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In differential geometry, a smooth surface in three dimensions has a parabolic point when the Gaussian curvature is zero. Typically such points lie on a curve called the parabolic line
which separates the surface into regions of positive and negative Gaussian curvature.
Points on the parabolic line give rise to folds on the Gauss map: where a ridge crosses a parabolic line there is a cusp of the Gauss map.[1]
^Ian R. Porteous (2001) Geometric Differentiation, Chapter 11 Ridges and Ribs, pp 182–97, Cambridge University Press ISBN 0-521-00264-8 .
dimensions has a parabolic point when the Gaussian curvature is zero. Typically such points lie on a curve called the parabolicline which separates the...
A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio...
surface: when the surface has zero Gaussian curvature, (that is along a parabolicline) the Gauss map will have a fold catastrophe. This fold may contain cusps...
Universal parabolic constant Confocal conic sections § Confocal parabolas The tangential plane just touches the conical surface along a line, which passes...
An apse line, or line of apsides, is an imaginary line defined by an orbit's eccentricity vector. It is strictly defined for elliptic, parabolic, and hyperbolic...
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly...
A parabolic trough collector (PTC) is a type of solar thermal collector that is straight in one dimension and curved as a parabola in the other two, lined...
surface will be locally saddle shaped. At parabolic points, one of the principal curvatures is zero. Parabolic points generally lie in a curve separating...
catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting...
quad-headlamps, and a large crest grille. The side profile features a parabolicline, and a fastback-type side view. The rear uses taillamp styling similar...
separated by a curve of points with zero Gaussian curvature called a parabolicline. When a surface has a constant zero Gaussian curvature, then it is a...
models. A parabolic solar cooker. Parabolic solar cooker used to cook Paella. Solar tea kettle in Tibet Solar cooker in rural Uganda Parabolic solar cookers...
with the low beam and high beam together. Viewed from the side, the ParabolicLine extending from the front to the rear of the car maintains a certain...
In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency...
and can be more focused than line array loudspeakers allowing sound to be sent to isolated audience targets. The parabolic loudspeaker has been used for...
curvature is zero are called parabolic. In general, parabolic points form a curve on the surface called the parabolicline. The first fundamental form...
a single real line (actually a coincident pair of lines), or only at the vertex. These cases give rise to the hyperbolic, parabolic or elliptic cylinders...
In stock and securities market technical analysis, parabolic SAR (parabolic stop and reverse) is a method devised by J. Welles Wilder Jr., to find potential...
the parabolic segment that it forms in red and the focal parameter in green. (The focus of the parabola is the point F and the directrix is the line L.)...
convergence (such as line search). Moreover, not requiring the computation or approximation of function derivatives makes successive parabolic interpolation...
asymptote y = x2 + 2x + 3, which is known as a parabolic asymptote because it is a parabola rather than a straight line. Asymptotes are used in procedures of curve...
parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate...
circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The...
of a circular paraboloid is widely used in astronomy for parabolic reflectors and parabolic antennas. The surface of a rotating liquid is also a circular...
culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4 3 {\displaystyle {\tfrac {4}{3}}} that...
In optimization, line search is a basic iterative approach to find a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f : R...
with a reduced opening reflecting the car's electric powertrain), and "ParabolicLine" profile. Other styling details include a coupe-like profile, large...
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