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Generalization of the concept of parallel lines
A parallel curve of a given (progenitor) curve is the envelope of a family of congruent (equal-radius) circles centered on the curve. It generalises the
Parallel_curve
System of moving vectors in differential geometry
differential geometry, parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the
Parallel_transport
Relation used in geometry
non-straight parallel curves and non-flat parallel surfaces, which keep a fixed minimum distance and do not touch each other or intersect. The parallel symbol
Parallel_(geometry)
Shape with same width in all directions
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in
Curve_of_constant_width
Curve used in computer graphics and related fields
A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay, French pronunciation: [bezje]) is a parametric curve used in computer graphics and related fields. A sequence
Bézier_curve
pedal curve Fish curve Orthotomic Parallel curve Pedal curve Radial curve Roulette Strophoid Bathtub curve Bell curve Calibration curve Curve of growth
List_of_curves
Type of spline curve
the curve, and of the parallel curves to the given curves. For these reasons, researchers have investigated the use of Pythagorean hodograph curves as
Pythagorean_hodograph_curve
Measure of a fixed-income instrument's sensitivity to interest rates
basis point. Duration-based estimates work best for small, parallel shifts in the yield curve. Macaulay duration is the present-value-weighted average time
Duration_(finance)
Centers of curvature of a curve
given curve is reproduced. Parallel curves have the same evolute. Proof: A parallel curve with distance d {\displaystyle d} off the given curve has the
Evolute
Plane curve: conic section
In mathematics, a parabola (/pəˈræbələ/ pə-RA-bə-lə) is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially
Parabola
Fastest curve descent without friction
mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is the one
Brachistochrone_curve
Curve traced by a string as it is unwrapped from another curve
evolvent) is a particular type of curve that is dependent on another shape or curve. An example of the involute of a curve is the locus of a point on a piece
Involute
Length of a line segment
a point to a curve can be used to define its parallel curve, another curve all of whose points have the same distance to the given curve. The Euclidean
Euclidean_distance
Osculating circle Osculating plane Osgood curve Parallel (curve) Parallel transport Parametric curve Bézier curve Spline (mathematics) Hermite spline Beta
List_of_curves_topics
Digital signature scheme
Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves. It is
EdDSA
Distance from a point to the boundary of a set
needed] Distance function Level-set method Eikonal equation Parallel curve (also known as offset curve) Signed arc length Signed area Signed measure Signed volume
Signed_distance_function
Measurement of risk in a portfolio
not provide a very deep analysis. The overall effects of a parallel change in the yield curve are supplied but there is none of the more detailed analysis
Fixed-income_attribution
Topics referred to by the same term
between the axes of hypoid or offset-facing gears Offset (geometry), see parallel curve Offset (geophysics), the distance between a source and receiver of seismic
Offset
Mathematical measure of how much a curve or surface deviates from flatness
the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained
Curvature
Curve defined as zeros of polynomials
mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective
Algebraic_curve
Approach to public-key cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC
Elliptic-curve_cryptography
Relationships among bond yields of different maturities
"parallel shift". There is no single yield curve describing the cost of money for everybody. The most important factor in determining a yield curve is
Yield_curve
Neighborhood of a submanifold
direct description for these spaces). Parallel curve – Generalization of the concept of parallel lines (aka offset curve) Tube lemma – Lemma in topology Raoul
Tubular_neighborhood
Type of plane curve
convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going
Convex_curve
Computer scientist
tagged with Hermite data. Later work addressed reconstruction from non-parallel curve networks and cross-sections, and variational reconstruction from point
Tao_Ju
Diagnostic plot of binary classifier ability
A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the performance of a binary classifier model (although it
Receiver operating characteristic
Receiver_operating_characteristic
Curve that is common to two geometric objects
an intersection curve is a curve that is common to two geometric objects. In the simplest case, the intersection of two non-parallel planes in Euclidean
Intersection_curve
Curve formed by a hanging chain
regarded as a curve and that it is so flexible any force of tension exerted by the chain is parallel to the chain. The analysis of the curve for an optimal
Catenary
Mathematical term
plane curve at a point as the slope of its tangent line at that point. When the curve is approximated by a series of points, the slope of the curve may
Slope
Derived representation of a digital image
marching cubes algorithm. Signed distance function Function representation Parallel curve Level sets methods for distance computation. Gibson, Sarah F. Frisken;
Distance_transform
Province of Canada
border on the 49th parallel and the northern border on the 60th parallel curve to the left as one proceeds east, as do all parallels in the Northern Hemisphere
Saskatchewan
Job scheduling method in computing
In parallel processing, the Hilbert curve scheduling method turns a multidimensional task allocation problem into a one-dimensional space filling problem
Hilbert_curve_scheduling
Operation in mathematical morphology
(morphology) Mathematical morphology Opening (morphology) Minkowski addition Parallel curve Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0-12-637240-3
Dilation_(morphology)
Cubic plane curve
about this curve in a 1690 publication in Acta Eruditorum, concerned with geometrical optics. He showed that it arises as the caustic of parallel light rays
