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The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):
The name of these lines derives from the fact that they were added by Galileo to an earlier version of his sector. These lines are used for squaring circular segments, that is finding the side length of a square that is equal in area to a circular segment with a given chord length and height, where the segment is at most a semicircle.
The minor sector is shaded in green while the major sector is shaded white. A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. [1]
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
Arc length s of a logarithmic spiral as a function of its parameter θ. Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification.
A cleaning company has been fined $171,000 after federal investigators found 11 children working a "dangerous" overnight shift at a meat processing plant in Iowa.
Just as the area below a line is proportional to the length of the line between boundaries, and the area of a circular sector is a ratio of the arc length (=) of the sector (=), the area between an involute and its bounding circle is also proportional to the involute's arc length =: = = for < <.