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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 ...
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e. a semi-ellipse, centered at (0, 0):
The circle of radius with center at (,) in the – plane can be broken into two semicircles each of which is the graph of a function, + and , respectively: + = + (), = (), for values of ranging from to + .
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
The moment of inertia for a semicircle, best expressed in cylindrical coordinates, is = (,,).Solving the integral, one finds that the moment of inertia of a semicircle is =, exactly the same for a hoop of the same radius.
Let R be the radius of the arc which forms part of the perimeter of the segment, θ the central angle subtending the arc in radians, c the chord length, s the arc length, h the sagitta of the segment, d the apothem of the segment, and a the area of the segment.
The semicircular canals are a component of the bony labyrinth that are at right angles from each other and contain their respective semicircular duct. At one end of each of the semicircular ducts is a dilated sac called a membranous ampulla, which is more than twice the diameter of the ducts.
where (h, k) is the center of the ellipse in Cartesian coordinates, in which an arbitrary point is given by (x, y).The semi-major axis is the mean value of the maximum and minimum distances and of the ellipse from a focus — that is, of the distances from a focus to the endpoints of the major axis