  We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves
by using ideas from SYZ mirror symmetry. The conjecture claims that when a
Calabi-Yau manifold $X$ degenerates to a union of two quasi-Fano manifolds
(Tyurin degeneration), a mirror Calabi-Yau manifold of $X$ can be constructed
by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds.
The two crucial ideas in our proof are to obtain a complex structure by gluing
the underlying affine manifolds and to construct the theta functions from the
Landau-Ginzburg superpotentials.
