Angle AOB forms a central angle of circle O

A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is (by definition) equal to the central angle itself. It is also known as the arc segment's angular distance.area of circle = radius x radius x pi Image File history File links Sector_central_angle_arc. ... Image File history File links Sector_central_angle_arc. ... ∠, the angle symbol. ... Circle illustration This article is about the shape and mathematical concept of circle. ... In Euclidean geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of a circle. ...

Coordinates

On a sphere or ellipsoid, the central angle is delineated along a great circle. The usually provided coordinates of a point on a sphere/ellipsoid is its common latitude ("Lat"), , and longitude ("Long"), . The "point", , is actually——relative to the great circle it is being measured on——the transverse colatitude ("TvL"), and the central angle/angular distance is the difference between two TvLs, . A sphere is a symmetrical geometrical object. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the... Latitude,usually denoted symbolically by the Greek letter phi, , gives the location of a place on Earth north or south of the equator. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ...

Calculation of TvL

The calculation of and can be found using a common subroutine:

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Each point has at least two values, both a forward and reverse value.

Occupying great circle

The arc path, , tracing the great circle that a central angle occupies, is measured as that great circle's azimuth at the equator, introducing an important property of spherical geometry, Clairaut's constant: In mathematical analysis, Clairauts theorem states that if has continuous second partial derivatives at then for In words, the partial derivatives of this function commute. ...

From this and relationships to ,area of circle = radius x radius x pi

Angular distance formulary

The angular distance can be calculated either directly as the TvL difference, or via the common coordinates (here, either SA_w, SB_w value set can be used):

and, using half-angles,

There is also a logarithmical form:

See also

• inscribed angle

In geometry, an inscribed angle is formed when two secant lines of a circle (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. ...

External links

• Central Angle of an Arc definition With interactive animation
• Central Angle Theorem described With interactive animation
• Inscribed and Central Angles in a Circle