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The transformation sends the circle to an ellipse by stretching or shrinking the horizontal and vertical diameters to the major and minor axes of the ellipse. The square gets sent to a rectangle circumscribing the ellipse. The ratio of the area of the circle to the square is π /4, which means the ratio of the ellipse to the rectangle is also π /4
An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where
Arc distances on a great circle are the same as the distance between the same points on a sphere, and on the hemispheres into which the circle divides the sphere.. The Riemannian unit circle of length 2 π can be embedded, without any change of distance, into the metric of geodesics on a unit sphere, by mapping the circle to a great circle and its metric to great-circle distance.
Other uncommon metric units of area include the tetrad, the hectad, and the myriad. The acre is also commonly used to measure land areas, where 1 acre = 4,840 square yards = 43,560 square feet. An acre is approximately 40% of a hectare. On the atomic scale, area is measured in units of barns, such that: [13] 1 barn = 10 −28 square meters.
A circular mil is a unit of area, equal to the area of a circle with a diameter of one mil (one thousandth of an inch or 0.0254 mm). It is equal to π /4 square mils or approximately 5.067 × 10 −4 mm 2. It is a unit intended for referring to the area of a wire with a circular cross section.
Moments of inertia may be expressed in units of kilogram metre squared (kg·m 2) in SI units and pound-foot-second squared (lbf·ft·s 2) in imperial or US units. The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The ...
In particular, for measuring great-circle distances on the Earth or other spherical or near-spherical surfaces, distances that have been used include the haversine distance giving great-circle distances between two points on a sphere from their longitudes and latitudes, and Vincenty's formulae also known as "Vincent distance" for distance on a ...
historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot. For some purposes, conversions from one system of units to another are needed to be exact, without increasing or decreasing the precision of the expressed quantity.