The Archimedes spiral (in polar form $r=a+b\alpha$ with $a, b\in\mathbb{R}^>$), invented by the famous Greek mathematician, develops in such a way that the distance between one spiral and another always remains the same.
I have read that spiders first weave the supporting structure and then, starting from the center, cover the threads with a spiral, always maintaining the same distance between one spiral and the next. The Archimedean spiral represents the fastest (the spider weaves the web every morning) and most regular (equal distance between spiral arms) method of covering, while the logarithmic spiral would leave increasingly larger meshes as one moves from the center, making the web unsuitable for holding small flying insects.
There is an equation:
$$r:=r(\alpha)=\lambda n\alpha\tag 1$$
where:
[$r$] is the radius of the spiral (or rather its distance from the center at the point considered);
[$\lambda$] constant that defines the pitch between the spiral arms,
[$n$] is the number of revolutions made by the spiral,
[$\alpha$] the angle considered.
How is it possible to find the relation $$(1) \iff \color{red}{r=a+b\alpha}\equiv\color{blue}{\lambda n\alpha}$$ and how does the cardioid or asteroid exist an analytical mathematical expression of a spider webs?