ABSTRACT
The logarithmic spiral has a remarkable property: the curve intersects all rays whose origin is O at a constant angle. To prove this fact let us find an angle formed by a vector tangent to the spiral and by the polar axis cp = 0. Denote by (.x(p), y(cp)) the position vector of the spiral in Cartesian coordinates. It is clear that
Therefore
Hence
(f y + ($I= e 2 y 2 + I ) . The unit vector tangent to the spiral has the following form:
where
A curve, represented by the equation
is called a spirul winding onto a circle. As p + -m the function p(p) tends to po, i.e. the curve winds onto the circle with its center at the pole 0 and with radius equal to p().
