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Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In England Frisius's method was included in the growing number of books on surveying which appeared from the middle of the century onwards, including William Cuningham's Cosmographical Glasse (1559), Valentine Leigh's Treatise of Measuring All Kinds of Lands (1562), William Bourne's Rules of Navigation (1571), Thomas Digges's Geometrical ...
The formula above is obtained by combining the composite Simpson's 1/3 rule with the one consisting of using Simpson's 3/8 rule in the extreme subintervals and Simpson's 1/3 rule in the remaining subintervals. The result is then obtained by taking the mean of the two formulas.
A surveyor using a total station A student using a theodolite in field. Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them.
A is the cross-sectional area of the tape; square centimeters; E is the modulus of elasticity of the tape material; newtons per square centimeter; The correction is added to to obtain the corrected distance: = + The value for A is given by:
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity.
In surveying, free stationing (also known as resection) is a method of determining a location of one unknown point in relation to known points. [1] There is a zero point of reference called a total station. The instrument can be freely positioned so that all survey points are at a suitable sight from the instrument.
J. M. Tienstra [] (1895-1951) was a professor of the Delft university of Technology where he taught the use of barycentric coordinates in solving the resection problem. It seems most probable that his name became attached to the procedure for this reason, though when, and by whom, the formula was first proposed is unknown.