A plane transcendental curve the equation of which in polar coordinates has the form:
It is described by a point $M$ moving at a constant rate along a straight line $d$ that rotates around a point $O$ lying on that straight line. At the starting point of the motion, $M$ coincides with the centre of rotation $O$ of the straight line (see Fig.). The length of the arc between the points $M_1(\rho_1,\phi_1)$ and $M_2(\rho_2,\phi_2)$ is
The area of the sector bounded by an arc of the Archimedean spiral and two radius vectors $\rho_1$ and $\rho_2$, corresponding to angles $\phi_1$ and $\phi_2$, is
An Archimedean spiral is a so-called algebraic spiral (cf. Spirals). The generalization of the Archimedean spiral is called a neoid, the equation of which in polar coordinates is
The spiral was studied by Archimedes (3rd century B.C.) and was named after him.
|||A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)|
|[a1]||E.H. Lockwood, "A book of curves" , Cambridge Univ. Press (1961)|
Archimedean spiral. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Archimedean_spiral&oldid=32532