Form Generation through Mathematics

Patricia Correa
Max Enrollment:
Jan 20-24 from 9-2
42 Kirkland, Room 42-1-G
Mathematics has been constantly present in the rationalization of form in architecture as a study of patterns and proportions to generate aesthetically intriguing geometries, which can potentially embed enhanced structural performance. Yet, somehow its basic definitions and origins aren\'t always thoroughly understood. It is a powerful tool that can enable us as designers to construct sophisticated, logical, and harmonically elegant forms. This course seeks to guide the students to a deeper understanding of mathematical functions of curves and surfaces as drivers of form generation processes.
The course will begin with the definitions of curves on the Euclidean plane (line, conic sections, trigonometric functions, algebraic curves, quartic plane curves, hypocycloids, among others) in search of extracting their slope, degree, roots, asymptotes, congruence and similarities to generate geometrical transformations within them. These concepts will be transposed to surfaces (minimal, quadric, algebraic, ruled, among others) in order to manipulate them through their equations. Related topics include the conversion to/from explicit, implicit and parametric functions, coordinate transformations between the prototypical Cartesian system to polar, cylindrical and spherical system in relation to the topology of the surface or curve being described. Interactive transformations of the curves and surfaces defined will be visualized with plotting software such as Mathematica or Surf X 3D, Grasshopper and C# for Rhino.
The students will perform a series of graphing and modeling exercises. At the end of this course, students will have gained a sufficient understanding of the mathematical language for surface definitions and its direct relation to shape. They will also have the appropriate knowledge of the digital tools to translate this language to topological forms.
Students do not need to be familiar with Grasshopper, C#, or calculus. The course will start from a basic level, making sure everyone is understanding the subject and enjoying it.
Must download SurfX3D (available free online); Must bring laptop