The Parterre actually predates the creation of the Enid A. Haupt Garden. In celebration of America's bicentennial, a parterre, inspired by a design from the 1876 Centennial Exposition's Horticultural Hall in Philadelphia, was created behind the Smithsonian Castle in the south yard. When the Enid A. Haupt Garden was created the parterre was saved and incorporated into the new formal garden.

What is a Parterre?

A parterre is an embroidered, flat flower bed, where the dirt, grass, edging shrubs and flowers together form elaborate, compartmentalized patterns. The term (parterre de broderie) was used by gardeners to the French court in the seventeenth century; however, the idea may have been introduced by Catherine de Medici and her Italian gardeners a century earlier. The word parterre may, in fact, come from the Italian, partire - to divide as opposed to from the French par terre - on the ground.
From Penelope Hobhouse's Gardening through the Ages (Simon & Schuster,1992).