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The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.
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]
This is an accepted version of this page This is the latest accepted revision, reviewed on 25 December 2024. Measure of a two-dimensional surface A sphere of radius r has surface area 4 πr 2. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is ...
The value 75.4 = 24 π, where 24 π substitutes for factor of 12 π in the formula for a volume of frustum of a cone encompassing a full tree using one base circumference, converting it to a volume formula that uses a basal circumference that is the average of circumferences C 1 and C 2.
Basal area is the cross-sectional area of trees at breast height (1.3m or 4.5 ft above ground). It is a common way to describe stand density. In forest management, basal area usually refers to merchantable timber and is given on a per hectare or per acre basis. If one cut down all the merchantable trees on an acre at 4.5 feet (1.4 m) off the ...
Parrs Wood is an area of East Didsbury, in south Manchester, England. It was formerly the estate surrounding Parrs Wood House, an 18th-century Georgian villa. [1] Today the area incorporates part of Wilmslow Road and is home to Parrs Wood High School and Sixth Form Centre, a Tesco supermarket, and Parrs Wood Entertainment Centre.
The English surveyor Edward Hoppus introduced the unit in his 1736 manual of practical calculations. [ 2 ] [ 3 ] The tables include reference to stone as well as timber, as stone can similarly suffer wastage during processing into regular pieces.
In geometric measure theory the area formula relates the Hausdorff measure of the image of a Lipschitz map, while accounting for multiplicity, to the integral of the Jacobian of the map. It is one of the fundamental results of the field that has connections, for example, to rectifiability and Sard's theorem .