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Buffon's needle was the earliest problem in geometric probability to be solved; [2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is. This can be used to design a Monte Carlo method for approximating the number π ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: [1] Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Artificial satellites move along curved orbits, rather than in straight lines, because of the Earth's gravity. Translated from Latin, Newton's first law reads, Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon. [note 3]
The integral of the Dirac delta function. Saw-tooth wave. Square wave. Triangle wave. Rectangular function. Floor function: Largest integer less than or equal to a given number. Ceiling function: Smallest integer larger than or equal to a given number. Sign function: Returns only the sign of a number, as +1 or −1.
Julian Corbett. Sir Julian Stafford Corbett (12 November 1854 at Walcot House, Kennington Road, Lambeth – 21 September 1922 at Manor Farm, Stopham, Pulborough, Sussex [1]) was a prominent British naval historian and geostrategist of the late 19th and early 20th centuries, whose works helped shape the Royal Navy 's reforms of that era.
Line–line intersection. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line. Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection. In three-dimensional Euclidean geometry, if two lines are not in ...
The Mandelbrot set (/ ˈmændəlbroʊt, - brɒt /) [1][2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not ...
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