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The primary grid pattern is of quarter sections (1 ⁄ 2 mi × 1 ⁄ 2 mi (800 m × 800 m)). 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]
In a common square grid layout known as a 1,000-Acre Sectional System, adjacent parallel roads were 100 chains or 1 + 1 ⁄ 4 miles (2.0 km) apart, and arranged as ten 100-acre lots each 20 chains by 50 chains [7] so that two consecutive concession roads and two consecutive side roads enclosed a square of 1,000 acres (4.0 km 2). Another system ...
In the original Homestead Act of 1862, during the Lincoln administration, each settler was allocated 160 acres (0.65 km 2) of land, a quarter-section. Later amendments of the Homestead Act allocated more land, as much as 640 acres (2.6 km 2), a section. This was a good revision to apply to land that was drier or more desolate than the earlier ...
The rod, perch, or pole (sometimes also lug) is a surveyor's tool [1] and unit of length of various historical definitions. In British imperial and US customary units, it is defined as 16 + 1 ⁄ 2 feet, equal to exactly 1 ⁄ 320 of a mile, or 5 + 1 ⁄ 2 yards (a quarter of a surveyor's chain), and is exactly 5.0292 meters.
One acre equals 1 ⁄ 640 (0.0015625) square mile, 4,840 square yards, 43,560 square feet, [2] or about 4,047 square metres (0.4047 hectares) (see below).While all modern variants of the acre contain 4,840 square yards, there are alternative definitions of a yard, so the exact size of an acre depends upon the particular yard on which it is based.
LSDs can be "quarter-quarter sections" (square land parcels roughly 1 ⁄ 4 mi [400 m] on a side, comprising roughly 40 acres [160,000 m 2] in area)—but this is not necessary. Many are other fractions of a section (a half-quarter section—roughly 80 acres [320,000 m 2] in area is common). LSDs may be square, rectangular, and occasionally ...
Leagues can be divided or undivided (some leagues exist without labors). Labors cannot exist without leagues. A labor is one million square varas. Therefore, a league is 25 million. "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 ...
Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + 1 / 4 + 1 / 16 + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − 1 / 4 and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.