Curves

right|thumb|A parabola, one of the simplest curves, after (straight) lines

geometric line segment whose endpoints both lie on the curve

curve joining points with equal value on a 2D graphic representation

thumb|upright=1.35|(l-r) Tension, compression and torsion coil springs thumb|upright|A machine screw thumb|The right-handed helix for with arrowheads showing direction of increasing

point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave to convex, or vice versa

fractal composed of triangles

property of a curve

line that intersects a curve at least twice

template made from metal, wood or plastic composed of many different curves; used in manual drafting to draw smooth curves of varying radii

segment of a circle

thumb|The blue parabola is the involute of the red curve. The red curve is the evolute of the blue parabola, and can be constructed as the locus of all centers of curvature of the blue parabola. right|thumb|The evolute of a curve (in this case, an ellipse) is the envelope of its normals.

course of learning of or proficiency in something by an individual or a group, over time

connected series of line segments

radius of a circle which best approximates a curve in a given point

the line from which the seaward limits of a state's territorial sea and certain other maritime zones of jurisdiction are measured; normally, a sea baseline follows the low-water line of a coastal state

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 British engineer Denys Fisher and first sold in 1965.

circle of immediate corresponding curvature of a curve at a point

formulas in differential geometry

curve for failure rates over time

[[File:Allgemeine strophoide5.svg|thumb|right|upright=1.25|Construction of a strophoid.

where the curve is not given by a smooth embedding of a parameter

unsolved problem in geometry of whether every simple closed curve in the plane contains four points at the corners of a square

[[File:Allgemeine zissoide_english.svg|thumb|upright=1.5|

thumb|A Secant line|secant ogive of sharpness E = 120/100= 1.2 thumb|The ogive shape of the Space Shuttle external tank thumb|right|Ogive on a 9×19mm Parabellum cartridge

point of extreme curvature on a curve

In geometry, a quadratrix () is a curve that can be used for quadrature, constructing the area under another curve.

mathematical measure of how much a curve twists

point at a distance from the curve equal to the radius of curvature lying on the normal vector

numerical invariant that describes the linking of two closed curves in three-dimensional space

methods for drawing in approximation a curve defined by an equation

path on the surface of the Earth or another body directly below an aircraft or satellite

convex planar shape whose width is the same regardless of the orientation of the curve

thumb|right|An acnode at the origin (curve described in text)

thumb|Harmonograph thumb|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, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.

curve traced by a pursuer chasing a pursuee

term from classical mechanics

graph used by hydrologists and geologists to determine whether a river will erode, transport, or deposit sediment

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 and straightedge constructions, so they do not contradict the well known theorem which states that an arbitrary angle cannot be trisected with that type of construction. There is a variety of such curves and the methods used to construct an angle trisector differ according to the curve. Examples include: Limaçon trisectrix (some sources refer to this curve as simply the trisectrix.) Trisectrix of

study of curves from a differential point of view

The superformula is a generalization of the superellipse and was proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula, which expired effective 2020-05-10.

generalization of the concept of parallel lines

curve in hyperbolic plane whose points have the same orthogonal distance from a given straight line

plane curve defined by an implicit equation

thumb|Schematic representation of the theoretical (T) and the empirical (E) horopter.

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220px|right|thumb| A blue horocycle in the Poincaré disk model and some red normals. The normals converge asymptotically to the upper central [[ideal point.]]

equation in geometry

motion of an object in a curved path

Definition in differential equations

curve formed by connecting intermittent points on a rose curve

concept in differential geometry

set of three congruent geometrical helices with the same axis

thumb|right|300px|A crunode at the origin of the curve defined by y^2 - x^2(x+1)=0.

300px|thumb|ellipsoid with isophotes (red)

mathematical structure

smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation