Cylinder (geometry) in the context of Higher dimensional

A music box (American English) or musical box (British English) is an automatic musical instrument in a box that produces musical notes by using a set of pins placed on a revolving cylinder or disc to pluck the tuned teeth (or lamellae) of a steel comb. The popular device best known today as a "music box" developed from musical snuff boxes of the 18th century and were originally called carillons à musique (French for "chimes of music"). Some of the more complex boxes also contain a tiny drum and/or bells in addition to the metal comb.

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior.

Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms, cubes (and other polyhedrons), cylinders, cones (including truncated) and other solids of revolution.

A horn is any of a family of musical instruments made of a tube, usually made of metal and often curved in various ways, with one narrow end into which the musician blows, and a wide end from which sound emerges. In horns, unlike some other brass instruments such as the trumpet, the bore gradually increases in width through most of its length—that is to say, it is conical rather than cylindrical. In jazz and popular-music contexts, the word may be used loosely to refer to any wind instrument, and a section of brass or woodwind instruments, or a mixture of the two, is called a horn section in these contexts.

A collet /ˈkɒlɪt/ is a segmented sleeve, band or collar. One of the two radial surfaces of a collet is usually tapered (i.e a truncated cone) and the other is cylindrical. The term collet commonly refers to a type of chuck that uses collets to hold either a workpiece or a tool (such as a drill), but collets have other mechanical applications.

An external collet is a sleeve with a cylindrical inner surface and a conical outer surface. The collet can be squeezed against a matching taper such that its inner surface contracts to a slightly smaller diameter, squeezing the tool or workpiece to hold it securely. Most often the collet is made of spring steel, with one or more kerf cuts along its length to allow it to expand and contract. This type of collet holds the external surface of the tool or workpiece being clamped. This is the most usual type of collet chuck. An external collet clamps against the internal surface or bore of a hollow cylinder. The collet's taper is internal and the collet expands when a corresponding taper is drawn or forced into the collet's internal taper.

A pipe is a tubular section or hollow cylinder, usually but not necessarily of circular cross-section, used mainly to convey substances which can flow — liquids and gases (fluids), slurries, powders and masses of small solids. It can also be used for structural applications; a hollow pipe is far stiffer per unit weight than the solid members.

In common usage the words pipe and tube are usually interchangeable, but in industry and engineering, the terms are uniquely defined. Depending on the applicable standard to which it is manufactured, pipe is generally specified by a nominal diameter with a constant outside diameter (OD) and a schedule that defines the thickness. Tube is most often specified by the OD and wall thickness, but may be specified by any two of OD, inside diameter (ID), and wall thickness. Pipe is generally manufactured to one of several international and national industrial standards. While similar standards exist for specific industry application tubing, tube is often made to custom sizes and a broader range of diameters and tolerances. Many industrial and government standards exist for the production of pipe and tubing. The term "tube" is also commonly applied to non-cylindrical sections, i.e., square or rectangular tubing. In general, "pipe" is the more common term in most of the world, whereas "tube" is more widely used in the United States.

In geometry, two or more objects are said to be concentric when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyhedra, parallelograms, cones, conic sections, and quadrics.

Geometric objects are coaxial if they share the same axis (line of symmetry). Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, conic sections, and surfaces of revolution.

A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).The volume bounded by the surface created by this revolution is the solid of revolution.

Examples of surfaces of revolution generated by a straight line are cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere of which it is then a great circle, and if the circle is rotated around an axis that does not intersect the interior of a circle, then it generates a torus which does not intersect itself (a ring torus).

The screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. It is one of the six classical simple machines. The most common form consists of a cylindrical shaft with helical grooves or ridges called threads around the outside. The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut can rotate around a stationary screw shaft. Geometrically, a screw can be viewed as a narrow inclined plane wrapped around a cylinder.

Like the other simple machines a screw can amplify force; a small rotational force (torque) on the shaft can exert a large axial force on a load. The smaller the pitch (the distance between the screw's threads), the greater the mechanical advantage (the ratio of output to input force). Screws are widely used in threaded fasteners to hold objects together, and in devices such as screw tops for containers, vises, screw jacks and screw presses.

In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions. It is contrasted with tension or traction, the application of balanced outward ("pulling") forces, and with shearing forces, directed so as to displace layers of the material parallel to each other. The compressive strength of materials and structures is an important engineering consideration.

In uniaxial compression, the forces are directed along one direction only, so that they act towards decreasing the object's length along that direction. The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or all over the side surface of a cylinder, so as to reduce its area (biaxial compression), or inwards over the entire surface of a body, so as to reduce its volume.

A screw thread is a helical structure used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped around a cylinder or cone in the form of a helix, with the former being called a straight thread and the latter called a tapered thread. A screw thread is the essential feature of the screw as a simple machine and also as a threaded fastener.

The mechanical advantage of a screw thread depends on its lead, which is the linear distance the screw travels in one revolution. In most applications, the lead of a screw thread is chosen so that friction is sufficient to prevent linear motion being converted to rotary, that is so the screw does not slip even when linear force is applied, as long as no external rotational force is present. This characteristic is essential to the vast majority of its uses. The tightening of a fastener's screw thread is comparable to driving a wedge into a gap until it sticks fast through friction and slight elastic deformation.

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure. This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to cylinders, cones, pyramids, parallelepipeds, prisms, and frustums.

The side or point opposite the base is often called the apex or summit of the shape.

A rivet is a permanent mechanical fastener. Before being installed, a rivet consists of a smooth cylindrical shaft with a head on one end. The end opposite the head is called the tail. On installation, the deformed end is called the shop head or buck-tail.

Because there is effectively a head on each end of an installed rivet, it can support tension loads. However, it is much more capable of supporting shear loads (loads perpendicular to the axis of the shaft).