Gaspard Monge was born at Beaune on May 10, 1746, and died at Paris on July 28, 1818. He was the son of a small pedlar, and was educated in the schools of the Oratorians, in one of which he subsequently became an usher. A plan of Beaune which he had made fell into the hands of an officer who recommended the military authorities to admit him to their training school at Mézières. His birth, however, precluded his receiving a commission in the army, but his attendance at an annexe of the school where surveying and drawing were taught was tolerated, though he was told that he was not sufficiently well born to be allowed to attempt problems which required calculation. At last his opportunity came. A plan of a fortress having to be drawn from the data supplied by certain observations, he did it by a geometrical construction. At first the officer in charge refused to receive it, because etiquette required that not less than a certain time should be used in making such drawings, but the superiority of the method over that then taught was so obvious that it was accepted; and in 1768 Monge was made professor, on the understanding that the results of his descriptive geometry were to be a military secret confined to officers above a certain rank.
In 1780 he was appointed to a chair in mathematics in Paris, and this with some provincial appointments which he held gave him a comfortable income. The earliest paper of any special importance which he communicated to the French Academy was one in 1781, in which he discussed the lines of curvature drawn on a surface. These had been first considered by Euler in 1760, and defined as those normal sections whose curvature was a maximum or a minimum. Monge treated them as the locus of those points on the surface at which successive normals intersect, and thus obtained the general differential equation. He applied his results to the central quadrics in 1795. In 1786 he published his well-known work on statics.
Monge eagerly embraced the doctrines of the revolution. In 1792 he became minister of the marine, and assisted the committee of public safety in utilizing science for the defence of the republic. When the Terrorists obtained power he was denounced, and escaped the guillotine only by a hasty flight. On his return in 1794 he was made a professor at the short-lived Normal school, where he gave lectures on descriptive geometry; the notes of these were published under the regulation above alluded to. In 1796 he went to Italy on the roving commission which was sent with orders to compel the various Italian towns to offer pictures, sculpture, or other works of art that they might possess, as a present or in lieu of contributions to the French republic for removal to Paris. In 1798 he accepted a mission to Rome, and after executing it joined Napoleon in Egypt. Thence after the naval and military victories of England he escaped to France.
Monge then settled down at Paris, and was made professor at the Polytechnic school, where he gave lectures on descriptive geometry; these were published in 1800 in the form of a textbook entitled Géométrie descriptive . This work contains propositions on the form and relative position of geometrical figures deduced by the use of transversals. The theory of perspective is considered; this includes the art of representing in two dimensions geometrical objects which are of three dimensions, a problem which Monge usually solved by the aid of two diagrams, one being the plan and the other the elevation. Monge also discussed the question as to whether, if in solving a problem certain subsidiary quantities introduced to facilitate the solution become imaginary, the validity of the solution is thereby impaired, and he shewed that the result would not be affected. On the restoration he was deprived of his offices and honours, a degradation which preyed on his mind and which he did not long survive.
Most of his miscellaneous papers are embodied in his works, Application de l'algèbre à la géométrie , published in 1805, and Application de l'analyse à la géométrie , the fourth edition of which, published in 1819, was revised by him just before his death. It contains among other results his solution of a partial differential equation of the second order.
背景介绍和作者介绍
加斯帕尔·蒙日是一位杰出的法国数学家和科学家，1746年出生于法国博讷。蒙日出身卑微，是小贩的儿子，他的一生充满了决心和智慧，克服了社会障碍。尽管由于他的出身，他早期遇到了一些障碍，但他以极大的热情追求教育，并很快在几何学和数学领域脱颖而出。他的工作为描述几何学奠定了基础，描述几何学是数学的一个分支，它帮助我们用二维表示三维物体——这是工程、建筑和艺术中的一项关键技能。
蒙日经历了法国历史上动荡的时期，包括法国大革命。他不仅是一位科学家，也是一位公共服务人员，他利用自己的知识来支持革命政府。他的职业生涯包括担任教授、部长和拿破仑的科学顾问。他对数学和科学的贡献与他所处时代的社会和政治变革深深交织在一起。
详细解读和意义
加斯帕尔·蒙日的故事不是虚构的故事，而是一个关于毅力、创新和教育力量的真实故事。他发展描述几何学是我们在可视化和解决空间问题方面的一个突破。这种方法允许通过二维绘图来理解复杂的三维形状，这在当今的许多领域中是基础。
蒙日在曲率线、静力学和微分方程方面的工作也极大地促进了数学的理解。他的方法将理论见解与实际应用相结合，展示了抽象数学如何解决现实世界的问题。此外，他在法国大革命期间所扮演的角色突出了科学与政治如何相互交织，有时会带来巨大的个人风险。
给学生的经验教训和见解
学生们在阅读蒙日的故事时，可以学到几个有价值的经验教训：
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克服障碍： 蒙日的早期生活告诉我们，背景或社会地位并不能决定一个人的潜力。只要有奉献精神和努力工作，任何人都可以取得伟大的成就。
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教育的重要性： 蒙日的成功建立在他深厚的知识和持续的学习之上。这鼓励学生重视他们的教育，并努力深入理解学科。
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创新和创造力： 蒙日在几何学方面的新方法表明，创造性思维如何带来突破。应该鼓励学生跳出思维定式，从新的角度解决问题。
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科学与社会： 蒙日参与政治提醒我们，科学并非与世界隔绝。知识可以用来服务社会，为重要事业做出贡献。
日常生活中的实际应用
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在学习中： 蒙日的描述几何学可以激励学生提高他们的空间推理能力，这在数学、物理和艺术等学科中很有用。
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在解决问题中： 他的例子鼓励学生在面对难题时保持耐心和毅力，因为他们知道创新的解决方案往往需要时间和精力。
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在社会交往中： 了解蒙日面对政治危险时的勇气，可以激励学生捍卫自己的信仰，并为他们的社区做出积极贡献。
培养积极的品质
为了体现蒙日精神，学生们可以：
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培养好奇心和对学习的热爱，探索课堂以外的学科。
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通过将失败视为学习的机会来培养韧性。
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通过尝试新的想法和方法来拥抱创造力。
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认识到为社会做贡献的价值，无论是通过科学、艺术还是社会行动。
结论
加斯帕尔·蒙日的生活和工作为年轻的学习者提供了丰富的灵感。他从卑微的出身到成为数学先驱和历史上的关键人物的旅程，展示了教育、创新和勇气的力量。通过学习他的故事，学生们不仅可以获得知识，还可以获得以决心和正直追求自己目标的动力。
