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In geometry, the area enclosed by a circle of radius r is πr 2.Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
The circle and the triangle are equal in area. 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.
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.
A circle circumference and radius are proportional. The area enclosed and the square of its radius are proportional. The constants of proportionality are 2 π and π respectively. The circle that is centred at the origin with radius 1 is called the unit circle. Thought of as a great circle of the unit sphere, it becomes the Riemannian circle.
The area of the circle equals π times the shaded area. The area of the unit circle is π. [153] π appears in formulae for areas and volumes of geometrical shapes based on circles, such as ellipses, spheres, cones, and tori. Below are some of the more common formulae that involve π. [154] The circumference of a circle with radius r is 2πr. [155]
The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1] More generally, the perimeter is the curve length around any closed figure. Circumference may also refer to the circle itself, that is, the locus corresponding to the edge of a disk. The circumference of a sphere is the ...
For a circle, the ratio of the area to the circumference (the term for the perimeter of a circle) equals half the radius r. This can be seen from the area formula πr 2 and the circumference formula 2 πr .
It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. [12] An "equilateral rectangle" is, by definition, a square. This is an assertion that the area of a circle is the same as that of a square with the same perimeter.