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A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. [10] This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the ...
To measure planimetrics a planimeter or dot planimeter is used. This rather advanced analog technology is being taken over by simple image measurement software tools like, ImageJ , Adobe Acrobat , Google Earth Pro , Gimp , Photoshop and KLONK Image Measurement which can help do this kind of work from digitalized images.
For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x 2 + y 2 = 4; the area, the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives, in a way that can be applied to any curve.
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.
Position resection and intersection are methods for determining an unknown geographic position (position finding) by measuring angles with respect to known positions.In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.
The shortest distance between two points in plane is a Cartesian straight line. The Pythagorean theorem is used to calculate the distance between points in a plane. Even over short distances, the accuracy of geographic distance calculations which assume a flat Earth depend on the method by which the latitude and longitude coordinates have been ...
[1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. [ 4 ] [ 5 ] Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.
Let C be a conic in PG(2, F) where F is a field not of characteristic two, and let P be a point of this plane not on C. Two distinct secant lines to the conic, say AB and JK determine four points on the conic (A, B, J, K) that form a quadrangle. The point P is a vertex of the diagonal triangle of this quadrangle.