Computer methods in descriptive and differential geometry Monge's legacy
Kristen Anderson Wottreng, University of Illinois at Chicago, United States
University of Illinois at Chicago . Awarded
This thesis examines the mathematical history of Gaspard Monge (1746–1818) and his influence on the development and teaching of descriptive geometry and differential geometry at the end of the eighteenth century. Monge's mathematical ideas are investigated from the point of view of understanding what his methods were, how his methods were effective in the teaching of descriptive and differential geometry, and how they might apply to teaching a more explicitly descriptive course in undergraduate differential geometry today.
We examine Monge's educational, professional, and political life in relation to the mathematical climate in France during this time period. Our investigation proceeds chronologically and focuses on Monge's passion for studying and teaching mathematics, his career as a professor at the Military Academy Mezieres, his role in establishing the Ecole Poytechnique and the reform of the mathematical and technical education in France, his participation in the politics of the French Revolution, and his subsequent friendship with Napoleon which played an important role in the direction of his mathematical career.
We show examples in descriptive geometry of surfaces of revolution and their intersections which illustrate the merging of Monge's results with the technology of the Geometer's Sketchpad and conclude that the mathematical examples which provided new and interesting problems two hundred years ago, suitably interpreted, are effective examples today.
We show how Monge applied his visually descriptive approach, but in a more sophisticated and subtle manner, to the study of differential geometry of curves and surfaces in three dimensions. We interpret Monge's complex mathematical ideas through a more advanced use of Geometer's Sketchpad or the more powerful graphic capabilities of Maple V.5 in understanding the radius of curvature of space curves, evolutes of space curves, the curvature of surfaces, and ruled and developable surfaces.
Wottreng, K.A. Computer methods in descriptive and differential geometry Monge's legacy. Ph.D. thesis, University of Illinois at Chicago.
Citation reproduced with permission of ProQuest LLC.
For copies of dissertations and theses: (800) 521-0600/(734) 761-4700 or https://dissexpress.umi.com