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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.
Optical illusion is also used in film by the technique of forced perspective. Op art is a style of art that uses optical illusions to create an impression of movement, or hidden images and patterns. Trompe-l'œil uses realistic imagery to create the optical illusion that depicted objects exist in three dimensions.
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 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
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
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an area of only 30 units.
Interactive SVG of The Disappearing Bicyclist – in the SVG file, move the pointer to rotate the disc. A vanishing puzzle is a mechanical optical illusion comprising multiple pieces which can be rearranged to show different versions of a picture depicting several objects, the number of which depending on the arrangement of the pieces.
An optical illusion where the physical and subjective angles differ is then called a visual angle illusion or angular size illusion. Angular size illusions are most obvious as relative angular size illusions, in which two objects that subtend the same visual angle appear to have different angular sizes; it is as if their equal-sized images on ...