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A diameter of an ellipse is any chord passing through the centre of the ellipse. [1] For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis.
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.
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
The diameter is always attained by two points of the convex hull of the input. A trivial brute-force search can be used to find the diameter of points in time () (assuming constant-time distance evaluations) but faster algorithms are possible for points in low dimensions.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Thus, the angular diameter of Earth's orbit around the Sun as viewed from a distance of 1 pc is 2″, as 1 AU is the mean radius of Earth's orbit. The angular diameter of the Sun, from a distance of one light-year, is 0.03″, and that of Earth 0.0003″. The angular ...
′ ¯ is the diameter of a circle and ¯ ′ ¯. In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).
In fluid dynamics, Sauter mean diameter (SMD) is an average measure of particle size. It was originally developed by German scientist Josef Sauter in the late 1920s. [1] [2] It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest. Several methods have been devised to obtain a good estimate ...