In this paper, we first recall some basic properties of continued fractions. Based on these, we study symmetric continued fractions and give necessary and sufficient conditions on two rational numbers having symmetric continued fractions. To be more precise, Theorem 1.3 gives the conditions that the numerators and denominators of the rational numbers corresponding to two symmetric continued fractions should be subject. On the other hand, Theorem 1.4 says that these conditions are also sufficient.%本文对对称连分数做一些探讨,给出了两个有理数所对应的简单连分数互为对称连分数的充分必要条件. 定理1.3给出两个对称连分数化简后的既约分数的分子分母满足的条件;而定理1.4指出,如果两个有理数的分子分母满足这些条件,那么它们对应的简单连分数互为对称连分数.
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