Related papers: An Algebraic Structure for the Central Mexican Rit…
Ancient mesoamerican cultures built a short ritual 260 day calendar and used it for daily routinary life. Using simple arithmetic calculations it is first shown that by forcing the introduction of the the fundamental number 13 to calculate…
The family of Tibetan lunisolar calendars operates on a shared arithmetic axiom (67 lunar months = 65 solar months) that provides a rigid structure but causes observable seasonal drift. This study deconstructs the calendar through a…
Understanding how ancient Mesoamerican societies integrated mathematical ideas into calendrical design and monumental architecture requires approaches that acknowledge their distinct epistemological frameworks. While explicit textual…
The Mayan calendar is proposed to derive from an arithmetical model of naked-eye astronomy. The Palenque and Copan lunar equations, used during the Maya Classic period (200 to 900 AD) are solution of the model and the results are expressed…
The Ancient Egyptians wrote Calendars of Lucky and Unlucky Days that assigned astronomically influenced prognoses for each day of the year. The best preserved of these calendars is the Cairo Calendar (hereafter CC) dated to 1244--1163 B.C.…
In this paper we analyze, discuss and present the design of the Antikythera Mechanism s central front parts. Based on the aligned and of same scale visual images of Fragment C front/back face and the X-ray CT scacs, we designed and…
The Maya were known for their astronomical proficiency. This is demonstrated in the Mayan codices where ritual practices were related to astronomical events/predictions. Whereas Mayan mathematics were based on a vigesimal system, they used…
In the recent years several research efforts have focused on the concept of time granularity and its applications. A first stream of research investigated the mathematical models behind the notion of granularity and the algorithms to manage…
An ancient Egyptian Calendar of Lucky and Unlucky Days, the Cairo Calendar (CC), assigns luck with the period of 2.850 days. Previous astronomical, astrophysical and statistical analyses of CC support the idea that this was the period of…
In this recreative piece of work, we present Gauss' calendar formula with some examples to demonstrate how it is applied. Then, based on it, we give a formula for determining dates of particular week days of a given month, and some examples…
We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…
Presented with a new machine with a specific interconnect topology, algorithm designers use intuition about the symmetry of the algorithm to design time and communication-efficient schedules that map the algorithm to the machine. Is there a…
Conway's Doomsday Algorithm (1973) determines the day of the week for any date in the Gregorian calendar via three additive components: a century anchor, a year offset, and a month-day offset. The century anchor is a fixed four-entry table.…
Let $\phi:\Z/p\to GL_{n}(\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\Z/p$-action on the torus $X=\R^{n}/\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups…
Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization onwards, to which succeeding peoples made contributions. We…
On the basis of empirical Fischer projections, we developed an algebraic approach to central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral…
A new idea for a binary clock is presented. It displays the time using a triangular array of 15 bits. It is shown that such a geometric, triangular arrangement is only possible because our system of time divisions is based on a sexagesimal…
Summer 2015 marked the 100th anniversary of the excavation by J.W. Fewkes of the Sun Temple in Mesa Verde National Park, Colorado, an ancient complex prominently located atop a mesa, constructed by the ancestral Pueblo peoples approximately…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
An $N$ ${L} \choose {L/2}$-dimensional representation of the periodic Temperley-Lieb algebra $TL_L(x)$ is presented. It is also a representation of the cyclic group $Z_N$. We choose $x = 1$ and define a Hamiltonian as a sum of the…