Related papers: An ethnoarithmetic excursion into the Javanese cal…
We describe an ACL2 program that implements the Hebrew calendar and the formal verification of several of its properties, including the critical result that the algorithm that determines the placement of the new year ensures that the length…
The traditional cultures of Aboriginal Australians include a significant astronomical component, perpetuated through oral tradition, ceremony, and art. This astronomical component includes a deep understanding of the motion of objects in…
The Hebrew Calendar is based on very deep and complicated mathematics, involving diophantine approximation, but it is very surprising that the gaps between consecutive Christmas-in-Hanukkah years is always a member of the set {2,3,5,8}.…
Indonesian traditional villagers have a tradition for the sake of their own social and economic security named 'nyumbang'. There are wide variations of the traditions across the archipelago, and we revisit an observation to one in Subang,…
We investigate a type of lunar calendar known as lists of the 'nights of the moon', found throughout East Polynesia, including Rapa Nui (Easter Island). Using computational methods, we analyzed the lexical and structural divergence of 49…
We present a general description of the Iranian calendar and Nowruz, which starts at the precise instant when the Sun coincides with the vernal equinox. Although the paper aims at the basic astronomical elements of the calendar, historical…
For a sequence of tasks, each with a positive integer period, the pinwheel scheduling problem involves finding a valid schedule in the sense that the schedule performs one task per day and each task is performed at least once every…
While reading ancient texts one has to be cognizant of the assumptions made about the past. One has to ask: Are these assumptions valid? Are we projecting the present views into the past? A case in point is the dating of Vedanga Jyotisa.…
The traditional cultures of Aboriginal Australians include a significant astronomical component, which is usually reported in terms of songs or stories associated with stars and constellations. Here we argue that the astronomical components…
We present a novel technique to identify calendar-based (annual, monthly and daily) periodicities of an interval-based temporal pattern. An interval-based temporal pattern is a pattern that occurs across a time-interval, then disappears for…
The traditional cultures of Aboriginal Australians include a significant astronomical component, perpetuated through oral tradition, ceremony, and art. This astronomical knowledge includes a deep understanding of the motion of objects in…
In many applications it will be useful to know those patterns that occur with a balanced interval, e.g., a certain combination of phone numbers are called almost every Friday or a group of products are sold a lot on Tuesday and Thursday. In…
A 1-period is a complex number given by the integral of a univariate algebraic function, where all data involved -- the integrand and the domain of integration -- are defined over algebraic numbers. We give an algorithm that, given a finite…
The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and…
The field of ethnomathematics holds significance in the pursuit of comprehending how students can grasp, express, manipulate, and ultimately apply mathematical concepts. However, ethnomathematics is also considered a complex concept in…
Legal expert systems routinely rely on date computations to determine the eligibility of a citizen to social benefits or whether an application has been filed on time. Unfortunately, date arithmetic exhibits many corner cases, which are…
Dates and calendar periods (i.e., days, months, years) appear frequently in tasks involving analysis of software, data, and documents. Prior research has shown that computer logic involving dates and calendrical calculations is error-prone…
This short monograph is devoted to different historical calendars prevalent in India from ancient times. They are classified and described with astronomical and historical details. Relationship of the calendrical elements to modern…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
This article develops an algebraic model of the 260-day Central Mexican ritual calendar, the \textit{Tonalpohualli}. We represent the calendar as the cyclic group $\mathbb{Z}_{13}\oplus\mathbb{Z}_{20}$, where each day name is encoded by a…