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The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = 1 2 × 2πr × r, holds for a circle.
t. e. In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. [ 1] The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [ 2] More generally, the perimeter is the curve length around any closed figure.
Circular segment. 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: ⌓) is a region of a disk [ 1] which is "cut off" from the rest of the disk by a straight line.
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the ...
The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. Thus the circumference C is related to the radius r and diameter d by: = =.
Sphere. A sphere (from Greek σφαῖρα, sphaîra) [ 1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [ 2]
In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit -sphere is an -sphere of unit radius in - dimensional Euclidean space; the unit circle is a special case, the unit -sphere in the plane.
Disk (mathematics) In geometry, a disk ( also spelled disc) [ 1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [ 2] For a radius, , an open disk is usually denoted as and a closed disk is . However in the field of topology the closed ...