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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 existence of section lines made property descriptions far more straightforward than the old metes and bounds system. The establishment of standard east-west and north-south lines ("township" and "range lines") meant that deeds could be written without regard to temporary terrain features such as trees, piles of rocks, fences, and the like, and be worded in the style such as "Lying and ...
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 league and a labor" (4,605.5 acres; 18.638 km 2) was a common first land grant [4] and consisted of a league of land away from the river plus one extra labor of good riparian (river-situated) land. A headright of this much land was granted to "all persons [heads of families] except Africans and their descendants and Indians living in Texas ...
The 'perfect acre' [2] is a rectangular area of 43,560 square feet, bounded by sides 660 feet (a furlong) long and 66 feet (a chain) wide (220 yards by 22 yards) or, equivalently, 40 rods by 4 rods. An acre is therefore 160 square rods or 10 square chains. The name perch derives from the Ancient Roman unit, the pertica.
If the square mile is divided into quarters, each quarter has a side length of 1 ⁄ 2 mile (880 yards) and is 1 ⁄ 4 square mile in area, or 160 acres. These subunits are typically then again divided into quarters, with each side being 1 ⁄ 4 mile long, and being 1 ⁄ 16 of a square mile in area, or 40 acres. In the United States, farmland ...
The faceoffs between the Chiefs and Bills have become one of the highlights of the NFL schedule, and a playoff rematch could be ahead.
In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any convex cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides.