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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]
Shape Figure ¯ ¯ Area rectangle area: General triangular area + + [1] Isosceles-triangular area: Right-triangular area: Circular area: Quarter-circular area [2]: Semicircular area [3]: Circular sector
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 } ):
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 ...
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 < <.
A circular measure was used in comparing circular cross-sections, e.g., of wires, etc. A circular unit of the ares is the area of the circle whose diameter is one linear unit. [1] For example, 1 circular mil is equivalent to 0.7854 square mil in area, 1 circular millimeter
A page from Archimedes' Measurement of a Circle. Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) [1] is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. [2] [3] The treatise is only a fraction of what was a longer work. [4] [5]
If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (⌢ and ⌢). That is, 2 ∠ C A B = ∠ D O E − ∠ B O C {\displaystyle 2\angle {CAB}=\angle {DOE}-\angle {BOC}} , where O is the centre of the circle (secant–secant ...