Statistical Law between Areas and Perimeters Created by a Moving Trajectory

Based on our interest in properties of human movement, we investigated Japanese GPS data, and arrived at the following three observations: (1) there is a strong correlation between the area of polygons created by human movement trajectories and their perimeters; (2) short-distance movement trajectories less than 5 km tend to enclose a large area like a circle; and (3) long-distance movement trajectories over 5 km tend to be straight. We also clarified the following four observations on individual attributes and external factors related to long-distance movements: (1) women tend to travel more linearly than men; (2) linearity is stronger on weekends and national holidays in areas with a large theme park; (3) linearity is weaker on weekends and holidays in areas with many historical tourist attractions; and (4) these variations are created by people visiting such areas. These properties should be incorporated when modeling the movement trajectories of humans.