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The product property holds much more generally, for fibrations with certain conditions. If : is a fibration with fiber F, with the base B path-connected, and the fibration is orientable over a field K, then the Euler characteristic with coefficients in the field K satisfies the product property: [10]
Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers ...
In computer graphics and computational geometry, a bounding volume (or bounding region) for a set of objects is a closed region that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations, such as by using simple regions, having simpler ways to test for overlap .
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. [ 1 ] It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides r {\displaystyle r} and g {\displaystyle ...
Watt recognized the problem as being related to the square–cube law, in that the surface-to-volume ratio of the model's cylinder was greater than that of the much larger commercial engines, leading to excessive heat loss. [4] Experiments with this model led to Watt's famous improvements to the steam engine.
The volume flux, through a tube bounded by a surface of some constant value ψ, is equal to 2πψ and is constant. [ 9 ] For this case of an axisymmetric flow, the only non-zero component of the vorticity vector ω is the azimuthal φ –component ω φ [ 11 ] [ 12 ]
This formula holds whether or not the cylinder is a right cylinder. [7] This formula may be established by using Cavalieri's principle. A solid elliptic right cylinder with the semi-axes a and b for the base ellipse and height h. In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the ...