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In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area. It follows that.
The radar chart is a chart and/or plot that consists of a sequence of equi-angular spokes, called radii, with each spoke representing one of the variables. The data length of a spoke is proportional to the magnitude of the variable for the data point relative to the maximum magnitude of the variable across all data points.
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] It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the ...
Brahmagupta's formula. In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.
Count the number of elements (M) of the chart enclosed by the plan of the loaded area. The formula used to solve for the increase in pressure at the point being considered is 〖∆σ〗_z = (IV)qM, where IV = influence value, q = pressure on the loaded area, and M = number of elements enclosed by loaded area. [1]
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
The linear–log type of a semi-log graph, defined by a logarithmic scale on the x axis, and a linear scale on the y axis. Plotted lines are: y = 10 x (red), y = x (green), y = log (x) (blue). In science and engineering, a semi-log plot / graph or semi-logarithmic plot / graph has one axis on a logarithmic scale, the other on a linear scale.
Method of exhaustion. The method of exhaustion (Latin: methodus exhaustionis) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the n th polygon and the containing shape will ...