Internet Encyclopedia of Science
PLANE CURVES
A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

                   HOME
ABOUT
CATEGORIES
USE OF TEXT AND IMAGES
NEWSLETTER

  



cochleoid



A spiral curve that was first studied by J. Peck in 1700 and Bernouilli in 1726. Its name, meaning "snail-form" (kochlias is Greek for "snail"), was coined by Benthan and Falkenburg in 1884.

The cochleoid can be constructed as follows: given a point O and the y-axis. For all circles through O (hence tangent to the y-axis), place a constant distance on the circle. The collection of these points is the cochleoid. In Cartesian coordinates, it is given by the formula

(x 2 + y 2) tan-1(y/x) = ay


and in polar coordinates by

r = a sinθ / θ


The points of contact of parallel tangents to the cochleoid lie on a strophoid.


Related category

   • PLANE CURVES


Also on this site:

Encyclopedia of Alternative Energy & Sustainable Living
Encyclopedia of History





BACK TO TOP