Geometric Projections: Orthogonal and Monge Projections

This lecture introduces the concepts of orthogonal projection and Monge projection in descriptive geometry. It begins with the definition of point projection onto a plane, explaining how the intersection of a line through the point and the plane defines the projection. The instructor discusses the geometric properties preserved by parallel projection, such as alignment and the relationship between points in space and their projections. The lecture emphasizes the importance of visualizing these concepts using tools like GeoGebra. The instructor illustrates how to determine the projections of points and lines, highlighting the significance of the 'proche-tente' or tangent plane. The discussion extends to the properties of projections, including the conservation of alignment and section ratios. The lecture concludes with an introduction to the Monge method, which utilizes orthogonal projections on various planes, and the importance of understanding the coordinate system in three-dimensional space for accurate representation and visualization of geometric objects.