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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).
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 zygomaticus minor muscle is a muscle of facial expression. It originates from the zygomatic bone, lateral to the rest of the levator labii superioris muscle, and inserts into the outer part of the upper lip. It draws the upper lip backward, upward, and outward and is used in smiling.
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 Crofton formula, named after Morgan Crofton (1826–1915), (also Cauchy-Crofton formula) is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line intersects it.
The coordinate-independent definition of the square of the line element ds in an n-dimensional Riemannian or Pseudo Riemannian manifold (in physics usually a Lorentzian manifold) is the "square of the length" of an infinitesimal displacement [2] (in pseudo Riemannian manifolds possibly negative) whose square root should be used for computing curve length: = = (,) where g is the metric tensor ...
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 ...
This curve has total curvature 6 π, and index/turning number 3, though it only has winding number 2 about p.. 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: