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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 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 ...
The second expression is for a polar graph = ... This equation is a definition of . If the arc is a semicircle, then =. For an arbitrary circular arc: ...
If = + is the distance from c 1 to c 2 we can normalize by =, =, = to simplify equation (1), resulting in the following system of equations: + =, + =; solve these to get two solutions (k = ±1) for the two external tangent lines: = = + = (+) Geometrically this corresponds to computing the angle formed by the tangent lines and the line of ...
The equation can be written in parametric form using the trigonometric functions sine and cosine as = + , = + , where t is a parametric variable in the range 0 to 2 π, interpreted geometrically as the angle that the ray from (a, b) to (x, y) makes with the positive x axis.
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 I = m s 2 {\displaystyle I=ms^{2}} , exactly the same for a hoop of the same radius.
The red path is a hypocycloid traced as the smaller black circle rolls around inside the larger black circle (parameters are R=4.0, r=1.0, and so k=4, giving an astroid).
In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form y 2 − a 2 x 3 = 0 {\displaystyle y^{2}-a^{2}x^{3}=0} (with a ≠ 0 ) in some Cartesian coordinate system .