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A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, etc. of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is ...
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 ...
A sphere enclosed by its axis-aligned minimum bounding box (in 3 dimensions) In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie.
In geotechnical engineering, a caisson (/ ˈ k eɪ s ən,-s ɒ n /; borrowed from French caisson ' box ', from Italian cassone ' large box ', an augmentative of cassa) is a watertight retaining structure. [1] It is used, for example, to work on the foundations of a bridge pier, for the construction of a concrete dam, [2] or for the repair of ...
A percentage is typically added to neat volume to estimate loose (i.e. uncompacted) volumes for procurement purposes. With concrete work, neat volume is calculated assuming there is no bowing in the formwork , or, for cast-in-place concrete, that the surfaces in contact with the concrete have no voids or imperfections that would require a ...
Q mi = discharge capacity without freeboard (ft 3 /s) (In this case, freeboard is the vertical distance from the water surface to the dam crest when the water surface is at a lower elevation.) L = length of the spillway crest (ft) H = height of the sidewalls above the spillway crest (ft)
As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume. For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume.