Rotational symmetry in the context of "Symmetry"

A lathe (/leɪð/) is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, threading and turning, with tools that are applied to the workpiece to create an object with symmetry about that axis.

Lathes are used in woodturning, metalworking, metal spinning, thermal spraying, reclamation, and glass-working. Lathes can be used to shape pottery, the best-known such design being the potter's wheel. Most suitably equipped metalworking lathes can be used to produce most solids of revolution, plane surfaces, and screw threads or helices. Ornamental lathes can produce more complex three-dimensional solids. The workpiece is usually held in place by either one or two centers, at least one of which can typically be moved horizontally to accommodate varying workpiece lengths. Other work-holding methods include clamping the work about the axis of rotation using a chuck or collet, or attaching it to a faceplate using clamps or dog clutch. Lathes equipped with special lathe milling fixtures can be used to complete milling operations.

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.

A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces, a hyperboloid is characterized by not being a cone or a cylinder, having a center of symmetry, and intersecting many planes into hyperbolas. A hyperboloid has three pairwise perpendicular axes of symmetry, and three pairwise perpendicular planes of symmetry.

An optical axis is an imaginary line that passes through the geometrical center of an optical system such as a camera lens, microscope or telescopic sight. Lens elements often have rotational symmetry about the axis.

The optical axis defines the path along which light propagates through the system, up to first approximation. For a system composed of simple lenses and mirrors, the axis passes through the center of curvature of each surface, and coincides with the axis of rotational symmetry. The optical axis is often coincident with the system's mechanical axis, but not always, as in the case of off-axis optical systems.

Axial symmetry is symmetry around an axis or line (geometry). An object is said to be axially symmetric if its appearance is unchanged if transformed around an axis. The main types of axial symmetry are reflection symmetry and rotational symmetry (including circular symmetry for plane figures and cylindrical symmetry for surfaces of revolution). For example, a baseball bat (without trademark or other design), or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric.

Axial symmetry can also be discrete with a fixed angle of rotation, 360°/n for n-fold symmetry.

Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. The lens and cornea of an eye without astigmatism are nearly spherical, with only a single radius of curvature, and any refractive errors present can be corrected with simple glasses. In an eye with astigmatism, either the lens or the cornea is slightly egg-shaped, with higher curvature in one direction than the other. This gives distorted or blurred vision at any distance and requires corrective lenses that apply different optical powers at different rotational angles. Astigmatism can lead to symptoms that include eyestrain, headaches, and trouble driving at night. Astigmatism often is present at birth, but can change or develop later in life. If it occurs in early life and is left untreated, it may result in amblyopia.

The cause of astigmatism is unclear, although it is believed to be partly related to genetic factors. The underlying mechanism involves an irregular curvature of the cornea and protective reaction changes in the lens of the eye, called lens astigmatism, that has the same mechanism as spasm of accommodation. Diagnosis is by an eye examination called autorefractor keratometry (objective, allows to see lens and cornea components of astigmatism) and subjective refraction.

A guy-wire, guy-line, guy-rope, down guy, or stay, also called simply a guy, is a tensioned cable designed to add stability to a freestanding structure. They are used commonly for ship masts, radio masts, wind turbines, utility poles, and tents. A thin vertical mast supported by guy wires is called a guyed mast. Structures that support antennas are frequently of a lattice construction and are called "towers". One end of the guy is attached to the structure, and the other is anchored to the ground at some distance from the mast or tower base. The tension in the diagonal guy-wire, combined with the compression and buckling strength of the structure, allows the structure to withstand lateral loads such as wind or the weight of cantilevered structures. They are installed radially, usually at equal angles about the structure, in trios and quads. As the tower leans a bit due to the wind force, the increased guy tension is resolved into a compression force in the tower or mast and a lateral force that resists the wind load. For example, antenna masts are often held up by three guy-wires at 120° angles. Structures with predictable lateral loads, such as electrical utility poles, may require only a single guy-wire to offset the lateral pull of the electrical wires at a spot where the wires change direction.

Conductive guy cables for radio antenna masts can catch and deflect radiation in unintended directions, so their electrical characteristics must be included in the design. Often the guy wire is divided by strain insulators into isolated sections whose lengths are not resonant with the transmission frequencies.

In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point.

For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it would not be considered gyration.