Holes in the Polygon: Marguerite de Ponty and the Art Gallery Theorem
November 1, 2009, 1 annotation
The second floor of the three-floor Urs Fischer Exhibition—titled “Marguerite de Ponty” and now on view at the New Museum—is a dense installation composed of 51 chrome steel boxes. Enough has been or will be said about the work itself, which deserves the column inches. I’d like to talk about the installation not in terms of the art or its meaning, but, instead, from the point of view of the museum guard, and specifically from the perspective of how many guards are needed for surveillance.
At a conference at Stanford in August 1973 mathematician Victor Klee—in response to a request from Vasek Chvátal for an interesting geometric problem—posed the question of determining the minimum number of guards necessary to cover the interior walls of an art gallery. In what came to be known as the Art Gallery Theorem, Chvátal proved that “[n/3] guards are occasionally necessary and always sufficient to cover a polygon of n vertices.” A variation of the equation [3n/11] accounts for structures within the gallery, such as freestanding walls, by treating them as “holes” in the polygon.
When I visited the museum, the four second-floor guards seemed to have their hands full. Continually on the move from point to point, it’s a small wonder why they were so busy. According to [3n/11], the number of stationary museum guards required to cover every surface of the installation—with its four walls, elevator shaft, and 51 boxes (weighing in at a grand total of 212 vertices)—would be in the neighborhood of 58, a number that not only reaches the gallery’s maximum occupancy (for this installation it’s 40), but exceeds it by eighteen.
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November 12th, 2009 @
[...] Private Circulation examines the Urs Fischer show at the New Museum from the perspective of how many guards are needed for surveillance. [...]