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Learn the definition, examples, and properties of the Cartesian product of sets, a fundamental concept in set theory and mathematics. The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B.
Learn how to calculate the vector projection, scalar projection, and vector rejection of a vector onto or from another vector using dot product, angle, and matrix representation. See the properties, uses, and generalizations of these concepts in different dimensions and spaces.
A vector is a quantity that has both magnitude and direction, such as displacement, force or velocity. Learn about different types of vectors, vector spaces, vector operations and applications in geometry, physics and algebra.
Learn how to calculate the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. See different formulas, proofs and examples for lines defined by equations, points or normals.
Learn about barycentric coordinates, a coordinate system that specifies a point by reference to a simplex (a triangle, tetrahedron, etc.). Find out how they are related to Cartesian, affine and projective coordinates, and how they are used in geometry and computer-aided design.
The golden ratio is a mathematical constant that relates the lengths of two quantities when their ratio is the same as the ratio of their sum to the larger of the two quantities. It has been studied in geometry, art, nature and other fields for its aesthetic and symbolic properties.
Fixed-point arithmetic is a method of representing fractional numbers by storing a fixed number of digits of their fractional part. Learn about the advantages, disadvantages, and applications of fixed-point arithmetic, as well as the choice of scaling factors and the representation of negative values.
The cross product or vector product is a binary operation on two vectors in a three-dimensional space, denoted by a × b, that is perpendicular to both vectors and has magnitude equal to the area of the parallelogram they span. Learn about its formula, direction, handedness, generalizations, and uses in mathematics, physics, engineering, and computer programming.
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