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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]
The metes and bounds system was used to describe a town of a generally rectangular shape, 4 to 6 miles (6.4 to 9.7 km) on a side. Within this boundary, a map or plat was maintained that showed all the individual lots or properties. There are some difficulties with this system: Irregular shapes for properties make for much more complex descriptions.
A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles.
When counting dots near the boundary of the shape as 1/2, there are 69 interior dots and 20 boundary dots for an estimated area of 79, close to the actual area of 25 π ≈ 78.54. A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate ...
In U.S. land surveying under the Public Land Survey System (PLSS), a section is an area nominally one square mile (2.6 square kilometers), containing 640 acres (260 hectares), with 36 sections making up one survey township on a rectangular grid. [1]
This area is also equal to the area of the parallelogram A"ABB". The measuring wheel measures the distance PQ (perpendicular to EM). Moving from C to D the arm EM moves through the green parallelogram, with area equal to the area of the rectangle D"DCC". The measuring wheel now moves in the opposite direction, subtracting this reading from the ...
According to Carl Friedrich Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. [2] It can be known only through extensive gravitational measurements and calculations.
Common synonyms for geomorphometry are geomorphological analysis (after geomorphology), terrain morphometry, terrain analysis, and land surface analysis. Geomorphometrics is the discipline based on the computational measures of the geometry , topography and shape of the Earth's horizons, and their temporal change. [ 2 ]