## May 24, 2010

### LeWitt's Pyramid

Sol LeWitt's Four-Sided Pyramid, installed in 1999 at the National Gallery of Art Sculpture Garden in Washington, D.C., consists of concrete blocks precisely stacked to form a stark, eye-catching pyramid. In bright sunlight, the blindingly white blocks and shadows play curious visual tricks on the eye as you view the structure from different angles.

Although the blocks are rectangular, each one equivalent to two cubes attached side by side, LeWitt's structure can look like a huge pile of cubes from some viewpoints. The contrasting white blocks and dark shadows can also create a flip-flopping (isometric) optical illusion, where it isn't clear whether a given vertex is an inside or outside corner.

LeWitt used cubes and multiples of cubes, arranged in myriad ways, as basic components in many of his constructions, both solid and open. Repeating patterns and geometric regularity were also key elements of his art.

LeWitt's approach was to come up with a concept for each structure, often presented as a set of instructions that assistants could then use to construct the object. In the case of Four-Sided Pyramid, a team of engineers and stone masons, in collaboration with LeWitt, built the structure according to his plan.

The stepped shape of the terraced pyramid alludes to the setback design characteristic of many New York skyscrapers, including the Empire State Building. It also references the ziggurats (temples) of ancient Mesopotamia.

Math Problem: How many blocks make up each face of Sol LeWitt's pyramid? Assuming that the pyramid is solid and consists entirely of blocks that are twice as long as they are wide or tall, how many blocks make up the pyramid?

National Gallery of Art in the Classroom: Pyramid Math (pdf).

References:

Lancaster, R., and J. Sandefur. 2005. Sol LeWitt sculpture, four-sided pyramid. Mathematics Teacher 98(February):443.

Peterson, I. 2001. Fragments of Infinity: A Kaleidoscope of Math and Art. Wiley.

Photos by I. Peterson