Saturday, May 10, 2014

Caspar Monge and the Geometry

(1746 – 1818)
On May 10, 1746, French mathematician Gaspard Monge, Comte de Péluse was born. He is best known for being the inventor of descriptive geometry as the mathematical basis of technical drawing, and being the father of differential geometry. During the French Revolution Monge served as the Minister of the Marine, and was involved in the reform of the French educational system, helping to found the École Polytechnique.

Monge, the son of a merchant, was taught at the college of the Oratorians at Beaune and the Collège de la Trinité at Lyon. When Monge was only 17 years old, he was appointed teacher of physics. He began to invent his own instruments in order to complete a large-scale plan of the city of Beaune. Monge's work was very well received and it was displayed in the local library were it remained until today. A local engineer saw Monge's masterpiece as well and he recommended the young scientist to the École Royale du Génie at Mézières where he started as a draftsman.

However, Monge was unfortunately not allowed admission to the institution itself. He became widely known for his great manual skills, but his mathematical skills were not yet discovered. After a year at the École Royale, Monge was asked to produce a plan for a fortification in order to optimize the city's defense. Instead of calculating the problems, Monge found his solutions through drawings. As a result of Monge's work, his reputation grew dramatically. Monge was appointed instructor in experimental physics in 1770 and in 1786 he wrote and published his Traité élémentaire de la statique.

Gaspard Monge was known to be a very strong supporter of the French Revolution. He accepted the office of Minister of the Marine in 1792. When the Committee of Public Safety made an appeal to the academics to assist in the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his energy, writing the Description de l'art de fabriquer les canons and Avis aux ouvriers en fer sur la fabrication de l'acier. Monge made great contributions in the establishment of the school for public works, later on the École Polytechnique. There, Monge was appointed professor for descriptive geometry and later on even director of the institute.

In the following period, Monge joined Napoleon Bonaparte's expedition to Egypt, taking part in the scientific work of the Institut d'Égypte and the Egyptian Institute of Sciences and Arts. After Egypt, he followed Bonaparte to Syria and returned to France in 1798. Gaspard Monge passed away on 28 July, 1818 and in Beanue, a statue portraying him was erected a few years after. Monge is considered the father of differential geometry because of his work Application de l'analyse à la géométrie, in which he introduced the concept of lines of curvature of a surface in 3-dimensional space. He developed a general method of applying geometry to problems of construction. He also introduced two planes of projection at right angles to each other for graphical description of solid objects. These techniques were generalized into a system called géométrie descriptive, which is now known as orthographic projection, the graphical method used in modern mechanical drawing.

At yovisto, you may be interested in a video lecture on Differential Geometry by Professor Wildberger.

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