arXiv subjects
Publications and source records attributed to Kazuo Muroi.
In this article, we study similarity of triangles in the Susa Mathematical Texts (\textbf{SMT}). We also suggest that the Susa scribes were aware of intercept theory because they used this theorem in solving a complicated system of equations.
This article studies the systems of equations appearing in the Susa Mathematical Texts (\textbf{SMT}) and the different approaches used by the Susa scribes to solve them.
This article discusses the reasons for the choice of the sexagesimal system by ancient Sumerians. It is shown that Sumerians chose this specific numeral system based on logical and practical reasons which enabled them to deal with big numbers easily and even perform the multiplications and divisions in this system. I shall also discuss how the Sumerians calculated the area of a large field and measured a large quantity of barley according to their seemingly complicated but really systematic methods.
In this article, we study some of quadratic equations and their solutions found in the Susa Mathematical Texts (\textbf{SMT}). We show that the Susa scribes used this group of equations in different problems and took a standard approach, known as completing the square, to find solutions
This article studies the application of the Pythagorean theorem in the Susa Mathematical Texts (\textbf{SMT}) and we discuss those texts whose problems and related calculations demonstrate its use. Among these texts, \textbf{SMT No.\,1} might be the most important as it contains a geometric application of the Pythagorean theorem.
In this article, we study the problems found in the Susa Mathematical Texts No.\,24 and No.\,25 (\textbf{SMT No.\,24} and \textbf{SMT No.\,25}) which concern excavation projects such as canals and holes. We also examine certain Elamite structures, such as the canal systems serving Susa and a reservoir at the ziggurat of Chogha Zanbil, in whose construction geometry might well have played an important role.
This article studies three-dimensional objects and their volumes in Elamite mathematics, particularly those found in the Susa Mathematical Tablet No.\,14 (\textbf{SMT No.\,14}). In our discussion, we identify some basic solids whose volumes have been correctly computed in Babylonian and Elamite mathematics. We also show that the Elamite scribes knew the right formula for calculating the volume of a certain pyramid which is a rare phenomenon occurring in the Babylonian mathematical tablets.
In this article, we study a particular group of plane figures whose constants are listed in the Susa Mathematical Tablet No.\,3 (\textbf{SMT No.\,3}). We explain possible ways to define these figures and seek to demonstrate that the Susa scribes used complicated calculations to obtain such numbers. We also give examples of circular figures used for Elamite artifacts through which one can appreciate the significance of these figures in Elamite art.
The bisection of trapezoids by transversal lines has many examples in Babylonian mathematics. In this article, we study a similar problem in Elamite mathematics, inscribed on a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We seek to demonstrate that this problem is different from typical Babylonian problems about bisecting trapezoids by transversal lines. We also identify some of the possible mathematical ideas underlying this problem and the innovative approach that might have motivated its design.
In this article, we study the inscription on the reverse of Susa Mathematical Text No.\,2, a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We focus on the formula given in this text for the approximate area of a regular heptagon. We give a geometric explanation for the formula and show that this approximation is more accurate than other contemporaneous formulas in Babylonian mathematics and even that of Greek mathematician Heron who proved it almost 1800 years later. We also consider the possible ways the Susa scribes might have applied this formula to construct the regular heptagon for inscription on a clay tablet.
In this paper I shall clarify three cubic equations of Babylonian mathematics, whose solutions have not been fully explained; BM 85200, no.6 and no.7, and YBC 4669 B2.
In this paper I shall show that the formula 0:4,48 times circumference squared for the area of a circle, which occurs in a few Babylonian mathematical texts, can be traced back to at the latest the twenty-third century BCE.
In the present paper I shall clarify that the origin of compound interest goes back 4400 years to Sumer by showing the Sumerian scribe of Enmetena Foundation Cone calculated seventh power of four-thirds.
In the middle of the third millennium BC the Sumerians must have noticed that the reciprocal of the number 7,in contrast to the numbers 1,2,3,4,5,and 6,could not be expressed by a finite sexagesimal fraction but it recurred every three places.Since the number 7 is the first natural number that has such a property, it was of particular interest to them and became the representative of their number mysticism.
In the present paper I shall clarify the Babylonian method by which many large tables of reciprocals could be constructed.
In the present paper I shall reveal two circular figures hidden behind the Susa mathematical text no.3,lines 5 and 6 with my own analysis of the text.
In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-gál "the reciprocal of (the number) n", which is often abbreviated to igi-n, and igi-te-en whose meaning is somewhat abstract, that is, "a proportion (of something)" or "the ratio (of something to another)"(1). Thus the mathematical meanings of the two terms are quite clear, but we have not been able to clarify their literal meanings or their origins so far. In the present paper I shall offer a most probable interpretation of the early term, igi-n-gál, and a definite solution to the etymology of the later term, igi-te-en, both of which are based on my analysis of several mathematical terms that concern multiplication or division.