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Isophote

In geometry, an isophote is a curve on an illuminated surface that connects points of equal brightness. One supposes that the illumination is done by parallel light and the brightness b is measured by

Secant line

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant intersec

Ogive

An ogive (/ˈoʊdʒaɪv/ OH-jive) is the roundly tapered end of a two-dimensional or three-dimensional object. Ogive curves and surfaces are used in engineering, architecture and woodworking.

Hypercycle (geometry)

In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis). Given a straight line L and a po

Bézier curve

A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula.

Inflection point

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a smooth plane curve at which the curvature

Frenet–Serret formulas

In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space R3, or the geometric prope

Polygonal chain

In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points called its vertices. The curve itself consists of t

Pursuit curve

In geometry, a curve of pursuit is a curve constructed by analogy to having a point or points representing pursuers and pursuees; the curve of pursuit is the curve traced by the pursuers. With the pat

Horocycle

In hyperbolic geometry, a horocycle (from Greek ὅριον (hórion) 'border', and κύκλος (kúklos) 'circle'), sometimes called an oricycle, oricircle, or limit circle, is a curve whose normal or perpendicul

Intersection curve

In geometry, 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 3-space is a line. In general, an

Cesàro equation

In geometry, the Cesàro equation of a plane curve is an equation relating the curvature (κ) at a point of the curve to the arc length (s) from the start of the curve to the given point. It may also be

Whewell equation

The Whewell equation of a plane curve is an equation that relates the tangential angle (φ) with arclength (s), where the tangential angle is the angle between the tangent to the curve and the x-axis,

Transcendental curve

In analytical geometry , a transcendental curve is a curve that is not an algebraic curve. Here for a curve, C, what matters is the point set (typically in the plane) underlying C, not a given paramet

Circular arc

A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the centre of th

Position line

A position line or line of position (LOP) is a line (or, on the surface of the earth, a curve) that can be both identified on a chart (nautical chart or aeronautical chart) and translated to the surfa

Negative pedal curve

In geometry, a negative pedal curve is a plane curve that can be constructed from another plane curve C and a fixed point P on that curve. For each point X ≠ P on the curve C, the negative pedal curve

Steinmetz curve

A Steinmetz curve is the curve of intersection of two right circular cylinders of radii and whose axes intersect perpendicularly. In case of the Steimetz curves are the edges of a Steinmetz solid. If

Pseudoholomorphic curve

In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauc

Sectrix of Maclaurin

In geometry, a sectrix of Maclaurin is defined as the curve swept out by the point of intersection of two lines which are each revolving at constant rates about different points called poles. Equivale

Pedal curve

In mathematics, a pedal 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 and a given fixed pedal p

Subtangent

In geometry, the subtangent and related terms are certain line segments defined using the line tangent to a curve at a given point and the coordinate axes. The terms are somewhat archaic today but wer

Cissoid

In geometry, a cissoid ((from Ancient 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 passing thr

Recursive wave

A recursive wave is a self-similar curve in three-dimensional space that is constructed by iteratively adding a helix around the previous curve.

Hyperbolic growth

When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function has a hyperbola as a

Areal velocity

In classical mechanics, areal velocity (also called sector velocity or sectorial velocity) is a pseudovector whose length equals the rate of change at which area is swept out by a particle as it moves

Curve orientation

In mathematics, an orientation of a curve is the choice of one of the two possible directions for travelling on the curve. For example, for Cartesian coordinates, the x-axis is traditionally oriented

Osculating curve

In differential geometry, an osculating curve is a plane curve from a given family that has the highest possible order of contact with another curve.That is, if F is a family of smooth curves, C is a

Tortuosity

Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuos

Ground track

A ground track or ground trace is the path on the surface of a planet directly below an aircraft's or satellite's trajectory. In the case of satellites, it is also known as a suborbital track, and is

Triple helix

In the fields of geometry and biochemistry, a triple helix (plural triple helices) is a set of three congruent geometrical helices with the same axis, differing by a translation along the axis. This m

Torsion of a curve

In the differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken together, the curvature and the torsion of a s

Asymptotic curve

In the differential geometry of surfaces, an asymptotic curve is a curve always tangent to an asymptotic direction of the surface (where they exist). It is sometimes called an asymptotic line, althoug

French curve

A French curve is a template usually made from metal, wood or plastic composed of many different segments of the Euler spiral (aka the clothoid curve). It is used in manual drafting and in fashion des

Tendril perversion

Tendril perversion is a geometric phenomenon sometimes observed in helical structures in which the direction of the helix transitions between left-handed and right-handed. Such a reversal of chirality

Glissette

In geometry, a glissette is a curve determined by either the locus of any point, or the envelope of any line or curve, that is attached to a curve that slides against or along two other fixed curves.

Circular algebraic curve

In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a

Harmonograph

A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves or related drawings of greater complexity. The devices,

Dual curve

In projective geometry, a dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to its dual, sending each

N-curve

We take the functional theoretic algebra C[0, 1] of curves. For each loop γ at 1, and each positive integer n, we define a curve called n-curve. The n-curves are interesting in two ways. 1.
* Their f

Affine curvature

Special affine curvature, also known as the equiaffine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve that remains unchanged under a special affine t

Truncus (mathematics)

In analytic geometry, a truncus is a curve in the Cartesian plane consisting of all points (x,y) satisfying an equation of the form where a, b, and c are given constants. The two asymptotes of a trunc

Orthoptic (geometry)

In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle. Examples: 1.
* The orthoptic of a parabola is its directrix (proof: see ),

Horosphere

In hyperbolic geometry, a horosphere (or parasphere) is a specific hypersurface in hyperbolic n-space. It is the boundary of a horoball, the limit of a sequence of increasing balls sharing (on one sid

Circle's circumference

No description available.

