Curvature estimation and architecture of the Parthenon

Abstract

Curvature in the Wundt–Hering illusion (the fan illusion) in the horizontal and vertical orientations is estimated for slightly concave and convex lines, as well as for straight lines. These estimates were compared with estimates of the curvature of imaginary (interpolated) lines through points that lie on the rays of a fan, as well as with estimates of the curvature of analogous lines when there is no image of a fan. It is shown that estimates of the curvature of the real lines and imaginary lines through the points where they intersect the fan are different and depend on the orientation of the stimuli. They also differ from the estimates obtained for the curvature of real and interpolated lines when there is no image of a fan. Two-dimensional projections of the Parthenon have convex horizontal and vertical lines, even though the temple is perceived as ideally rectilinear. The distortions of the curvature estimates that we found straighten convex lines in the architecture of the Parthenon, whose “curvature,” in our opinion, is generated by the Wundt–Hering illusion and the tilt illusion.