Constructive geometry

Syllabus


  1. Affinity and collineation. Affinity in the space and in the plane; collineation in the space and in the plane; image of a point, line, line segment and of a triange; image of a line at infinity.

  2. Ellipse. Construction of an ellipse; image of a circle in the affinity and in the collineation.

  3. Monge projection 1. Definition; image of a point, line, plane; trace points and trace lines; principal and slope lines; intersections of planes; intersection of a line with a plane.

  4. Monge projection 2. Flipping; length of a line segment; slope of a line; third image plane; distance from a point to a plane; plane sections of solids.

  5. Mongeo projection 3. Revolution of a plane into the base plane; construction of a regular n-gon lying in a plane in general position; a line perpendicular to a plane; regular solids with bases in a plane in general position.

  6. Axonometry. General axonometry; image of a point, line and a plane; intersection of two planes; intersection of a line with a plane; a solid in a general axonometry.

  7. Orthogonal axonometry. Construction of units; construction of an orthogonal axonometry from the Monge projection; revolution of a base plane into the image plane; regular solids with bases in a base plane.

  8. Projection with elevations 1. Definition; image of a point, line and a plane; intersections; revolution of a plane into the image plane; regular solids with bases in a plane in general position.

  9. Projection with elevations 2. Topographical surfaces; curve of the greatest slope; profile; construction of a road passing through a given terrain; roofs and drains.

  10. Central projection 1. Definition; image of a point, line and a plane; intersections; length of a line segment lying in a plane; angle of two intersecting lines; a line perpendicular to a plane; revolution of a plane; regular solids with bases in a plane in general position.

  11. Central projection 2. Construction of a central projection from the Monge projection.

  12. Repetition.

  13. Repetition.

Keywords: Affinity, collineation, ellipse, Monge projection, axonometry, projection with elevations, central projection.