George Hart

The elliptic hyperboloid is a beautiful quadratic surface that is “doubly ruled,” meaning that the surface, although curved, contains two straight lines through each point. This property allows it to be used in architectural applications where designers wish to achieve an elegant curve using cost-effective straight stock. Here it is applied to the design of a walk-through archway in the teaching garden at the University of British Columbia in Vancouver. Thank you to the many students, staff and faculty who participated in its construction.

Traditional long sword dancing is an art form that produces stable patterns of interwoven segments. These structures, sometimes called “popsicle stick bombs,” are surprisingly rich mathematically and raise subtle difficulties for those attempting to analyze their stability. Dancers look for sequences of movements that will produce a desired configuration, an algorithmic question that is particularly challenging if the arms and swords are required to maintain a simple closed loop during the dance.