Center(redirected from Broca's center)
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center,in politics, a party following a middle course. The term was first used in France in 1789, when the moderates of the National Assembly sat in the center of the hall. It can refer to a separate party in a political system, e.g., the Catholic Center party of imperial and Weimar Germany, or to the middle group of a party consisting of several ideological factions.
in machine building, a device used to position a work-piece or mandrel on lathes, rotary grinders, and other machine tools, as well as on checking and measurement instruments.
One end of a center has a working conical surface with a vertex angle of 60° or 90°; the other has a shank with a shallow cone used to secure the center in the headstock spindle or tailstock spindle, which is an axially adjustable sleeve. If it is necessary to bore the end face of a workpiece, an opening is provided on the dead center so that a cutting tool may protrude. Machining of hollow workpieces calls for larger-diameter centers in the shape of truncated cones that fit into a conical, chamfered hole in the workpiece. Live centers, which are set in the spindle of the machine tool, have serrations on a conical working surface to transmit motion to the workpiece. In order to prevent slippage of the workpiece at higher machine speeds, the dead center may be replaced with a live center running on roller bearings. Centers are fabricated from hardened steel.
in mathematics. (1) A point O is said to be the center of symmetry of a geometric configuration if for every point A of the configuration there is another point A′ of the configuration such that O is the midpoint of the line joining A and A′. A curve or surface that has such a center is said to be central. The circle, ellipse, and hyperbola are the simplest examples of central curves, and the sphere, ellipsoid, and hyperboloid (of one or two sheets) are the simplest examples of central surfaces. It is possible for a configuration to have infinitely many centers of symmetry; for example, the centers of symmetry of a configuration consisting of two parallel lines lie on the line equidistant from the two given lines. (See alsoSYMMETRY.)
(2) The center of similitude of radially related configurations is the point S at which lines joining corresponding points of the configurations intersect (Figure 1).
(3) If all integral curves in the neighborhood of a singular point of a differential equation are closed and enclose the singular point, that point is said to be a center (Figure 2). Centers belong to the class of singular points whose character generally is not preserved when small changes are made in the right-hand side of the equation.