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**Geometric terms of location** describe directions or positions relative to the shape of an object. These terms are used in descriptions of engineering, physics, and other sciences, as well as ordinary day to day discourse.

Though these terms by themselves may be somewhat ambiguous, they are usually used in a context in which their meaning is clear. For example, when referring to a drive shaft it is clear what is meant by axial or radial directions. Or, in a free body diagram, one may similarly infer a sense of orientation by the forces or other vectors represented.

**See also:*** Anatomical terms of location *

Common geometric terms of location are:

**Adjacent**- next to**Axial**– along the center of a round body, or the axis of rotation of a body**Azimuthal**or**circumferential**– following around a curve or circumference of an object. For instance, the pattern of cells in Taylor–Couette flow varies along the azimuth of the experiment.**Collinear**- in the same line**Degree of freedom**- axis direction, see six degrees of freedom**Elevation**- along a curve from a point on the horizon to the zenith, directly overhead.**Depression**– along a curve from a point on the horizon to the nadir, directly below.**Lateral**– spanning the width of a body. The distinction between width and length may be unclear out of context.**Lineal**– following along a given path. The shape of the path is not necessarily straight (compare to linear). For instance, a length of rope might be measured in lineal meters or feet. See arc length.**Longitudinal**– spanning the length of a body.**Orthogonal**– at right angles to a line, or more generally, on a different axis.**Parallel**- in the same direction**Perpendicular**- at right angles to, synonym to orthogonal**Radial**– along a direction pointing along a radius from the center of an object, or perpendicular to a curved path.**Tangential**– intersecting a curve at a point and parallel to the curve at that point.**Transverse**– orthogonal to a specified direction, such as a particle trajectory or an axis of rotation.**Vertical**– spanning the length of a body.

In plane geometry, an **angle** is the figure formed by two rays, called the *sides* of the angle, sharing a common endpoint, called the *vertex* of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

In mathematics, a **spherical coordinate system** is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the *radial distance* of that point from a fixed origin, its *polar angle* measured from a fixed zenith direction, and the *azimuthal angle* of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system.

A **rotation** is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called *rotation axes*. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution, typically when it is produced by gravity. The axis is called a **pole**.

**Polarization** is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string *(see image)*; for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids.

**Orbital inclination** measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

In elementary geometry, the property of being **perpendicular** (**perpendicularity**) is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects.

In astronomy, an **analemma** is a diagram showing the position of the Sun in the sky, as seen from a fixed location on Earth at the same mean solar time, as that position varies over the course of a year. The diagram will resemble the figure 8. Globes of Earth often display an analemma.

A **gear** or **cogwheel** is a rotating machine part having cut teeth or, in the case of a cogwheel, inserted teeth, which mesh with another toothed part to transmit torque. Geared devices can change the speed, torque, and direction of a power source. Gears almost always produce a change in torque, creating a mechanical advantage, through their gear ratio, and thus may be considered a simple machine. The teeth on the two meshing gears all have the same shape. Two or more meshing gears, working in a sequence, are called a gear train or a *transmission*. A gear can mesh with a linear toothed part, called a rack, producing translation instead of rotation.

A **circle of latitude** on Earth is an abstract east–west circle connecting all locations around Earth at a given latitude.

In mathematics and physics, the **right-hand rule** is a common mnemonic for understanding orientation of axes in three-dimensional space.

In physics, **circular motion** is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.

**Rotational symmetry**, also known as **radial symmetry** in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.

In classical geometry, a **radius** of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin *radius*, meaning ray but also the spoke of a chariot wheel. The plural of radius can be either *radii* or the conventional English plural *radiuses*. The typical abbreviation and mathematical variable name for radius is **r**. By extension, the diameter **d** is defined as twice the radius:

In optics a **ray** is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray theory does not describe phenomena such as diffraction, which require wave theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

In Gaussian optics, the **cardinal points** consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the **focal points**, the **principal points**, and the **nodal points**. For *ideal* systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points. The only ideal system that has been achieved in practice is the plane mirror, however the cardinal points are widely used to *approximate* the behavior of real optical systems. Cardinal points provide a way to analytically simplify a system with many components, allowing the imaging characteristics of the system to be approximately determined with simple calculations.

In geometry, a **plane of rotation** is an abstract object used to describe or visualize rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotation it can be used in other dimensions, such as two, four or more dimensions.

The **Rayleigh sky model** describes the observed polarization pattern of the daytime sky. Within the atmosphere Rayleigh scattering of light from air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky to be blue. The polarization is characterized at each wavelength by its degree of polarization, and orientation.

In astronomy, geography, and related sciences and contexts, a *direction* or *plane* passing by a given point is said to be **vertical** if it contains the local gravity direction at that point. Conversely, a direction or plane is said to be **horizontal** if it is perpendicular to the vertical direction. In general, something that is vertical can be drawn from up to down, such as the y-axis in the Cartesian coordinate system.

In geometry, an object has **symmetry** if there is an operation or transformation that maps the figure/object onto itself. Thus, a symmetry can be thought of as an immunity to change. For instance, a circle rotated about its center will have the same shape and size as the original circle, as all points before and after the transform would be indistinguishable. A circle is thus said to be *symmetric under rotation* or to have *rotational symmetry*. If the isometry is the reflection of a plane figure about a line, then the figure is said to have reflectional symmetry or line symmetry; it is also possible for a figure/object to have more than one line of symmetry.

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