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The chessboard paradox [1] [2] or paradox of Loyd and Schlömilch [3] is a falsidical paradox based on an optical illusion. A chessboard or a square with a side length of 8 units is cut into four pieces. Those four pieces are used to form a rectangle with side lengths of 13 and 5 units.
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 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
The optical illusion is that the area labeled A appears to be a darker color than the area labeled B. However, within the context of the two-dimensional image, they are of identical brightness, i.e., they would be printed with identical mixtures of ink, or displayed on a screen with pixels of identical color. [1]
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 simplest method for solving a system of linear equations is to repeatedly eliminate variables. This method can be described as follows: In the first equation, solve for one of the variables in terms of the others. Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown.