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Encyclopedia Britannica - Main :: COM-COR |
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CONCHOID (Gr. oyXn, shell, and ethos, form) , a plane curve invented by the Greek mathematician Nicomedes, who devised a mechanical construction for it and applied it to the problem of the duplication of the cube
angle
Proclus
' Double
original
The conchoid is generated as follows: Let 0 be a fixed point and BC a fixed straight line; draw any line through 0 intersecting BC in P and take on the line PO two points X, X', such that PX = PX' = a constant quantity. Then the locus of X and X' is the conchoid. The conchoid is also the locus of any point on a rod which i A, is constrained to move so that it & C always passes through a fixed point, while a fixed point on the rod travels along a straight line. To obtain the equation to the curve, draw AO perpendicular to BC, and let A0=a; let the constant quantity PX = PX' = b. Then taking 0 as pole
axis
cusp
axis
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