Magical thinking is the attribution of causal relationships between actions and events which seemingly cannot be justified by reason and observation. In religion, folk religion, and superstitious beliefs, the correlation posited is often between religious ritual, prayer, sacrifice, or the observance of a taboo, and an expected benefit or recompense. In clinical psychology, magical thinking can cause a patient to experience fear of performing certain acts or having certain thoughts because of an assumed correlation between doing so and threatening calamities. Magical thinking may lead people to...

Taxicab geometry, considered by Hermann Minkowski in 19th century Germany, is a form of geometry in which the usual distance function of metric or Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, L1 distance or norm (see Lp space), city block distance, Manhattan distance, or Manhattan length, with corresponding variations in the name of the geometry. The latter names allude to the grid layout of most streets on the island of Manhattan...

In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to...

A squircle is a mathematical shape with properties between those of a square and those of a circle. It is a special case of superellipse. The word "squircle" is a portmanteau of the words "square" and "circle". == Equation == In a Cartesian coordinate system, the squircle centered on the point (a, b) with axes parallel to the coordinate axes is described by the equation: where r is the minor radius of the squircle (cf. equation of a circle). The case that is centered on the origin (that is, with a = b = 0) is called Lamé's special quartic. == Generalisation == The squircle is a specific case ...