@inbook{10.2307/j.ctt7t77g.22,
ISBN = {9780691142494},
URL = {http://www.jstor.org/stable/j.ctt7t77g.22},
abstract = {The Room Lemma confines one period of$\Gamma (p/q)$to a certain parallelogram$R(p/q)$when$(p/q)$is odd. In this section we explain a sharper result, along the same lines, that confines one period of$\Gamma (p/q)$to a union of two parallelograms. The reader might want to glance at Figure 19.1 before reading the definitions that follow.Given an odd rational$A = (p/q)$, we construct the even rationals${A_ \pm } = {p_ \pm }/{q_ \pm }$. We let${A'}$be the inferior predecessor ofA, and we let$A{\kern 1pt} *$be the superior predecessor, as in ยง4.1. For each rational, we use Equation 3.2 to construct the correspondingVand},
bookauthor = {Richard Evan Schwartz},
booktitle = {Outer Billiards on Kites (AM-171)},
pages = {171--180},
publisher = {Princeton University Press},
title = {The Decomposition Theorem},
year = {2009}
}