In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. 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.
geometry, the area enclosed by acircleof radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter...
Acircle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of...
(as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a "polygonal area". The areaofa shape can be measured...
the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the areaofa given circle by...
A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion ofa disk (a closed region bounded by a circle)...
the problem of dividing acircle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number ofareas created by the...
In geometry, calculating the areaofa triangle is an elementary problem encountered often in many different situations. The best known and simplest formula...
is only a fraction of what was a longer work. Proposition one states: The areaof any circle is equal to a right-angled triangle in which one of the sides...
The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio ofacircle's circumference to its diameter, approximately equal...
Maynard James Keenan. A Perfect Circle released three of their four studio albums in the early 2000s: their debut Mer de Noms in 2000, a follow-up, Thirteenth...
moment ofarea, or second area moment, or quadratic moment ofarea and also known as the area moment of inertia, is a geometrical property of an area which...
the perimeter ofacircle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment...
of exhaustion as a way to compute the area inside acircle by filling the circle with a sequence of polygons with an increasing number of sides and a...
method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the areaofacircle, the surface area and volume ofa sphere...
is a method to square the circle, although it does imply various incorrect values of the mathematical constant π, the ratio of the circumference ofa circle...
figure its name. Myers's original circle covers only about 6.7% of the Earth's total surface area, with a radius of around 4,000 kilometers (2,500 mi)...
constant. It generalizes acircle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured...
areaofacircle, the surface area and volume ofa sphere, areaof an ellipse, the area under a parabola, the volume ofa segment ofa paraboloid of revolution...
Acircleof competence is the subject area which matches a person's skills or expertise. The concept was developed by Warren Buffett and Charlie Munger...
vanish by the data of the problem."[italics added](p 73) Given the Venn's assignments, then, the unshaded areas inside the circles can be summed to yield...
and each circle is surrounded by six other circles. For circlesof diameter D and hexagons of side length D, the hexagon area and the circlearea are, respectively:...
A vicious circle (or cycle) is a complex chain of events that reinforces itself through a feedback loop, with detrimental results. It is a system with...
by the areaof the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. The first...
subtracted from the area of the large circle (with diameter BC). Since the areaofacircle is proportional to the square of the diameter (Euclid's Elements...
Giving the areaofa segment ofa unit sphere in steradians is analogous to giving the length of an arc ofa unit circle in radians. Just like a planar angle...
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