Orientation (geometry) in the context of Shape (geometry)

In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal' and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or an-, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

A shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type.In geometry, shape excludes information about the object's position, size, orientation and chirality.A figure is a representation including both shape and size (as in, e.g., figure of the Earth).

A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes.A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved surface (a two-dimensional space).

In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.

In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined.See:

Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere. When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation.

Angular distance appears in mathematics (in particular geometry and trigonometry) and all natural sciences (e.g., kinematics, astronomy, and geophysics). In the classical mechanics of rotating objects, it appears alongside angular velocity, angular acceleration, angular momentum, moment of inertia and torque.

Rotational symmetry, also known as radial symmetry in geometry, 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.

Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids.

In physics, angular velocity (symbol ω or ⁠${\displaystyle {\vec {\omega }}}$⁠, the lowercase Greek letter omega), also known as the angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.

The magnitude of the pseudovector, ${\displaystyle \omega =\|{\boldsymbol {\omega }}\|}$, represents the angular speed (or angular frequency), the angular rate at which the object rotates (spins or revolves). The pseudovector direction ${\displaystyle {\hat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}/\omega }$ is normal to the instantaneous plane of rotation or angular displacement.

Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise.

The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where Earth's axis of rotation meets its surface. This point is distinct from Earth's north magnetic pole. The South Pole is the other point where Earth's axis of rotation intersects its surface, in Antarctica.

In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin, orientation, and scale have been specified in physical space. It is based on a set of reference points, defined as geometric points whose position is identified both mathematically (with numerical coordinate values) and physically (signaled by conventional markers).An important special case is that of an inertial reference frame, a stationary or uniformly moving frame.

For n dimensions, n + 1 reference points are sufficient to fully define a reference frame. Using rectangular Cartesian coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance from the origin along each of the n coordinate axes.

Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will result.

This concept assumes that the rotation is also stable, such that no torque is required to keep it going. The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.

The near side of the Moon is the hemisphere of the Moon that is facing Earth. While Earth keeps turning through its near side to the Moon, changing in the course of a day the part it faces toward the Moon, the Moon keeps the same surface (or "face") oriented to Earth. This is due to the Moon rotating on its axis at the same rate that the Moon orbits the Earth—a phenomenon known as tidal locking. The opposite hemisphere is the far side.

The Moon is directly illuminated by the Sun, and the cyclically varying viewing conditions from Earth cause the lunar phases. The near side when dark is faintly visible due to earthshine, which is indirect sunlight reflected from the surface of Earth and onto the Moon.

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

In astronomy, precession refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes.

Body relative directions (also known as egocentric coordinates) are geometrical orientations relative to a body such as a human person's body or a road sign.The most common ones are: left and right; forward and backward; up and down.They form three pairs of orthogonal axes.

A gyroscope (from Ancient Greek γῦρος gŷros 'round' and σκοπέω skopéō 'to look') is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, due to the conservation of angular momentum.

Gyroscopes based on other operating principles also exist, such as the microchip-packaged MEMS gyroscopes found in electronic devices (sometimes called gyrometers), solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope.

The sense of balance or equilibrioception is the perception of balance and spatial orientation. It helps prevent humans and nonhuman animals from falling over when standing or moving. Equilibrioception is the result of a number of sensory systems working together; the eyes (visual system), the inner ears (vestibular system), and the body's sense of where it is in space (proprioception) ideally need to be intact.

The vestibular system, the region of the inner ear where three semicircular canals converge, works with the visual system to keep objects in focus when the head is moving. This is called the vestibulo-ocular reflex (VOR). The balance system works with the visual and skeletal systems (the muscles and joints and their sensors) to maintain orientation or balance. Visual signals sent to the brain about the body's position in relation to its surroundings are processed by the brain and compared to information from the vestibular and skeletal systems.