The history of the Eiffel Tower and ... "Descriptive Geometry"

    For students of technical specialties of universities as a historical reference.
    The head of the automotive-mechanical department of the Lozovsky branch of the Kharkov Automobile and Highway College, a teacher of the highest category, Kozhokaru Elena Vladimirovna


    125 years ago, March 31, 1889 , the official opening of the most recognizable architectural landmark of Paris - the Eiffel Tower. Now she is known throughout the world as a symbol of France.

    During the construction of Gustav Eiffeldecided to engrave under the first balcony of the tower, on all four sides, the names of 72 of the most famous French engineers, mathematicians and scientists who made a significant contribution to the history of the development of science. Moreover, there is no alphabetical or chronological order of the names on the tower.


    Eiffel Tower, Paris

    On the Southeast side, the number “54” shows the name of Gaspard Monge (1746-1818) , a famous French mathematician, geometer, one of the founders of the famous Polytechnic School in Paris and a participant in the introduction of the metric system of weights and measures figure.

    Gaspard Monge was not only one of the organizers of the Polytechnic School in Paris, but also its long-term director. Monge was born in Bon Côte d'0r. Brilliantly graduated from the School of Military Engineers in Mezieres, from 1768. became a professor of mathematics, and since 1771. - also a professor of physics at this school. Since 1780 taught hydraulics at the Louvre School (Paris). He was engaged in mathematical analysis, chemistry, meteorology, practical mechanics. During the French bourgeois revolution, he worked in a commission to establish a new system of measures and weights, then he was the Minister of the Sea and the organizer of the French national defense. During the Directory he became close to Napoleon Bonoparte, took part in his campaign in Egypt and the founding of the Egyptian Institute in Cairo (1798); was elevated to the rank of count. Gaspard Monge received worldwide recognition, having created in the 70s of the XVIII century. modern methods of projection drawing and its basis - descriptive geometry. The same title was given to the main work of Monge on these issues, published in 1799.


    Fig. 1 The exposition dedicated to Gaspard Monge at the Paris Polytechnic School.

    The creation of the tract "Descriptive Geometry" ("Geometrie descriptive") served as the beginning and basis of the work that allowed the new Europe to master the geometric knowledge of Ancient Greece.

    In accordance with the method proposed by Gaspard Monge (orthogonal projection method), two mutually perpendicular projection planes are considered in space. One of the projection planes P 1 is located horizontally (horizontal projection plane), and the second P 2 is vertical (frontal projection plane). The planes are infinite and opaque.

    Projection planes divide the space into four dihedral angles - quarters. When considering orthogonal projections, it is assumed that the observer is in the first quarter at an infinitely large distance from them. If the complete information about the distance of a point relative to the projection plane is presented not using numerical marks, but using the second projection of a point built on the second projection plane, then such a drawing is called two-picture or complex.

    The intersection line of the projection planes is called the coordinate axis and is denoted x 12 .

    Since these planes are opaque, only those geometric objects that are located within the first quarter will be visible to the observer.

    In order to obtain a flat drawing consisting of the indicated projections, the plane P 1 is combined by rotation around the x 12 axis with the plane P 2 (Fig. 2). A projection drawing, in which the projection planes with everything that is shown on them, combined in a certain way with one another, is called a Monge diagram (from French. Epure - a drawing (Fig. 3) or a complex drawing.

    Geometric objects of the drawing are divided into: linear ( point, straight line, plane), nonlinear (curved line, surface) and composite (polyhedra, one-dimensional and two-dimensional contours).



       Fig. 2 System of three planes of projections Fig. 3 Drawing (diagram)     
    


    So, gradually accumulated and fragmented among themselves, the rules and techniques for constructing images were introduced by scientists into the system and developed in his classical work. More than two hundred years have passed since Gaspard Monge published his Descriptive Geometry in France . Since then, as a discipline and as a separate science, brought to life by the genius of Monge due to the urgent need for improving engineering technology, it began to spread with incredible speed from France to other countries. Today, “Descriptive Geometry” has taken its rightful place among the other fundamental disciplines of higher technical school as the main academic discipline, without knowledge of which a complete engineering education is unthinkable.

    The work of Monge, originally printed as a textbook, has not lost its significance to this day and forms the bulk of the training course on image methods . It showed the general character of the versatile activities of the great French scientist: his deep research mind, which pushed science forward, and the tireless energy aimed at applying theoretical calculations to the practice of engineering.

    The name of Gaspard Monge , immortalized on the Eiffel Tower, confirms this.

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