  Canonical forms of positive geometries play an important role in revealing
hidden structures of scattering amplitudes, from amplituhedra to associahedra.
In this paper, we introduce "stringy canonical forms", which provide a natural
definition and extension of canonical forms for general polytopes, deformed by
a parameter $\alpha'$. They are defined by real or complex integrals regulated
with polynomials with exponents, and are meromorphic functions of the
exponents, sharing various properties of string amplitudes. As $\alpha' \to 0$,
they reduce to the usual canonical form of a polytope given by the Minkowski
sum of the Newton polytopes of the regulating polynomials, or equivalently the
volume of the dual of this polytope, naturally determined by tropical
functions. At finite $\alpha'$, they have simple poles corresponding to the
facets of the polytope, with the residue on the pole given by the stringy
canonical form of the facet. There is the remarkable connection between the
$\alpha' \to 0$ limit of tree-level string amplitudes, and scattering equations
that appear when studying the $\alpha' \to \infty$ limit. We show that there is
a simple conceptual understanding of this phenomenon for any stringy canonical
form: the saddle-point equations provide a diffeomorphism from the integration
domain to the interior of the polytope, and thus the canonical form can be
obtained as a pushforward via summing over saddle points. When the stringy
canonical form is applied to the ABHY associahedron in kinematic space, it
produces the usual Koba-Nielsen string integral, giving a direct path from
particle to string amplitudes without an a priori reference to the string
worldsheet. We also discuss a number of other examples, including stringy
canonical forms for finite-type cluster algebras (with type A for string
amplitudes), and other natural integrals over the positive Grassmannian.
