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Euclidean division reduces all the steps between two exchanges into a single step, which is thus more efficient. Moreover, the quotients are not needed, thus one may replace Euclidean division by the modulo operation, which gives only the remainder. Thus the iteration of the Euclidean algorithm becomes simply r k = r k−2 mod r k−1.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
The rotation group SO(3) can be described as a subgroup of E + (3), the Euclidean group of direct isometries of Euclidean . This larger group is the group of all motions of a rigid body : each of these is a combination of a rotation about an arbitrary axis and a translation, or put differently, a combination of an element of SO(3) and an ...
The 1-skeleton of the triangulation by Euclidean equilateral triangles is not hyperbolic (it is in fact quasi-isometric to the Euclidean plane). A triangulation of the plane R 2 {\displaystyle \mathbb {R} ^{2}} has a hyperbolic 1-skeleton if every vertex has degree 7 or more.
For example Euclidean spaces of dimension n, and more generally n-dimensional Riemannian manifolds, naturally have the structure of a metric measure space, equipped with the Lebesgue measure. Certain fractal metric spaces such as the Sierpiński gasket can be equipped with the α-dimensional Hausdorff measure where α is the Hausdorff dimension .
This is a list of television films produced for the cable networks Hallmark Channel (HC) and Hallmark Movies & Mysteries (HMM). Such films are currently called Hallmark Channel Original Movies and Hallmark Mysteries.
Overtaking is prohibited either for all vehicles or for certain kinds of vehicles only (e.g. lorries, motorcycles). In the USA, this is usually phrased as "no passing zone" and indicated by a rectangular, black-on-white sign on the right side of the road that says "DO NOT PASS", and/or by a solid yellow line painted on the roadway marking the left limit of traffic (centerline), and sometimes ...
In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle (or ). Greek theta variant in cursive form. The cursive form ϑ was retained by Unicode as U+03D1 ϑ GREEK THETA SYMBOL, separate from U+03B8 θ GREEK SMALL LETTER THETA. (There is also U+03F4 ϴ GREEK CAPITAL THETA ...