Differentiable curve

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have

Horopter

The horopter was originally defined in geometric terms as the locus of points in space that make the same angle at each eye with the fixation point, although more recently in studies of binocular visi

Hjulström curve

The Hjulström curve, named after Filip Hjulström (1902–1982), is a graph used by hydrologists and geologists to determine whether a river will erode, transport, or deposit sediment. It was originally

Gallery of curves

This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves.

Tacnode

In classical algebraic geometry, a tacnode (also called a point of osculation or double cusp) is a kind of singular point of a curve. It is defined as a point where two (or more) osculating circles to

Helix

A helix (/ˈhiːlɪks/) is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as th

Ampersand curve

No description available.

Spirograph

Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by Brit

Von Neumann's elephant

Von Neumann's elephant is a problem in recreational mathematics, consisting of constructing a planar curve in the shape of an elephant from only four fixed parameters. It originated from a discussion

List of curves topics

This is an alphabetical index of articles related to curves used in mathematics.
* Acnode
* Algebraic curve
* Arc
* Asymptote
* Asymptotic curve
* Barbier's theorem
* Bézier curve
* Bézout's t

Singular point of a curve

In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied

Shields formula

The Shields formula is a formula for the stability calculation of granular material (sand, gravel) in running water. The stability of granular material in flow can be determined by the Shields formula

Strophoid

In geometry, a strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the pole) as follows: Let L be a variable line passing through O and intersecting C at K. Now l

Cell survival curve

A cell survival curve is a curve used in radiobiology. It depicts the relationship between the fraction of cells retaining their reproductive integrity and the absorbed dose of radiation. Conventional

Linear referencing

Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing in engineering and construction, in which the locations of physical featu

W-curve

In geometry, a W-curve is a curve in projective n-space that is invariant under a 1-parameter group of projective transformations. W-curves were first investigated by Felix Klein and Sophus Lie in 187

Linking number

In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times t

Great ellipse

A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on t

Sierpiński triangle

The Sierpiński triangle (sometimes spelled Sierpinski), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subd

Geodesics on an ellipsoid

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a

Curve of constant width

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 all directions. The shape bounded by a curve of

Variation diminishing property

In mathematics, the variation diminishing property of certain mathematical objects involves diminishing the number of changes in sign (positive to negative or vice versa).

Orthogonal trajectory

In mathematics an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally. For example, the orthogonal trajectories of a pencil of concentric cir

Radius of curvature

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For sur

Contour line

A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a pla

Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a

Superformula

The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are

Chord (geometry)

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line se

Arc length

Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is a

Space cardioid

The space cardioid is a 3-dimensional curve derived from the cardioid. It has a parametric representation using trigonometric functions.

Evolute

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the res

Vertex (curve)

In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature, and some authors define a vertex to

Trisectrix

In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such a method falls outside those allowed by compass a

Sinuosity

Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclid

Hemihelix

A hemihelix is a curved geometric shape consisting of a series of helices with alternating chirality, connected by a perversion at the reversals. The formation of hemihelices with periodic distributio

Menger sponge

In mathematics, the Menger sponge (also known as the Menger cube, Menger universal curve, Sierpinski cube, or Sierpinski sponge) is a fractal curve. It is a three-dimensional generalization of the one

Vieth-Muller circle

No description available.

Parent function

In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions ha

Total curvature

In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: The total curv

Sierpiński carpet

The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions; another is Cantor dust. The technique of subd

Center of curvature

In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the

Mosely snowflake

The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–Menger type of fractal obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust

Curve sketching

In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required f

Intrinsic equation

In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location an

Crunode

In mathematics, a crunode (archaic) or node is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines at the point of intersection. A crunode is also kn

Osculating circle

In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair

Maurer rose

In geometry, the concept of a Maurer rose was introduced by Peter M. Maurer in his article titled A Rose is a Rose...[1]. A Maurer rose consists of some lines that connect some points on a rose curve.

Bathtub curve

The bathtub curve is widely used in reliability engineering and deterioration modeling. It describes a particular form of the hazard function which comprises three parts:
* The first part is a decrea

List of mathematic operators

In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering, physics and mathematics. Many are integral operators and differe

Curve-fitting compaction

Curve-fitting compaction is data compaction accomplished by replacing data to be stored or transmitted with an analytical expression. Examples of curve-fitting compaction consisting of discretization

Position circle

A position circle is a circle that can be measured both from a chart and from the surface of the earth for the purpose of position fixing. For the purposes of land or coastal navigation, a position ci

Quadratrix

In geometry, a quadratrix (from Latin quadrator 'squarer') is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are th

Inverse curve

In inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle with center O and radius k the inverse of a

Bean curve

No description available.

Learning curve

A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usual

Free-form deformation

In computer graphics, free-form deformation (FFD) is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another h

List of curves

This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, p

Quadratrix of Hippias

The quadratrix or trisectrix of Hippias (also quadratrix of Dinostratus) is a curve which is created by a uniform motion. It is one of the oldest examples for a kinematic curve (a curve created throug

Parallel curve

A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines. It can also be defined as a curve whose points ar

Acnode

An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are "isolated point or hermit point". For example the equation has an acnode at the

Affine geometry of curves

In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under th

Equichordal point

In geometry, an equichordal point is a point defined relative to a convex plane curve such that all chords passing through the point are equal in length. Two common figures with equichordal points are

Inscribed square problem

The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of s

Implicit curve

In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation

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