A course in the mathematics of design

AbstractA project-oriented course on the Mathematics of Design taught for the past six years to freshman architecture students at the New Jersey Institute of Technology is described. The course uses mathematics as the organizing force linking scientific, artistic and cultural subject areas together. The sequence of topics is graph theory with application to planning a floor plan; polyhedra applied to Platonic solids; tilings of the plane with application to lattice designs; tiling of three-dimensional space and space-filling polyhedra; similarity, proportion and the golden mean with application to architectural design; transformations; mirrors and symmetry; and vectors applied to analysis of polyhedra and ruled surfaces. The mathematical elements of each topic lead students to carry out a two- or three-dimensional construction. Students are helped to focus on the ideas behind their work by writing a series of essays