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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.
Area is the measure of a region 's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to ...
The area of the circle equals π times the shaded area. The area of the unit circle is π. 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. [149] The circumference of a circle with radius r is 2πr.
The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle. Its symmetry group is the orthogonal group O (2, R ). The group of rotations alone is the circle group T. All circles are similar.
Curve fitting[ 1][ 2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [ 3] possibly subject to constraints. [ 4][ 5] Curve fitting can involve either interpolation, [ 6][ 7] where an exact fit to the data is required, or smoothing, [ 8][ 9] in which a "smooth" function is ...
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 ...
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