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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.
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.
The circumference of a circle with radius r is 2πr. The area of a circle with radius r is πr 2. The area of an ellipse with semi-major axis a and semi-minor axis b is πab. The volume of a sphere with radius r is 4 / 3 πr 3. The surface area of a sphere with radius r is 4πr 2.
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.
Proposition one. Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
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 .
The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.
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 ...