A preliminary investigation into mathematical properties of the field in which every point is defined by the reciprocal of the distance from the boundary

The boundary with fence built around the field is necessary to prevent animals from escaping. This study was designed, apart temporarily from animal agriculture, to investigate mathematical properties of the field in which every point was defined by the reciprocal of the distance from the boundary. The results obtained were as follows. (1) The larger the boundary size was, the lower the rate at which the reciprocal of the distance increased when approaching the boundary from the center of the field. (2) The boundary size did not influence the rate at which the reciprocal of the distance decreased when moving outside the boundary. (3) When based on the reciprocal of the distance from the boundary, getting through the boundary was to get over the gap of &inf; mathematically. (4) Applying the present results to psychological responses that animals might make to every point in the field surrounded by electric fence remains to be investigated. It was suggested that mathematical properties of the field were explained by the boundary size and the reciprocal of the distance from the boundary to every point in the field.