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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 ...
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: β ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. [8]
Using radians, the formula for the arc length s of a circular arc of radius r and subtending a central angle of measure π is =, and the formula for the area A of a circular sector of radius r and with central angle of measure π is A = 1 2 θ r 2 . {\displaystyle A={\frac {1}{2}}\theta r^{2}.}
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: β), 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]
In Euclidean geometry, an arc (symbol: β) 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.
Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of dπ at the centre of the circle), each with an area of β 1 / 2 β · r 2 · dπ (derived from the expression for the area of a triangle: β 1 / 2 β · a · b · sinπ ...
Arc (geometry), a segment of a differentiable curve Circular arc, a segment of a circle; Arc (topology), a segment of a path; Arc length, the distance between two points along a section of a curve; Arc (projective geometry), a particular type of set of points of a projective plane; arc (function prefix) (arcus), a prefix for inverse ...
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