Abstract

Originating in a mathematical study of a series of binocular visual phenomena experienced in certain demonstrations developed by The Hanover Institute (formerly Dartmouth Eye Institute), the following analysis shows that even binocular vision does not provide absolute localization of objects. On the contrary, a series of vertical targets may furnish binocularly the same angular clues, if their location, their inclination, and their shape are suitably chosen. Although the straight lines where the possible equivalent vertical targets intersect the horizontal plane represent only a special, so to speak degenerated subset of the whole set of equivalent conic sections, their mathematical analysis reveals that two theorems of projective geometry dealing with projective properties of conic sections find an interesting application in the field of binocular vision. In the introduction, two actual experiments are described. The geometrical construction and the computations on which these experiments are based are discussed in the last section where two additional theoretically possible experiments are suggested.

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