Search results
Results from the WOW.Com Content Network
Arc length is the distance between two points along a section of a curve. ... The History of Curvature; Weisstein, Eric W. "Arc Length". MathWorld.
2.4 Arc-length, curvature and torsion from Cartesian coordinates. 3 See also. 4 References. Toggle the table of contents. List of common coordinate transformations. 3 ...
Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius. Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic ...
Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.
The real number k(s) is called the oriented curvature or signed curvature. It depends on both the orientation of the plane (definition of counterclockwise), and the orientation of the curve provided by the parametrization. In fact, the change of variable s → –s provides another arc-length parametrization, and changes the sign of k(s).
In Euclidean geometry, an arc (symbol: ⌒) is a connected subset of a differentiable curve. Arcs of lines are called segments, rays, or lines, depending on how they are bounded. A common curved example is an arc of a circle, called a circular arc. In a sphere (or a spheroid), an arc of a great circle (or a great ellipse) is called a great arc.
Arc measurement, [1] sometimes called degree measurement [2] (German: Gradmessung), [3] is the astrogeodetic technique of determining the radius of Earth and, by extension, its circumference.
There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include: The Whewell equation relates arc length and the tangential angle. The Cesàro equation relates arc length and curvature.