Related papers: Sexagesimal Calculations in Ancient Sumer
Egyptologists and historians of mathematics around 1930 did an admirable job in showing that problem 14 of the newly discovered Moscow Papyrus from around 1850 BCE amounts to a general and exact calculation of the volume of a truncated…
Modern excavations yielded a distribution of the house areas in the ancient Egyptian city Akhetaten, which was populated for a short period during the 14th century BC. Assuming that the house area is a measure of the wealth of its…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Starting from any given rational-sided, right triangle, for example the $(3,4,5)$-triangle with area $6$, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We propose a scheme or procedure for doing practical calculations with generalized seniority. It reduces the total computing time by calculating and storing in advance a set of intermediate quantities, taking advantage of the memory…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.
We briefly discuss the history of X-ray polarimetry for astronomical applications including a guide to the appropriate statistics. We also provide an introduction to some of the new techniques discussed in more detail elsewhere in these…
This article provides information about the factors that necessitated the need to adjust the calendar during the time of Umar Khayyam, the method of choosing the beginning of the year, and the length of the months. It also attempts to…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
High-precision pulsar timing relies on a solar-system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a…
The production of complex astronomical data is accelerating, especially with newer telescopes producing ever more large-scale surveys. The increased quantity, complexity, and variety of astronomical data demand a parallel increase in skill…
Small area population estimates are useful for decision making in the private and public sectors. However, in small areas (i.e., those that are difficult to reach and with small population sizes) computing demographic quantities is…