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We study the decision problem of disjunctive linear arithmetic over the reals from the perspective of computational geometry. We show that traversing the linear arrangement induced by the formula's predicates, rather than the DPLL(T) method of traversing the Boolean space, may have an advantage when the number of variables is smaller than the number of predicates (as it is indeed the case in the standard SMT-Lib benchmarks). We then continue by showing a branching heuristic that is based on approximating T-implications, based on a geometric analysis. We achieve modest improvement in run time comparing to the commonly used heuristic used by competitive solvers.