We present exploratory analyses of three cases in which groups of four (quartets) worked with video recordings of choreographed performances from the opening ceremony of the 2016 Rio Olympic Games. We asked quartets to view the recordings, explain what performers were doing by reenacting what they noticed in the video, and create their own performances using props akin to those in the recording. In response, participants explored symmetries and transformations of quadrilaterals and triangles. We contribute to research on distributed, embodied mathematical learning at four levels. First, we argue for design research that engages in creative re-use by "foraging" in public media for performances with mathematical potential, then designing activities that invite learners to "dissect and reenact" these performances to explore that potential. Second, we analyze quartets' work as a form of "ensemble learning" that hybridizes dance and mathematics. Third, we describe interactions that produced "intercorporeality" in the material work of quartets. Finally, we argue for reenactment as a supplement to methods of Interaction Analysis, using our own analysis as an illustration of this novel approach.