  The behavior of norms of roots of univariate trinomials $z^{s+t} + p z^t + q
\in \mathbb{C}[z]$ for fixed support $A = \{0,t,s+t\} \subset \mathbb{N}$ with
respect to the choice of coefficients $p,q \in \mathbb{C}$ is a classical late
19th and early 20th century problem. Although algebraically characterized by
P.\ Bohl in 1908, the geometry and topology of the corresponding parameter
space of coefficients had yet to be revealed. Assuming $s$ and $t$ to be
coprime we provide such a characterization for the space of trinomials by
reinterpreting the problem in terms of amoeba theory. The roots of given norm
are parameterized in terms of a hypotrochoid curve along a $\mathbb{C}$-slice
of the space of trinomials, with multiple roots of this norm appearing exactly
on the singularities. As a main result, we show that the set of all trinomials
with support $A$ and certain roots of identical norm, as well as its complement
can be deformation retracted to the torus knot $K(s+t,s)$, and thus are
connected but not simply connected. An exception is the case where the $t$-th
smallest norm coincides with the $(t+1)$-st smallest norm. Here, the complement
has a different topology since it has fundamental group $\mathbb{Z}^2$.
