A cylinder is a Surface in the space defined by a right (d), called generating , passing by a variable point describing a Courbe planes closed (c), called direct curve and keeping a fixed direction. One also speaks about cylindrical surface . The prism S (whose Cubic S and Parallélépipède S rectangles) is particular cases of cylinder.

One can consider a cylinder as a cone whose top “is rejected ad infinitum”.

By extension, if a cylinder is cut by two parallel plans strictly , the solid obtained is still called a cylinder. If these plans are perpendicular S to the generating right-hand side, it is said that the cylinder is right . The distance separating the two parallel plans is called the height cylinder and the surface delimited by the direct curve is called the bases cylinder. If one notes H the height of the cylinder and With the surface of his base, then its Volume V is given by the equality: V = has × H.

Cylinder of cross-section

A cylinder of cross-section is a cylinder whose direct curve is a Cercle and whose generating right-hand side is perpendicular to the plan containing the directing circle.

In the space brought back to the orthonormal Reference mark $\backslash \; (O,\; \backslash \; vec\; I,\; \backslash \; vec\; J,\; \backslash \; vec\; K)$, the cylinder of axis $\backslash \; (z\text{'}\; Z)$ has as an equation: $\backslash \; x^2+y^2=r^2$ where $\backslash \; r$ is the radius directing circle.

Note: the majority of people think that the term cylinder applies exclusively to the cylinder of cross-section.

Mechanics

• the cylinders are the parts which guide the movement of the Piston S in various devices:
• Cylinder of an Engine spark-ignition
• transmitting and receiving Cylinder of hydraulic Brake
• Cylinder of Steam engine

• Cylinder of safety of Lock

• the term Cylindrée which is derived from the word cylinder is not solely used for the systems rolls/piston.

Roll in volume

There exists a more formal mathematical definition cylinder, which includes all the internal points. This definition is generalizable with N dimensions of a Euclidean Espace. In $\backslash \; mathbb\; \{R\}\; ^n$, the cylinder of cross-section and ray R , of axis $\backslash \; mathrm\; \{Vect\}\; \backslash \; left\; (e\_3,\; e\_4,\; \backslash \; ldots,\; e\_n\; \backslash \; right)$, is defined by:

$C\; =\; \backslash \; \{X\; \backslash \; in\; \backslash \; mathbb\; \{R\}\; ^n;\; x\_1^2\; +\; x\_2^2\; \backslash \; Leq\; R^2\; \backslash \}$

See too

External bond

• A. Javary, Treated descriptive geometry , 1881, (on Gallica): Cones and cylinders, sphere and surfaces of the second degree

• the shortest way on the cylinder

Simple: Cylinder

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