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LIMAC

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Originally appearing in Volume V16, Page 691 of the 1911 Encyclopedia Britannica.
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LIMAC ,ON (from the See also:

Lat. limax, a slug), a See also:curve invented by Blaise See also:Pascal and further investigated and named by Gilles Personne de See also:Roberval. It is generated by the extremities of a See also:rod which is constrained to move so that its See also:middle point traces out a circle, the rod always passing through a fixed point on the circumference. The polar See also:equation is r=a+b See also:cos 0, where 2a=length of the rod, and b=See also:diameter of the circle. The curse may be regarded as an epitrochoid (see Epicyctom) in which the See also:rolling and fixed circles have equal radii. It is the inverse of a central conic for the See also:focus, and the first See also:positive pedal of a circle for any point. The See also:form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a See also:cardioid (q.v.); if a is less than b, the curve has a See also:node within the circle; the particular See also:case when b= 2a is known as the See also:trisectrix (q.v.). In the figure (1) is a limacon, (2) the cardioid, (3) the trisectrix. Properties of the limagon may be deduced from its See also:mechanical construction; thus the length of a See also:focal chord is See also:constant and the normals at the extremities of a focal chord intersect on a fixed circle. The See also:area is (b2+See also:a2/2)sr, and the length is expressible as an elliptic integral.

End of Article: LIMAC

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