recycling symbol appears in newspapers and magazines and on signs, bottles, envelopes, cardboard cartons, trash receptacles, and many other containers.

If you look closely, however, you'll see all sorts of variants of this ubiquitous symbol.

In the version of the recycling symbol on this trash container, the two arrows with the same twist are in the lower two corners.

The original design was the result of a contest sponsored by the Container Corporation of America (CCA) as a special event in response to the first Earth Day in 1970. Art and design students were invited to create a symbol to represent paper recycling. The winning logo, selected from more than 500 entries, was submitted by Gary Dean Anderson, then an art student at the University of Southern California.

"The figure was designed as a Möbius strip to symbolize continuity within a finite entity," Anderson recounted in an article published in the May 1999 issue of the trade magazine Resource Recycling.

"I used the [logo's] arrows to give directionality to the symbol. I envisioned it with the small edge or the point of the triangle at the bottom," Anderson said. "I wanted to suggest both the dynamic (things are changing) and the static (it's a static equilibrium, a permanent kind of thing). The arrows, as broad as they are, draw back to the static side."

Anderson's original design was then refined by William J. Lloyd, design manager in CCA's public relations department. He sharpened the lines and rotated the symbol so that the stylized outline of a tree can be seen in its center.

Initially, CCA licensed the design to trade associations for a nominal fee. The company later dropped its application to register the logo as a service mark, leaving it in the public domain.

In the 1970s, the American Paper Institute and the American Forest and Paper Association started promoting use of this symbol to describe recyclable and recycled paper products. Its use spread rapidly and expanded to many other items.

The original design had three bent arrows—two bent in the same direction and one bent in the opposite direction. That still leaves room for variants—the lone, differently twisted arrow can be in any one of three positions, and the arrow portion can be on top or on the bottom.

Some users of the symbol even invert the design, with a point of the triangle toward the bottom.

A more striking variant has three identical bent arrows. Perhaps it was introduced accidentally, when someone failed to notice that the direction of the twists in the arrows makes a difference.

Set within a hexagon, this version of the recycling symbol features three arrows with the same twist, with the arrow heads in the foreground rather than the background.

One possibility is that an illustrator drew just one bent, twisted arrow, made two copies of it, and put the arrows in a triangle pattern, never realizing that the original symbol was meant to conform to the shape of a standard half-twist Möbius band.

A Möbius surface has only one side and one edge. You can make a Möbius strip by gluing together the two ends of a long strip of paper after giving one end a half twist.

Interestingly, the mutant recycling symbol is based on a somewhat different surface—a one-sided band formed by gluing together the two ends of a long strip of paper after giving one end three half-twists instead of just one (as you would have in a standard Möbius strip).

The standard recycling symbol (top left) and an alternative version (top right) can be represented by continuous folded ribbons, showing that the standard form is a Möbius band made with one half-twist (bottom left) and the alternative is a one-sided band with three half-twists (bottom right).

If you were to lay a string along the strip's edge until the string's ends meet and pulled the string tight, you would end up with a trefoil knot in the string. If you did this with a standard Möbius band, you wouldn't get a knot.

The version of the recycling symbol used in Santa Clara, Calif., joins the arrows of the mutant three-arrow form to create a trefoil knot, with a Möbius-like twist.

A few years ago, the original design was the dominant form. Nowadays, you're as likely to see the mutant version as you are to see the original.

In this mutant form, the arrow heads are in the background rather than the foreground.

What's fascinating about the entire recycling-symbol episode is how a geometric shape that came out of pure mathematical research, done in the 19th century by August Ferdinand Möbius (1790–1868), has become a modern cultural icon.


Dyer, J.C. The history of the recycling symbol. Dyer Consequences.

Jones, P., and J. Powell. 1999. Gary Anderson has been found! Resource Recycling (May).

Long, C. 1996. Möbius or almost Möbius. College Mathematics Journal 27(September):277.

Photos by I. Peterson

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