Arc length

Arc length, Distance along a curve.

Arc length image

Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment is also called rectification of a curve. The advent of infinitesimal calculus led to a general formula that provides closed-form solutions in some cases. General approach A curve in the plane can be approximated by connecting a finite number of points on the curve using line segments to create a polygonal path. Since it is straightforward to calculate the length of each linear segment (using the Pythagorean theorem in Euclidean space, for example), the total length of the approximation can be found by summing the lengths of each linear segment; that approximation is known as the (cumulative) chordal distance.If the curve is not already a polygonal path, using a progressively larger number of segments of smaller lengths will result in better approximations.

Circular arc
4 months ago

Circular arc ... will subtend an angle greater than π radians. The length (more precisely, arc length) of an arc of a circle with radius r and subtending an angle θ...

Circular segment
6 months ago

Circular segment ... the arc in radians, c the chord length, s the arc length, h the sagitta (height) of the segment, and a the area of the segment. Usually, chord length and...

Degree of curvature
6 months ago

Degree of curvature ... or rope of a prescribed length. In an n-degree curve, the forward bearing changes by n degrees over the standard length of arc or chord. The usual distance...

Circular sector
6 months ago

Circular sector ... {\displaystyle r} the radius of the circle, and L {\displaystyle L} is the arc length of the minor sector. A sector with the central angle of 180° is called...

Cycloid
6 months ago

Cycloid ... on a half arc of cycloid describing a cycloid arc equal to the one it was lying on once unwrapped (see also cycloidal pendulum and arc length). There are...

Curvature
6 months ago

Curvature ... function of the parameter s, which may be thought as the time or as the arc length from a given origin. Let T(s) be a unit tangent vector of the curve at...

Gas metal arc welding
5 months ago

Gas metal arc welding ... Gas metal arc welding (GMAW), sometimes referred to by its subtypes metal inert gas (MIG) and metal active gas (MAG) is a welding process in which an...

Lemniscate of Bernoulli
6 months ago

Lemniscate of Bernoulli ... coordinates: Q = 2 s − 1 {\displaystyle Q=2s-1\,} The determination of the arc length of arcs of the lemniscate leads to elliptic integrals, as was discovered in...

Triangle wave
6 months ago

Triangle wave ... abs((((x-p/4)%p)+p)%p - p/2) - a. The arc length per period for a triangle wave, denoted by s, is given in terms of the amplitude a and period length p by s = ( 4 a ) 2...

Differentiable curve
6 months ago

Differentiable curve ... various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus. One...

Helix
6 months ago
Arc welding
6 months ago
Arc
5 months ago
Archimedean spiral
6 months ago
Radian
6 months ago
Curve
6 months ago
Gas tungsten arc welding
6 months ago
Milliradian
1 month ago
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