Tschirnhausen_cubic
Graph of wealth or income distribution
In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for
Lorenz_curve
Type of pitch in baseball
the hands of a clock at 12 and 6. The axis of rotation of a 12–6 curve is parallel with the level ground and perpendicular to its flight path. Pitchers
Curveball
Construct allowing differentiation of tangent vector fields of manifolds
along a curve has a characteristic feature: the point of contact of the tangent plane with the surface always moves with the curve under parallel translation
Affine_connection
Four-bar straight-line mechanism
not claim it did so. Rather, it traces out Watt's curve, a lemniscate or figure eight shaped curve; when the lengths of its bars and its base are chosen
Watt's_linkage
Function in economics
choice theory, the income-consumption curve (also called income expansion path and income offer curve) is a curve in a graph in which the quantities of
Income–consumption_curve
Curve generated by the projections of a fixed point on the tangents of another curve
curve of a given curve results from the orthogonal projection of a fixed point on the tangent lines of this curve. More precisely, for a plane curve C
Pedal_curve
Curved triangle with constant width
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed
Reuleaux_triangle
Method of representing curves and surfaces in computer graphics
Casteljau. They worked nearly parallel to each other, but because Bézier published the results of his work, Bézier curves were named after him, while de
Non-uniform_rational_B-spline
Mapping function that preserves data point locality
and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to
Z-order_curve
of parallel curves in the lamination merge to become a single family, as shown in the illustration. Although the switch consists of three curves ending
Train_track_(mathematics)
curve or bearing area curve (BAC) describes the surface texture of an object. The curve can be found from a profile trace by drawing lines parallel to
Abbott-Firestone_curve
Glissette Inverse curve Involute Isoptic including Orthoptic Orthotomic Negative pedal curve Pedal curve Parallel curve Radial curve Roulette Strophoid
List_of_mathematical_shapes
Anatomical curvature in human skull
angle with the curve of Spee to adapt for favorable loading of force on the teeth. The long axis of each lower tooth is aligned nearly parallel to their individual
Curve_of_Spee
Rotating circular machine part with teeth that mesh with another toothed part
quietly. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then
Gear
Physical law about electrical discharge in gases
The curve he found of voltage versus the pressure-gap length product (right) is called Paschen's curve. He found an equation that fit these curves, which
Paschen's_law
Figure-eight-shaped curve
(/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt, -kɪt/) is any of several figure-eight or ∞-shaped curves. The word comes from the Latin lēmniscātus, meaning "decorated with ribbons"
Lemniscate
Plane curve: conic section
mathematics, a hyperbola (/haɪˈpɜːrbələ/ hy-PUR-bə-lə) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for
Hyperbola
First-order method for approximating parallel transport of a vector along a curve
Schild's ladder is a first-order method for approximating parallel transport of a vector along a curve using only affinely parametrized geodesics. The method
Schild's_ladder
Macroeconomic model relating interest rates and output
the CORE Econ project. Parallelly, texts by Akira Weerapana and Stephen Williamson have outlined approaches where the LM curve is replaced with a real
IS–LM_model
Curve whose range contains the unit square
In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or
Space-filling_curve
Chart displaying multivariate data
are required to specify a curve and also a pair of curves may not have a unique intersection. Hence by using curves in parallel coordinates instead of lines
Parallel_coordinates
Mirror with a curved reflecting surface
A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved
Curved_mirror
H_{2}(M;\mathbb {Z} )} and γ ′ {\displaystyle \gamma ^{\prime }} is the parallel curve to γ induced by the trivialization of the tubular neighbourhood of γ
Casson_invariant
Geometrical concept
by cutting planes that are parallel to a coordinate plane (a plane determined by two coordinate axes) are called level curves or isolines. More specifically
Cross_section_(geometry)
Types of electrical circuits
connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether
Series_and_parallel_circuits
Point where the derivative of a function is zero or undefined (in certain cases)
equation of a curve. A critical point of such a curve, for the projection parallel to the y-axis (the map (x, y) → x), is a point of the curve where ∂ g ∂
Critical_point_(mathematics)
Curve in a road that has claimed lives because of numerous crashes
Dead Man's Curve is an American nickname for a curve in a road that has claimed many lives because of numerous crashes. A curve on Sunset Boulevard in
Dead_Man's_Curve
Sums vector sets A and B by adding each vector in A to each vector in B
(a.k.a. Quermassintegral or intrinsic volume) Parallel curve – Generalization of the concept of parallel lines Shapley–Folkman lemma – Sums of sets of
Minkowski_addition
In synchronous machines, the V curve (also spelled as V-curve) is the graph showing the relation of armature current as a function of field current in
V_curve
Mathematical vector components
given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component
Tangential and normal components
Tangential_and_normal_components
Photosynthetic part of a vascular plant
veins curve near the margin without joining adjacent secondary veins. Pinnate 2. Parallelodromous (parallel-veined, parallel-ribbed, parallel-nerved
Leaf
Probability distribution
poor model. A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy,
Normal_distribution
Function in mathematics
tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections
Connection_(mathematics)
Directions or positions relative to the shape and position of an object
Tangential – intersecting a curve at a point and parallel to the curve at that point. Collinear – in the same line Parallel – in the same direction. Transverse
