Magnitude (astronomy)In astronomy, magnitude is measure of the brightness of an object, usually in a defined passband. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus. Magnitude values do not have a unit. The scale is logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is times brighter than the magnitude 1 higher.
Four-accelerationIn the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity). Four-acceleration has applications in areas such as the annihilation of antiprotons, resonance of strange particles and radiation of an accelerated charge. In inertial coordinates in special relativity, four-acceleration is defined as the rate of change in four-velocity with respect to the particle's proper time along its worldline.
Absolute magnitudeAbsolute magnitude (M) is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly , without extinction (or dimming) of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale.
Tangent spaceIn mathematics, the tangent space of a manifold is a generalization of to curves in two-dimensional space and to surfaces in three-dimensional space in higher dimensions. In the context of physics the tangent space to a manifold at a point can be viewed as the space of possible velocities for a particle moving on the manifold. In differential geometry, one can attach to every point of a differentiable manifold a tangent space—a real vector space that intuitively contains the possible directions in which one can tangentially pass through .
SpeedIn everyday use and in kinematics, the speed (commonly referred to as v) of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero.
AirfoilAn airfoil (American English) or aerofoil (British English) is a streamlined body that is capable of generating significantly more lift than drag. Wings, sails and propeller blades are examples of airfoils. Foils of similar function designed with water as the working fluid are called hydrofoils. When oriented at a suitable angle, a solid body moving through a fluid deflects the oncoming fluid (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection.
Rotation formalisms in three dimensionsIn geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
Proper accelerationIn relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, because the same gravity acts equally on the inertial observer. As a consequence, all inertial observers always have a proper acceleration of zero.
Cylindrical coordinate systemA cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.
Fixed-wing aircraftA fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinct from rotary-wing aircraft (in which the wings form a rotor mounted on a spinning shaft or "mast"), and ornithopters (in which the wings flap in a manner similar to that of a bird).
Tangent bundleIn differential geometry, the tangent bundle of a differentiable manifold is a manifold which assembles all the tangent vectors in . As a set, it is given by the disjoint union of the tangent spaces of . That is, where denotes the tangent space to at the point . So, an element of can be thought of as a pair , where is a point in and is a tangent vector to at . There is a natural projection defined by . This projection maps each element of the tangent space to the single point .
Squaring the circleSquaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi () is a transcendental number.
