In geometry, a centre (Commonwealth English) or center (American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point in some sense in the middle of the object. According to the specific definition of centre taken into consideration, an object might have no centre. If geometry is regarded as the study of isometry groups, then a centre is a fixed point of all the isometries that move the object onto itself.
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👉 Centre (geometry) in the context of Great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.
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Centre (geometry) in the context of Radius
In classical geometry, a radius (pl.: radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its vertices. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel. The typical abbreviation and mathematical symbol for radius is R or r. By extension, the diameter D is defined as twice the radius:
If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.
Centre (geometry) in the context of Circle
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.
Centre (geometry) in the context of Antisolar point
The antisolar point is the abstract point on the celestial sphere directly opposite the Sun from an observer's perspective. This means that the antisolar point lies above the horizon when the Sun is below it, and vice versa. On a sunny day, the antisolar point can be easily found; it is located within the shadow of the observer's head. Like the zenith and nadir, the antisolar point is not fixed in three-dimensional space, but is defined relative to the observer. Each observer has an antisolar point that moves as the observer changes position.
The antisolar point forms the geometric center of several optical phenomena, including subhorizon haloes, rainbows, glories, the Brocken spectre, and heiligenschein. Occasionally, around sunset or sunrise, anticrepuscular rays appear to converge toward the antisolar point near the horizon. However, this is an optical illusion caused by perspective; in reality, the "rays" (i.e. bands of shadow) run near-parallel to each other.