Calendrical Computations

Abstract

Abstract Different calendar systems all provide distinguishable means to the same end, a basis for calculating and recording time. The research presented in this paper evaluates and performs numerical and data analysis on specific calendar systems developed throughout history, namely the Mayan and Gregorian calendars. Mathematical representations and formulas work in conjunction with these calendar systems. Thus, these methods are used to derive and interpret specific functions related to the calendar which will be further discussed. Additionally, the characteristics of a calendar system can be used to implement various applications for computers and mobile devices. Methods used throughout the research include the powerful use of Mathematica, a language used for computational mathematics, as well as the tried and true pencil and paper method of solving several modular arithmetic examples; additionally, the use of HTML, CSS, and JavaScript helps create applications using various calendrical functions. As a result, the calendar systems described in this paper were explained based on mathematical concepts and exploited to create new applications that interpret said results to produce new apps with different design interfaces utilizing different aspects of the calendar. The results are conclusive in showing the hand-drawn method of solving various elements concerning the Gregorian and Mayan calendar; in addition, the results present the successful production of apps from prototyping to coding in order to implement these methods. It is shown that calendrical computations are possible using modular arithmetic and logic to answer any question regarding calendar systems.