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For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
is the distance over which the initial time is achieved D 2 {\displaystyle D_{2}} is the distance for which the time is to be predicted Riegel expanded on his thesis in a 1981 article for American Scientist , stating that the formula t = a x b {\displaystyle t=ax^{b}} concerns activities in the "endurance range", namely lasting between 3.5 and ...
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...
Use equation 7 to generate the four constants ,,, from measured distances and time for each receiver . This will be a set of n − 1 {\displaystyle n-1} inhomogeneous linear equations. There are many robust linear algebra methods that can solve for ( x , y , z ) {\displaystyle (x,y,z)} , such as Gaussian elimination .
Given the coordinates of the two points (Φ 1, L 1) and (Φ 2, L 2), the inverse problem finds the azimuths α 1, α 2 and the ellipsoidal distance s. Calculate U 1, U 2 and L, and set initial value of λ = L. Then iteratively evaluate the following equations until λ converges:
By Barbier's theorem, the body's perimeter is exactly π times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body of constant width includes pairs of points that are farther apart than the width, and every curve of constant ...
In taxicab geometry, the lengths of the red, blue, green, and yellow paths all equal 12, the taxicab distance between the opposite corners, and all four paths are shortest paths. Instead, in Euclidean geometry, the red, blue, and yellow paths still have length 12 but the green path is the unique shortest path, with length equal to the Euclidean ...