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The widely accepted interpretation of, e.g. the Poggendorff and Hering illusions as manifestation of expansion of acute angles at line intersections, is an example of successful implementation of a "bottom-up," physiological explanation of a geometrical–optical illusion. Ponzo illusion in a purely schematic form and, below, with perspective clues
Consequently, the Gaussian theory only supplies a convenient method of approximating reality; realistic optical systems fall short of this unattainable ideal. Currently, all that can be accomplished is the projection of a single plane onto another plane; but even in this, aberrations always occurs and it may be unlikely that these will ever be ...
The Hollow-Face illusion is an optical illusion in which the perception of a concave mask of a face appears as a normal convex face. Hybrid image: A Hybrid image is an optical illusion developed at MIT in which an image can be interpreted in one of two different ways depending on viewing distance. Illusory contours
A version of the Zöllner illusion. The Zöllner illusion is an optical illusion named after its discoverer, German astrophysicist Johann Karl Friedrich Zöllner.In 1860, Zöllner sent his discovery in a letter to physicist and scholar Johann Christian Poggendorff, editor of Annalen der Physik und Chemie, who subsequently discovered the related Poggendorff illusion in Zöllner's original drawing.
The properties of the Fibonacci numbers also provide some deeper insight, why the optical illusion works so well. A square whose side length is the Fibonacci number f n {\displaystyle f_{n}} can be dissected using line segments of lengths f n , f n − 1 , f n − 2 {\displaystyle f_{n},f_{n-1},f_{n-2}} in the same way the chessboard was ...
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Impossible object: A type of optical illusion. Invalid proof: An apparently correct mathematical derivation that leads to an obvious contradiction. Logical fallacy: A misconception resulting from incorrect reasoning in argumentation. Paradox gun: A gun that has characteristics of both (smoothbore) shotguns and rifles.
The globe effect, also known as rolling ball effect, is an optical illusion which can occur with optical instruments used visually, in particular binoculars or telescopes. If such an instrument is rectilinear, or free of rectilinear distortion, some observers get the impression of an image rolling on a convex surface when the instrument is panned.