  In this paper, we discuss tensegrity from the perspective of nonlinear
algebra in a manner accessible to undergraduates. We compute explicit examples
and include the SAGE and Julia code so that readers can continue their own
experiments and computations. The entire framework is a natural extension of
linear equations of equilibrium, but to describe the space of solutions will
require (nonlinear) polynomials. In our examples, minors of a structured matrix
determine the singular locus of the algebraic variety of interest. At these
singular points, more interesting phenomena can occur, which we investigate in
the context of the tensegrity 3-prism, our running example. Tools from
algebraic geometry, commutative algebra, semidefinite programming, and
numerical algebraic geometry will be used. Although at first it is all linear
algebra, the examples will motivate the study of systems of polynomial
equations. In particular, we will see the importance of varieties cut out by
determinants of matrices.
