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Isometric projection and net of naive (1) and optimal (2) solutions of the spider and the fly problem. The spider and the fly problem is a recreational mathematics problem with an unintuitive solution, asking for a shortest path or geodesic between two points on the surface of a cuboid. It was originally posed by Henry Dudeney.
The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line = /. This distance can be found by first solving the linear systems {= + = /, and {= + = /, to get the coordinates of the intersection points. The solutions to the linear systems are the points
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
Proximity problems is a class of problems in computational geometry which involve estimation of distances between geometric objects.. A subset of these problems stated in terms of points only are sometimes referred to as closest point problems, [1] although the term "closest point problem" is also used synonymously to the nearest neighbor search.
In the Euclidean TSP (see below), the distance between two cities is the Euclidean distance between the corresponding points. In the rectilinear TSP, the distance between two cities is the sum of the absolute values of the differences of their x- and y-coordinates. This metric is often called the Manhattan distance or city-block metric. In the ...
It is possible to reduce the various geodesic problems into one of two types. Consider two points: A at latitude φ 1 and longitude λ 1 and B at latitude φ 2 and longitude λ 2 (see Fig. 1). The connecting geodesic (from A to B) is AB, of length s 12, which has azimuths α 1 and α 2 at the two endpoints. [1] The two geodesic problems usually ...
3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes. 4. Problem of the straight line as the shortest distance between two points. 5. Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group. 6. Mathematical treatment of the axioms ...