Gaspard Monge: Founder of descriptive geometry

GASPARD MONGE was born on May 10, 1746 at Beaune, France, the son of an astute knife-grinder. He received his education at the college in Lyons, which was run by a religious order. Impressed by his brilliance, the College superiors begged him to join their order. But his father did not give the consent. In 1762, Monge constructed a wonderful map of Beaune, employing the surveying instruments made by him for the purpose. An officer from the corps of engineers, who saw this map, used his influence to permit Monge to attend some courses at the military school, Mezieres. Fortunately for Monge's future career as a scientist, the officer omitted to state that on account of his humble birth, Monge would never be commissioned.

An important part of the regular course at Mezieres was the theory of fortification, in which the problem was to design the works so that no part should be exposed to the direct fire of the enemy. Monge handed in his solution which was checked and found to be correct. He soon became a member of the teaching staff in 1768.

This was the beginning of descriptive geometry, which is described later. For 15 years it was a jealously guarded military secret.

Monge's career spanned the period of revolution and the period of imperialism. Throughout the revolution he might have found himself on the scaffold!.

Monge worked in different capacities: Professor in the Military School at Mezieres (1765-80), Institute for Hydraulics, Louvre (1780-83), Examiner for candidates in the Navy (1783-89), Minister of the Navy (1792- 93), Director of the newly founded Ecole Polytechnique, Paris (from 1795).

What is Descriptive Geometry?

"One simply takes two planes at right angles to each other, one vertical and the other horizontal then projects the figure to be represented orthogonally on these planes, the projections of all edges and vertices being clearly indicated. The projection on the vertical plane is known as the ``elevation'', the other projection is called ``the plan''. Finally, the vertical plane is folded about the line of intersection of the two planes until it also is horizontal. This puts on one flat sheet of paper what we ordinarily visualise in 3D".

(A History of Mathematics by Carl B. Boyer, John Wiley & Sons, New York, 1991)

Monge was sworn not to divulge the above method and for 15 years, it was a jealously guarded military secret. Only in 1794, he was allowed to teach it in public at the Ecole Normale, Paris where Lagrange was among the auditors. ``With his application of analysis to geometry, this devil of a man will make himself immortal'', exclaimed Lagrange.

R.Parthasarathy

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