Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it at a new location and orientation and asked to mark the place where the cue had been. On some trials the geometry (size, aspect ratio) of the arena was varied between presentation and testing. Responses tended to lie somewhere between a location that maintained fixed distances from nearby walls and a location that maintained fixed ratios of the distances between opposing walls. The former were more common after expansions and for cued locations nearer to the edge while the latter were more common after contractions and for locations nearer to the center. The spatial distributions of responses predicted by various simple geometric models were compared to the data. The best fitting model was one derived from the response properties of "place cells" in the rat hippocampus, which matches the "proximities" 1/(d+c) of the cue to the four walls of the arena, where d is the distance to a wall and c is a global constant. Subjects also tended to adopt the same orientation at presentation and testing, although this was not due to using a view matching strategy, which could be ruled out in 50% of responses. Disoriented responses were most often seen where the cued location was near the center of the arena or where the long axis of a rectangular arena was changed between presentation and testing, suggesting that the geometry of the arena acts as a weak cue to orientation. Overall, the results suggest a process of visual landmark matching to determine orientation, combined with an abstract representation of the proximity of the cued location to the walls of the arena consistent with the neural representation of location in the hippocampus.