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Quarter-circular area [2] ... The points on the circle + = and above the axis = Arc of circle: The points on the curve (in polar coordinates ...
The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):
This diagram gives a visual analogue using a square: regardless of the size of the square, the added perimeter is the sum of the four blue arcs, a circle with the same radius as the offset. More formally, let c be the Earth's circumference, r its radius, Δc the added string length and Δr the added radius.
The polar Earth's circumference is simply four times quarter meridian: = The perimeter of a meridian ellipse can also be rewritten in the form of a rectifying circle perimeter, C p = 2πM r. Therefore, the rectifying Earth radius is: = (+) / It can be evaluated as 6 367 449.146 m.
The minor sector is shaded in green while the major sector is shaded white. A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. [1]
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
Earth's circumference equals the perimeter length. The equatorial circumference is simply the circle perimeter: C e =2πa, in terms of the equatorial radius, a. The polar circumference equals C p =4m p, four times the quarter meridian m p =aE(e), where the polar radius b enters via the eccentricity, e=(1−b 2 /a 2) 0.5; see Ellipse# ...
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.