Spiral equation

Question

Considering concentric arcs, of equal developed length, whose start point is aligned:

I am looking for the equation of the spiral passing through the end points.
Some help to solve this problem will be welcome!

Edit: The result

CiaPan · Answer

In polar coordinates, every arc starts at $theta=0$ and ends at $theta=L/r$, where $L$ is the length of each arc and $r$ is the radius for respective arc. So this is the equation:
$$theta=L/r.$$
In Cartesian coordinates:
$$(x,y) = left(rcdotcosfrac Lr,, rcdotsinfrac Lrright)$$
for $0 < r < infty.$
The spiral is called hyperbolic spiral, or a reciproke spiral – see my post Does the spiral Theta = L/R have a name? and the answer to it.

Spiral equation

One Answer

Add your own answers!

Ask a Question