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A volume table is a chart to aid in the estimation of standing timber volume. These tables are based on volume equations and use correlations between certain aspects of a tree to estimate the volume to a degree of certainty. The diameter at breast height (DBH) and the merchantable height are used to determine the total volume. Difficulties ...
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
The neiloid form often applies near the base of tree trunks exhibiting root flare, and just below limb bulges. The formula for the volume of a frustum of a neiloid: [25] V = (h)[A b + (A b 2 A u) 1/3 + (A b A u 2) 1/3 + A u], where A b is the area of the base and A u is the area of the top of the frustum. This volume may also be expressed in ...
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
The hoppus cubic foot (or ‘hoppus cube’ or ‘h cu ft’) was the standard volume measurement used for timber in the British Empire and countries in the British sphere of influence before the introduction of metric units. It is still used in the hardwood trade in some countries.
The pentagonal bifrustum is the dual polyhedron of a Johnson solid, the elongated pentagonal bipyramid.A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms).
Hutton's definitions in 1795 [4]. The ancient Greek mathematician Euclid defined five types of quadrilateral, of which four had two sets of parallel sides (known in English as square, rectangle, rhombus and rhomboid) and the last did not have two sets of parallel sides – a τραπέζια (trapezia [5] literally 'table', itself from τετράς (tetrás) 'four' + πέζα (péza) 'foot ...
In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold ...