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In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen.
His first novel, "Net een wenner" (Only One Winner) was published in 2005. [6] Badenhorst is married and has two children, Dirk (born 12 July 2004) and Suzanne (born 28 May 2007). He has Asperger syndrome [1] and campaigns for public awareness of the condition. [7]
We want to calculate probability distribution function of distance to the nearest neighbor (NN) particle. (The problem was first considered by Paul Hertz; [1] for a modern derivation see, e.g.,. [2]) Let us assume particles inside a sphere having volume , so that = /. Note that since the particles in the ideal gas are non-interacting, the ...
The hyperboloid model can be represented as the equation t 2 = x 1 2 + x 2 2 + 1, t > 1. It can be used to construct a Poincaré disk model as a projection viewed from (t = −1, x 1 = 0, x 2 = 0), projecting the upper half hyperboloid onto the unit disk at t = 0. The red geodesic in the Poincaré disk model projects to the brown geodesic on ...
The density of quartz is around 2.65 g/cm 3 but the dry bulk density of a soil can be less than half that value. Most soils have a dry bulk density between 1.0 and 1.6 g/cm 3 but organic soil and some porous clays may have a dry bulk density well below 1 g/cm 3.
A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity) d(x, y) = 0 if and only if x = y (identity of indiscernibles.
The volume of the limbs and branches can be significant. For example, the Middleton Live Oak (Quercus virginiana), height 67.4 feet, dbh 10.44 feet, crown spread 118 feet) was found to have a trunk volume of 970 ft 3 (24.5 m 3) and a branch volume of 3,850 ft 3 (109 m 3) [15] The branch volume was almost
Maxwell’s thermodynamic surface is an 1874 sculpture [1] made by Scottish physicist James Clerk Maxwell (1831–1879). This model provides a three-dimensional space of the various states of a fictitious substance with water-like properties. [2] This plot has coordinates volume (x), entropy (y), and energy (z).