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For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...
Upper semicircle with radius 1 and center (0, 0) and its derivative. ... plane can be broken into two semicircles each of which is the graph of a function, ...
The graphometer, semicircle or semicircumferentor is a surveying instrument used for angle measurements. It consists of a semicircular limb divided into 180 degrees and sometimes subdivided into minutes. The limb is subtended by the diameter with two sights at its ends. In the middle of the diameter a "box and needle" is fixed.
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
If the arc is a semicircle, then = ... Another example of a curve with infinite length is the graph of the function defined by f(x) = ...
The Wigner distribution coincides with a scaled and shifted beta distribution: if Y is a beta-distributed random variable with parameters α = β = 3 ⁄ 2, then the random variable 2RY – R exhibits a Wigner semicircle distribution with radius R. By this transformation it is straightforward to directly compute some statistical quantities for ...
If and are the radii of the small semicircles of the arbelos, the radius of an Archimedean circle is equal to = + This radius is thus = +.. The Archimedean circle with center (as in the figure at right) is tangent to the tangents from the centers of the small semicircles to the other small semicircle.
To construct the inverse P ' of a point P outside a circle Ø: . Draw the segment from O (center of circle Ø) to P.; Let M be the midpoint of OP. (Not shown) Draw the circle c with center M going through P.