Mark Weiser described ubiquitous computing as, “invisible, everywhere computing that does not live on a personal device of any sort, but is in the woodwork everywhere.”[11] The EasyLiving project at Microsoft Research is focused on those aspects of ubiquitous computing relevant to smart environments, including work in distributed computing, geometric world modeling, computer vision, and user interfaces. Though the need for research in distributed computing, perception, and interfaces is widely recognized, the importance of an explicit geometric world model for ubiquitous computing has not been well-articulated. This paper elucidates the role of geometry in ubiquitous computing, offering example scenarios which require or benefit greatly from geometric knowledge, and describing four primary benefits of a geometric model.