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The defining integral of arc length does not always have a closed-form expression, and numerical integration may be used instead to obtain numerical values of arc length. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification .
The integral I n is divided up into integrals each on some arc of the circle that is adjacent to ζ, of length a function of s (again, at our discretion). The arcs make up the whole circle; the sum of the integrals over the major arcs is to make up 2 πiF ( n ) (realistically, this will happen up to a manageable remainder term).
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (c. 1750). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse .
In anatomy, the zygomatic arch (colloquially known as the cheek bone), is a part of the skull formed by the zygomatic process of the temporal bone (a bone extending forward from the side of the skull, over the opening of the ear) and the temporal process of the zygomatic bone (the side of the cheekbone), the two being united by an oblique suture (the zygomaticotemporal suture); [1] the tendon ...
In practical applications it is often small: for example the triangles of geodetic survey typically have a spherical excess much less than 1' of arc. [14] On the Earth the excess of an equilateral triangle with sides 21.3 km (and area 393 km 2) is approximately 1 arc second. There are many formulae for the excess.
In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...
In mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the name elliptic integrals because [1] the second kind gives the arc length of an ellipse of unit semi-major axis and eccentricity (the ellipse being defined parametrically by = (), = ()).