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Circular segment. 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.
Arc length. When rectified, the curve gives a straight line segment with the same length as the curve's arc length. 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 ...
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 ...
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.
Let the length of A′B be c n, which we call the complement of s n; thus c n 2 +s n 2 = (2r) 2. Let C bisect the arc from A to B, and let C′ be the point opposite C on the circle. Thus the length of CA is s 2n, the length of C′A is c 2n, and C′CA is itself a right triangle on diameter C′C.
Visualization of the sagitta. 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 ...
The area of this sector is where is the radius at some angle , which is , the arc length of the circle so far "unwrapped" at angle . The area under the involute is the sum of all the infinitely many infinitely thin sectors i {\displaystyle i} through some angle θ n {\displaystyle \theta _{n}} .
The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle. Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines: = +.