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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
Butterfield compass graphometer A German graphometer in Göttingen, Stadtmuseum. The instrument is on its side. At the back, the socket for a Jacob's staff can be seen.. The graphometer, semicircle or semicircumferentor is a surveying instrument used for angle measurements.
For crossing wires that are insulated from one another, a small semi-circle symbol is commonly used to show one wire "jumping over" the other wire [3] [7] [8] (similar to how jumper wires are used). A common, hybrid style of drawing combines the T-junction crossovers with "dot" connections and the wire "jump" semi-circle symbols for insulated ...
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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):
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