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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.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions , to describe the sizes or locations of objects in the everyday world.
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
3D chess on Star Trek (from the episode "Court Martial") Tri-Dimensional Chess, Tri-D Chess, or Three-Dimensional Chess [a] is a chess variant which can be seen in many Star Trek TV episodes and movies, starting with the original series (TOS) and proceeding in updated forms throughout the subsequent movies and spinoff series. [9]
4D visualization Stereoscopic view Ref. 2048 4D: puzzle: Huon Wilson, based on 2048 by Gabriele Cirulli 2014 MIT: JavaScript: 2D sections: No [1] 4D Blocks: building blocks and trains John McIntosh 2013 Public Domain: Java: perspective projection: Yes [2] 4D Building Blocks: puzzle: Henryk Trappmann 2006 ? Java: parallel projection: Yes [3] 4D ...
An illusion closely related to the checker shadow illusion, which also relies on using implied visual shadows to seemingly darken a brighter region to the same color as a well-lit dark region, involves two squares placed at an angle, with the darker square being lit and the lighter square at an angle which receives poor light. [2]
The idea for a chess tournament contested by NFL players arose through Rensch’s friendship with Larry Fitzgerald, the legendary former Arizona Cardinals wide receiver and an avid chess player.
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