Geometric_terms_of_location
Straight figure with zero width and depth
that may or not be parallel to each other. For more general algebraic curves, lines could also be: i-secant lines, meeting the curve in i points counted
Line_(geometry)
S-curved form used in woodworking, moulding, textile weaving, and architecture
element, or curve—often seen in architecture and building trades—that has a serpentine or extended S shape (sigmoid). Ogees consist of a double curve, the combination
Ogee
Resistor Inductor Capacitor Circuit
which would follow the same curve as the current in the series circuit. A series resistor with the inductor in a parallel LC circuit as shown in Figure 4
RLC_circuit
Curve traced by a point on a rolling circle
example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under
Cycloid
28 lines which touch a general quartic plane curve in two places
theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines
Bitangents_of_a_quartic
Conjecture that the laws of physics prevent closed timelike curves
distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting
Chronology protection conjecture
Chronology_protection_conjecture
Topics referred to by the same term
the Treasury yield curve Z-spread — parallel spread of a bond yield over the zero-volatility Treasury yield curve Stress–strain curve — physical relationship
Yield_curve_(disambiguation)
Process for increasing the performance between two systems solving the same problem
efficiency curves are more often used for graphs than speedup curves, since all of the area in the graph is useful (whereas in speedup curves half of the
Speedup
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola
Conic_section
Economic model of price determination in a market
dependent upon price. Just as the supply curve parallels the marginal cost curve, the demand curve parallels marginal utility, measured in dollars. Consumers
Supply_and_demand
also lies in the Hessian. parallel 1. Meeting at the line or plane at infinity, as in parallel lines 2. A parallel curve is the envelope of a circle
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
In mathematics, straight line touching a plane curve without crossing it
(or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined
Tangent
Directional planes
are thus not even parallel even if their reference points are along the same vertical line, since a vertical line is slightly curved. At any given location
Vertical_and_horizontal
Device used to smooth and dampen abrupt changes in rotational speed/torque
two curved parallel arc springs, one inside the other, but the internal arc spring is shorter so that it acts later. The characteristic curve of the outer
Dual-mass_flywheel
Plane curve drawn by an odd number of circular arcs
fixed points along the intrados curve, leaving no room for architectural modification. Conversely, the multi-center curve offers greater design freedom
Basket-handle_arch
Closed section of the London Underground
a cutting parallel to the Metropolitan Railway (MR). The name derives from Cromwell Road which is immediately south of the site of the curve. The track
Cromwell_Curve
Concept in economics
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent
Indifference_curve
Unsolved problem about inscribing a square in a Jordan curve
considers the curves traced out by the midpoints of secant line segments to the curve, parallel to a given line. He shows that, when these curves are intersected
Inscribed_square_problem
Operation in calculus
solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded
Integral
complex curves, and parallels as circular arcs. Azimuthal In standard presentation, azimuthal projections map meridians as straight lines and parallels as
List_of_map_projections
Species of moth
not reaching the dorsum. Some faint whitish scales form two obscure parallel curved series. The hindwings are blackish. "Phylomictis Meyrick, 1890" at
Phylomictis_leucopelta
Prehistoric settlement site
rows, also aligned with their gables parallel, curve in the southern and northern areas of the settlement. These curved rows resemble the concentric house
Trinca (Chalcolithic settlement)
Trinca_(Chalcolithic_settlement)
Concept in differential geometry
For curved connections, holonomy has nontrivial local and global features. Any kind of connection on a manifold gives rise, through its parallel transport
Holonomy
Curve in radiobiology
The cell survival curve is a curve often used in radiobiology that represents the relationship between the amount of cells retaining reproductive capabilities
Cell_survival_curve
Best results achieved to date
generic 117.35-bit elliptic curve discrete logarithm problem on a binary curve, using an optimized FPGA implementation of a parallel version of Pollard's rho
Discrete_logarithm_records
Method of vehicle parking
There will be a point in the transition between these curves where all the car's wheels will be parallel with each other. Less-confident drivers may choose
Parallel_parking
Fractal composed of triangles
the curve either parallel to the original line segment or forming a 60° angle with it. At every iteration, this construction gives a continuous curve. In
Sierpiński_triangle
Mathematical space with two coordinates
of them are parallel, meaning they never intersect and stay at uniform distance from each-other. Two-dimensional spaces can also be curved, for example
Two-dimensional_space
Fan that induces gas flow mostly parallel to the shaft
surge Paralleling This situation occurs when the system resistance curve and static pressure curve of the fan intersect have similar slope or parallel to
Axial_fan_design
Plane curve constructed from two other curves and a fixed point
Greek κισσοειδής (kissoeidēs) 'ivy-shaped') is a plane curve generated from two given curves C1, C2 and a point O (the pole). Let L be a variable line
Cissoid
Algorithm for integer factorization
The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Interpretation of results of heating DNA
Melting curve analysis is an assessment of the dissociation characteristics of double-stranded DNA during heating. As the temperature is raised, the double
Melting_curve_analysis
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