Geometrical property of navigation

There is a tendency that a blind or a blind-folded subject fails to return to a starting point within the range of errors when he or she walks to a place, next turns to right or left, and then conies back to the starting point. We studied this tendency from a non-Euclidean geometrical point of view. In Experiment 1, total of 28 blind-folded subjects walked to construct a square, a regular triangle and a circle. The result showed that the location of the final reaching point was on the fronto-right side of the starting point in the square and triangle conditions and went over the starting point in the circle condition. In Experiment 2, 15 subjects judged visual properties (angles and distances) of a triangle and constructed the triangle by walking. The walking loci were compared with the visual properties. It was found that the walking loci were curved, differing from the visual properties. These results implied that the walking loci agree with the nature of elliptic geometry.