Tensegreties are physical 3D realizations of graphs (as in graph theory) made with rigid rods and strings in which the rods appear to float between cables. See examples in Google Images for tensegrity. In a pure tensegrity no two rods can touch each other. The rods prevent the vertices from moving any closer and the strings prevent the vertices from moving any further. Given a potential design for a tensegrity one can ask if it is rigid or flexible. The tools we have used so far are basic linear algebra and simple linear programming. In the Fall 2018 semester of this project some of these tools were explored and coded in Python to study the rigidity of some simple tensegrities. Students starting in Spring 2019 will use and develop these and develop new algorithms to investigate some of the following goals: (i) Given a graph and edge lengths discover some placement of vertices which yields a rigid structure and some placement which is flexible; (ii) Given a shape (for example an architectural structure) find a tensegrity that is close to that shape; (iii) Given a tensegrity, which rods can be replaced by strings without losing rigidity? (using less rods and more strings can make it lighter).
Completion of Calculus 3 and matrix or linear algebra (Math 225 or 415 or 416). At least two students should have some experience with Python.