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Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
As the definition of the unit contains π, it is easy to calculate area values in circular mils when the diameter in mils is known. The area in circular mils, A , of a circle with a diameter of d mils, is given by the formula: { A } c m i l = { d } m i l 2 . {\displaystyle \{A\}_{\mathrm {cmil} }=\{d\}_{\mathrm {mil} }^{2}.}
The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 / 2 × 2πr × r, holds for a circle.
For n trees, QMD is calculated using the quadratic mean formula: where is the diameter at breast height of the i th tree. Compared to the arithmetic mean, QMD assigns greater weight to larger trees – QMD is always greater than or equal to arithmetic mean for a given set of trees.
Thus, the outer diameter of a catheter in millimeters can be calculated by dividing the French size by 3. [2] For example, a catheter with a French size of 9 would have an outer diameter of approximately 3 mm. While the French scale aligns closely with the metric system, it introduces redundancy and the potential for rounding errors.
Formally, a Riemannian metric (or just a metric) on a smooth manifold is a choice of inner product for each tangent space of the manifold. A Riemannian manifold is a smooth manifold together with a Riemannian metric. The techniques of differential and integral calculus are used to pull geometric data out of the Riemannian metric. For example ...
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure 𝜃 is =, and the formula for the area A of a circular sector of radius r and with central angle of measure 𝜃 is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
More precisely, a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors to real numbers), and a metric field on M consists of a metric tensor at each point p of M that varies smoothly with p.