Known as the father of descriptive geometry, Gaspard Monge (1746-1818) was born in Beaune, Burgundy in France. Attending college at an early age, Monge showed mathematical talent early on. He drew a plan of his home town at age eighteen that brought him to the attention of the École Royale du Génie in Mézières where he became a draftsman in 1765. The next year he was asked to draw plans for a fortification. Putting his mathematical talent to use, Monge devised his own method of representing the vertical and horizontal components of an architectural drawing.

His new approach to geometry came to be known as descriptive geometry. Monge describes his new geometry as “representing with exactitude, within drawings that have but two dimensions, objects that have three.” In particular, by showing the vertical and horizontal projections of an object on one piece of paper (the paper is divided in half horizontally with the vertical projection on the top and the horizontal projection on the bottom) geometric properties can be employed to determine various elements of the surface depicted such as angles of intersection and lengths. All such properties of three-dimensional objects are essential for the accurate design and construction of various buildings, as well as other design objectives of engineering. The term descriptive geometry is still used for this method of representing the vertical and horizontal projections of an object. However, the modern term for the method is orthographic projection.

Label on Jullien's Collection of Reliefs |

France found this new geometry so important to fortification design that it was held as a state secret for several years. An example is the design of star forts. Star forts were invented in Italy in the fifteenth century and became common in Europe and the New World the following century. With the advent of larger cannons, fortifications needed to be more thoughtfully designed to withstand and deflect cannon fire. The broad bases and angled walls of star forts helped deflect cannon fire. The straight, angled walls allowed defenders to launch enfilade or flanking fire: firing crossways at the enemy from the points of the stars so the attackers have no safe place to fire from and keeps attackers further from the walls. Previously, forts often had rounded walls which allowed for “dead zones” where defenders could not fire upon the attackers. Beautiful images of star forts can be found online.

Monge went on to become a teacher at Mézières as well as a member of the Académie des Sciences. He further developed descriptive geometry, teaching it and publishing text books. The teaching of descriptive geometry quickly spread throughout France and ultimately at the United States Military Academy at West Point, founded in 1802. Other practitioners took up the mantel and published texts on descriptive geometry. One such teacher and text book writer was French mathematician A. Jullien.

Jullien, taught at the Lycee Sainte-Bartie in Paris. He wrote a descriptive geometry text book, *Cours élémentaire de géométrie descriptive*. The 3^{rd} edition published in 1881 is available online through Google Books. The reliefs or models in the Smithsonian collection are teaching aids made by Jullien to supplement this textbook, just as modern mathematical text books come with online applications that show the geometry of the mathematics being discussed. Each of the thirty reliefs show a construction of descriptive geometry. The reliefs start with the most simple of geometric ideas and progress to more sophisticated constructions. The models held by the Smithsonian were produced in the mid-1870s, but after 1873. In that year a set of Jullien models won a certificate of merit at the Scientific Exposition in Vienna.

The thirty models are housed in a hand-crafted wooden box lined in pink and cream stripped satin. A small pamphlet entitled *Notice Explicative *describing the assembly and concept of each model is also in the Smithsonian’s collections.

Box holding Jullien's Collection of Reliefs |

**References:**

Martínez, A.O., *Kinematics: The Lost Origins of Einstein’s Relativity, *Johns Hopkins Press, 2009, g. 45.

J. J. O'Connor and E F Robertson, *Gaspard Monge*, Mac Tutor History of Mathematics website, https://www-history.mcs.st-and.ac.uk/Biographies/Monge.html

*Types of Castles and The History of Castles: Star Forts,* https://www.castlesandmanorhouses.com/types_10_star.htm.

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