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If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder. In some elementary treatments, a cylinder always means a circular cylinder. [2]
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
For a product space, the cylinder σ-algebra is the one that is generated by cylinder sets. In the context of a Banach space X , {\displaystyle X,} the cylindrical σ-algebra A ( X , X ′ ) {\displaystyle {\mathfrak {A}}(X,X')} is defined to be the coarsest σ-algebra (that is, the one with the fewest measurable sets) such that every ...
Typical horizontal steam engine with double-acting cylinder. A double-acting cylinder is a cylinder in which the working fluid acts alternately on both sides of the piston. . In order to connect the piston in a double-acting cylinder to an external mechanism, such as a crank shaft, a hole must be provided in one end of the cylinder for the piston rod, and this is fitted with a gland or ...
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 ...
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where . ρ is the length of the vector projected onto the xy-plane,; φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π),
The above definition of a function is essentially that of the founders of calculus, Leibniz, Newton and Euler. However, it cannot be formalized, since there is no mathematical definition of an "assignment". It is only at the end of the 19th century that the first formal definition of a function could be provided, in terms of set theory.
Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, accretion disks in ...