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conchoid
[ kong-koid ]
noun
- a plane curve such that if a straight line is drawn from a certain fixed point, called the pole of the curve, to the curve, the part of the line intersected between the curve and its asymptote is always equal to a fixed distance. Equation: r = b ± a ²õ±ð³¦(θ).
conchoid
/ ˈ°ìÉ’Å‹°ìɔɪ»å /
noun
- geometry a plane curve consisting of two branches situated about a line to which they are asymptotic, so that a line from a fixed point (the pole) intersecting both branches is of constant length between asymptote and either branch. Equation: ( x – a )²( x ² + y ²) = b ² x ² where a is the distance between the pole and a vertical asymptote and b is the length of the constant segment
˜yÐÄvlog History and Origins
Example Sentences
Conchoid′al, pertaining to a conchoid: shell-like, applied to the fracture of a mineral; Concholog′ical, pertaining to conchology.—ns.
Apollonius was followed by Nicomedes, the inventor of the conchoid; Diocles, the inventor of the cissoid; Zenodorus, the founder of the study of isoperimetrical figures; Hipparchus, the founder of trigonometry; and Heron the elder, who wrote after the manner of the Egyptians, and primarily directed attention to problems of practical surveying.
The Greeks could not solve this equation, which also arose in the problems of duplicating a cube and trisecting an angle, by the ruler and compasses, but only by mechanical curves such as the cissoid, conchoid and quadratrix.
The new retrospective show of paintings by Kenneth Noland�their stripes and chevrons wedged uneasily into the conchoid spaces of New York's Guggenheim Museum�provides a dismaying lesson in how critical fashions change.
The conchoid has been employed by later mathematicians, notably Sir Isaac Newton, in the construction of various cubic curves.
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