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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.
The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. All circles are similar. [12] A circle circumference and radius are ...
The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π. π is commonly defined as the ratio of a circle's circumference C to its diameter d: [10] = The ratio is constant, regardless of the circle's size.
Perimeter. Perimeter is the distance around a two dimensional shape, a measurement of the distance around something; the length of the boundary. A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference .
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
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.
In the following lines, represents the radius of a circle, is its diameter, is its circumference, is the length of an arc of the circle, and is the angle which the arc subtends at the centre of the circle.
Circumcircle. In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius. The circumcenter is the point of intersection between the three perpendicular bisectors of the ...