Abstract
have the same numerator. These fractions simplify to 1 a3993 and 103993 respectively. _T3_102 355 In this paper, we provide a combinatorial interpretation for the numerators and denominators of continued fractions which makes this reversal phenomenon easy to see. Through the use of counting arguments, we illustrate how this and other important identities involving continued fractions can be easily visualized, derived, and remembered. We begin by defining some basic terminology. Given an infinite sequence of integers ao ? 0, a, ? 1, a2 ? 1,. let [ao, a n.a,] denote the finite continued fraction
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