Sections and Shadows of Four-Dimensional Objects

Methods of constructions of sections and shadows of four-dimensional objects are explained. We visualize images of an object and its section or shadow at the same time in a double orthogonal projection on two perpendicular three-dimensional spaces. Our techniques are similar to the methods used in Monge’s projection of the three-dimensional space. Constructions are created in the interactive 3D modeling software GeoGebra 5, in which the user can freely move some input elements. We focus on a synthetic approach to description of the four-dimensional space with the use of descriptive geometry tools.