Acclaimed Canadian modern dancer Sarah Chase uses combinatorics to create choreographies, and uses combinatoric choreographies to explore (and teach) phasing phenomena in nature and human relationships via the body moving in time and space. The setting of the film is the idyllic Tribune Bay on Hornby Island, BC, Canada, where Chase develops her dances inspired by tides, seasons and her community. This film accompanies Paper #59 in the Bridges 2013 program, Learning Mathematics Through Dance, which discusses Sarah Chase's work.
This short film follows up on a live workshop on the geometry of longsword locks from Bridges 2009. In traditional English longsword dancing, a team of dancers makes intricate moves while joined together by their wooden or metal 'swords'. An impressive element of the dance is the variety of traditional geometric, symmetrical sword locks (often stars) created through the movements of all the dancers. The film showcases a longsword dance and the locks created by the physical algorithms of the conjoined dancers' movement. After showing the dance, questions are offered to spark mathematical explorations by secondary or post-secondary students. These questions include topological and geometric ideas about crossings, angles and edges, and logic-related questions about categorizing lock types and discovering whether new locks could be created through analysis of the physical algorithms that create them. Slow-motion and repeated views help learners explore this rich source of geometry.