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Quadrats typically occupy an area of 0.25 m 2 and are traditionally square, but modern quadrats can be rectangular, circular, or irregular. [1] [2] A quadrat is suitable for sampling or observing plants, slow-moving animals, and some aquatic organisms. A photo-quadrat is a photographic record of the area framed by a quadrat.
giving the basic form of Brahmagupta's formula. It follows from the latter equation that the area of a cyclic quadrilateral is the maximum possible area for any quadrilateral with the given side lengths. A related formula, which was proved by Coolidge, also gives the area of a general convex
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].
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]
When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("north-east") quadrant. Similarly, a three-dimensional Cartesian system defines a division of space into eight regions or octants, [8] according to the signs of the coordinates of the points.
Both the constellation and the shower are named after an instrument called the quadrant, which was once used to measure the altitudes of stars and other bodies in the night sky. (Photo credit ...
A set of sides that can form a cyclic quadrilateral can be arranged in any of three distinct sequences each of which can form a cyclic quadrilateral of the same area in the same circumcircle (the areas being the same according to Brahmagupta's area formula). Any two of these cyclic quadrilaterals have one diagonal length in common. [17]: p. 84