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).