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One acre equals 1 ⁄ 640 (0.0015625) square mile, 4,840 square yards, 43,560 square feet, [2] or about 4,047 square metres (0.4047 hectares) (see below).While all modern variants of the acre contain 4,840 square yards, there are alternative definitions of a yard, so the exact size of an acre depends upon the particular yard on which it is based.
A circle containing one acre is cut by another whose center is on the circumference of the given circle, and the area common to both is one-half acre. Find the radius of the cutting circle. The solutions in both cases are non-trivial but yield to straightforward application of trigonometry, analytical geometry or integral calculus.
Since the equation of this circle is given in Cartesian coordinates by + =, the question is equivalently asking how many pairs of integers m and n there are such that m 2 + n 2 ≤ r 2 . {\displaystyle m^{2}+n^{2}\leq r^{2}.}
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points (x 1,y 1), (x 2,y 2), and (x 3,y 3). The shoelace formula can also be used to find the areas of other polygons when their vertices are known.
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.
Circle packing in a square is a packing problem in recreational mathematics where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square in order to maximize the minimal separation, d n , between points. [ 1 ]
As the name suggests, an acre-foot is defined as the volume of one acre of surface area to a depth of one foot.. Since an acre is defined as a chain by a furlong (i.e. 66 ft × 660 ft or 20.12 m × 201.17 m), an acre-foot is 43,560 cubic feet (1,233.5 m 3).