We explore how users approach and define personal space on large, public displays. Our results show that users of public displays use one of two strategies for visual search tasks: minimizers create a small window and work up close to the display, and maximizers expand content to its full resolution and work at a distance. We show that these interaction styles match predicted 'personal' and 'subtle' interaction zones, characterize typical width and height requirements for these interactions, and show that these requirements are independent of the on-screen content's dimensions. Finally, we suggest practical guidelines for defining workspaces during personal and subtle interaction on large, public displays.