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The Euclidean algorithm was probably invented before Euclid, depicted here holding a compass in a painting of about 1474. The Euclidean algorithm is one of the oldest algorithms in common use. [27] It appears in Euclid's Elements (c. 300 BC), specifically in Book 7 (Propositions 1–2) and Book 10 (Propositions 2–3). In Book 7, the algorithm ...
A classic result in computational geometry was the formulation of an algorithm that takes O(n log n). Randomized algorithms that take O( n ) expected time, [ 4 ] as well as a deterministic algorithm that takes O( n log log n ) time, [ 5 ] have also been discovered.
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.
Animation showing an application of the Euclidean algorithm to find the greatest common divisor of 62 and 36, which is 2. A more efficient method is the Euclidean algorithm, a variant in which the difference of the two numbers a and b is replaced by the remainder of the Euclidean division (also called division with remainder) of a by b.
Midpoint circle algorithm; Minimum bounding box; Minimum bounding box algorithms; Minimum bounding rectangle; Minimum-diameter spanning tree; Minkowski addition; Minkowski Portal Refinement; Möller–Trumbore intersection algorithm; Monotone polygon; Multiple line segment intersection
He applied computational geometric and discrete mathematics methods to the analysis of symbolically represented music in general, and rhythm in particular. In 2004 he discovered that the Euclidean algorithm for computing the greatest common divisor of two numbers implicitly generates almost all the most important traditional rhythms of the ...
Vector clock, an algorithm; Vector space model, an algebraic model for representing text documents; Vector (C++), a type in the C++ Standard Template Library; Euclidean vector, a geometric object with a direction and magnitude Vector graphics, images defined by geometric primitives as opposed to bitmaps
For a basis consisting of just two vectors, there is a simple and efficient method of reduction closely analogous to the Euclidean algorithm for the greatest common divisor of two integers. As with the Euclidean algorithm, the method is iterative; at each step the larger of the two vectors is reduced by adding or subtracting an integer multiple ...