The cochleoid, whose name means "snail-form" in Latin, was first considered by John Perks as referenced in Wallis et al. (1699). The cochleoid has also
been called the oui-ja board curve (Beyer 1987, p. 215). The points of contact
of paralleltangents to
the cochleoid lie on a strophoid.
Smith (1958, p. 327) gives historical references for the cochleoid, but corrections to the name and date mentioned as "discussed by J. Perk Phil. Trans.
1700" (actually John Perks, as mentioned in Wallis et al. 1699 and Pedersen
1963), the separateness of papers by Falkenburg (1844) and Benthem (1844), and the
spelling of the latter's name should all be noted.
Benthem, A. "De Slakkenlijn of Cochleoïde." Nieuw Arch. Wisk.10, 76-80, 1884.Beyer, W. H. CRC
Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 215,
1987.Falkenburg, C. "Die Cochleoïde." Archiv der Math.
u. Physik70, 259-267, 1884.Lawrence, J. D. A
Catalog of Special Plane Curves. New York: Dover, pp. 192 and 196, 1972.Luca,
L.; Ghimisi, S.; and Popescu, I. "Studies Regarding the Movement on the Cochleoid."
Advanced Materials Res.463-464, 147-150, 2012.MacTutor
History of Mathematics Archive. "Cochleoid." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cochleoid.html.Pedersen,
O. "Master John Perks and his Mechanical Curves." Centaurus8,
1-18, 1963.Smith, D. E. History
of Mathematics, Vol. 2: Special Topics of Elementary Mathematics. New
York: Dover, p. 327, 1958.Wallis, D.; Gregory, D.; and Caswell,
J. "A Letter of Dr. Wallis to Dr. Sloan, concerning the Quadrature
of the Parts of the Lunula of Hippocrates Chius, performed by Mr. John Perks;
with the further Improvements of the same, by Dr. David Gregory, and Mr. John
Caswell." Philos. Trans.21, 411-418, 1699.
![kappa(t)=(2sqrt(2)t^3[2t-sin(2t)])/([1+2t^2-cos(2t)-2tsin(2t)]^(3/2)).](/images/equations/Cochleoid/NumberedEquation2.svg)
