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Central Angle
A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). The central angle is also known as the arc's angular distance. The arc length spanned by a central angle on a sphere is called '' spherical distance''. The size of a central angle is or (radians). When defining or drawing a central angle, in addition to specifying the points and , one must specify whether the angle being defined is the convex angle (<180°) or the reflex angle (>180°). Equivalently, one must specify whether the movement from point to point is clockwise or counterclockwise. Formulas If the intersection points and of the legs of the angle with the circle form a diameter, then is a straight angle. (In radians, .) Let be the min ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sector Central Angle Arc
Sector may refer to: Places * Sector, West Virginia, U.S. Geometry * Circular sector, the portion of a disc enclosed by two radii and a circular arc * Hyperbolic sector, a region enclosed by two radii and a hyperbolic arc * Spherical sector, a portion of a sphere enclosed by a cone of radii from the center of the sphere Social and economic * Business sector, part of the economy which involves the trading and sale of products by companies * Economic sector, the manufacturing, finance and production of goods for consumers * Private sector, business activity created by private enterprise for profit * Public sector, delivers social services, infrastructure and institutions administered by government * Voluntary sector, a non-profit and voluntary part of an economy provided by organisations * The sector of the sector directive in government procurement in the European Union Computing * Cylinder-head-sector, an early method for giving addresses to blocks of data on a hard drive * Dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumference
In geometry, the circumference () is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure. Circumference may also refer to the circle itself, that is, the Locus (geometry), locus corresponding to the Edge (geometry), edge of a Disk (geometry), disk. The is the circumference, or length, of any one of its great circles. Circle The circumference of a circle is the distance around it, but if, as in many elementary treatments, distance is defined in terms of straight lines, this cannot be used as a definition. Under these circumstances, the circumference of a circle may be defined as the Limit (mathematics), limit of the perimeters of inscribed regular polygons as the number of sides increases without bound. The term circumference is used when measuring physical objects, as well as when considering abstrac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circles
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus: a ring-shaped object, the region bounded by two concentric circles. * Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude (mathematics), magnitude or Physical quantity, quantity of these types of geometric figures and in this context an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great-circle Navigation
Great-circle navigation or orthodromic navigation (related to orthodromic course; ) is the practice of navigating a vessel (a ship or aircraft) along a great circle. Such routes yield the shortest distance between two points on the globe. Course The great circle path may be found using spherical trigonometry; this is the spherical version of the ''inverse geodetic problem''. If a navigator begins at ''P''1 = (φ1,λ1) and plans to travel the great circle to a point at point ''P''2 = (φ2,λ2) (see Fig. 1, φ is the latitude, positive northward, and λ is the longitude, positive eastward), the initial and final courses α1 and α2 are given by formulas for solving a spherical triangle :\begin \tan\alpha_1&=\frac,\\ \tan\alpha_2&=\frac,\\ \end where λ12 = λ2 − λ1In the article on great-circle distances, the notation Δλ = λ12 and Δσ&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inscribed Angle
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle intercepting the same arc. The inscribed angle theorem appears as Proposition 20 in Book 3 of Euclid's ''Elements''. Note that this theorem is not to be confused with the Angle bisector theorem, which also involves angle bisection (but of an angle of a triangle not inscribed in a circle). Theorem Statement The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that intercepts the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the same arc of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chord (geometry)
A chord (from the Latin ''chorda'', meaning " bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a ''secant line''. The perpendicular line passing through the chord's midpoint is called '' sagitta'' (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's ''diameter''. In circles Among properties of chords of a circle are the following: # Chords are equidistant from the center if and only if their lengths are equal. # Equal chords are subtended by equal angles from the center of the circle. # A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. # If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circumscribed Circle
In geometry, a circumscribed circle for a set of points is a circle passing through each of them. Such a circle is said to ''circumscribe'' the points or a polygon formed from them; such a polygon is said to be ''inscribed'' in the circle. * Circumcircle, the circumscribed circle of a triangle, which always exists for a given triangle. * Cyclic polygon, a general polygon that can be circumscribed by a circle. The vertices of this polygon are concyclic points. All triangles are cyclic polygons. * Cyclic quadrilateral, a special case of a cyclic polygon. See also * Smallest-circle problem, the related problem of finding the circle with minimal radius containing an arbitrary set of points, not necessarily passing through them. * Inscribed figure {{sia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex polygon, convex'' or ''star polygon, star''. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties These properties apply to all regular polygons, whether convex or star polygon, star: *A regular ''n''-sided polygon has rotational symmetry of order ''n''. *All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. *Together with the property of equal-length sides, this implies that every regular polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supplementary Angles
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is a figure lying in a plane formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude or quantity of these types of geometric figures and in this context an angle consists of a number and unit of measurement. Angular measure or measure of angle are sometimes used to distinguish between the measurement an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
