
This
cochleoid ^{1)} has been
named to the snail ^{2}^{)} by Benthan
and Falkenburg (in 1884). Some relations with other curves are the following:
The first mathematicians to study the curve were J. Peck (1700) and Bernoulli (1726). 1) In Italian: cocleoide. 2) Kochlias (Gr.) = snail. 3) This can be proven as follows: let the circle have a radius t, and center C(t, 0).
Now we know that the length of the arc has to be equal to a constant, say a, what is the
same as φ t. With sin φ = y / t, this leads to t arcsin(y/t) = a (1). 