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The existence of the limiting pair correlation for angles between reciprocalgeodesics on the modular surface is established. An explicit formula isprovided, which captures geometric information about the length of reciprocalgeodesics, as well as arithmetic information about the associated reciprocalclasses of binary quadratic forms. One striking feature is the absence of a gapbeyond zero in the limiting distribution, contrasting with the analog Euclideansituation.

Pair correlation of angles between reciprocal geodesics on the modular surface