  In this paper, we prove a multiplicity result for rectangular pegs that there
is a generic class of smooth Jordan curves in which every curve admits two
geometrically distinct similar inscribed rectangles with aspect angle in
$(0,\frac{\pi}{2})$, based on the a priori existence result of rectangular peg
by Greene and Lobb [GL21], in which the rectangular peg problem is translated
into finding intersection points of two Lagrangian tori. The key insights are
certain generic geometric transversality of the two tori, and the
correspondence between the intersection points and the inscribed rectangles. We
present two distinct proofs: one involves the Lagrangian Floer homology, and
the other is differential topological in nature which employs a novel
computation formula for the algebraic intersection number. Moreover, such
generic doubling result can be further extended to cyclic quadrilateral pegs
based on [GL23]. In Appendix B, written jointly with Urs Frauenfelder, we
provide the detailed derivation of this computation formula.
