The method described in Examples 1 and 2 can be expressed in general terms as follows:
Finally, the Round Calendar date is the Tzolkin date followed by the Haab date.
More sophisticated mathematics students could approach these examples using more formal modular arithmetic notation. They would consider the dates in both the Tzolkin and the Haab calendars as ordered pairs (Number, God). In the Tzolkin Calendar, 1 ≤ Number ≤ 13 and God is taken from the Tzolkin 20-cycle of gods. The following day would have date given by (Number + 1 (mod 13), God + 1 (mod 20)) and, in fact, for any positive integer k, the day k days later would have date given by (Number + k (mod 13), God + k (mod 20)). In the Haab Calendar, 0 ≤ Number ≤ 19, and God is taken from the Haab 18-cycle of gods together with Uayeb. Here, the day after (Number, God) would have date (Number+1, God) if either God ≠ Uayeb and Number < 19, or God = Uayeb and Number < 4. Otherwise, the following day has date (0, God + 1 (mod 19)). Since the Haab date k days later, for any positive integer k, depends on how close the original date is to the five days of Uayeb, Haab dates for k > 1 are even more complicated to describe using modular notation.