# The Mathematical Tourist

March 31, 2010

## Knotted Staircase

It looks like a spiral staircase that had lost its way before finally winding back to its starting point. The looped sculpture, titled Révolutions, stands in a little park near the entrance to the Papineau Métro station in Montreal. Created by Michel de Broin, the artwork pays tribute to the curving iron stairs that serve as entries to many city residences.

Constructed from aluminum, the sculpture stands on several legs, lifted about 10 feet off the ground.

In this case, the elevated, twisty staircase forms a mathematical knot, with no end and no beginning. "Stairs are a symbol of progress, of linear inward and upward," de Broin notes, "but in the knot they become a continuous circuit."

When I saw the sculpture on a recent visit to Montreal, I couldn't quite figure out what type of knot it is. But I could tell right away that the loop was not one-sided or one-edged, like a Möbius strip. The main clue was the railing. It did not appear on all sides of the knotted, spiraling staircase as it would have if the surface were truly one-edged.

At the same time, knots and Möbius strips are not incompatible. Artists have been creating striking Möbius strip trefoil knots, for instance. John Robinson's Immortality is one notable example.

From any angle, Révolutions is an unexpected pleasure and a treat for mind and eye.

Comments are welcome. You can reach Ivars Peterson at ipeterson@maa.org or visit the blog version of this article at http://mathtourist.blogspot.com/.

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