Related papers: The Powers of 9 and Related Mathematical Tables fr…
Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton…
How were surfaces evaluated before the invention of the sexagesimal place value notation in Mesopotamia? This chapter examines a group of five tablets containing tables for surfaces of squares and rectangles dated to the Early Dynastic…
Pebbles (calculos in Latin) are the "bits" used in the Ancients' four function calculator / computer. The Ancient Computer's normal mode is to work with numbers in what we would call exponential notation. Decimal numbers can have up to 10…
Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a…
This illustrated article represents a popular account of the study of the Babylonian astronomical records of Enuma Anu Enlil tablet series i.e. of the Venus Tablet of Ammisaduqa and of two lunar eclipses linked with the IIIrd dynasty of Ur,…
Ever since it was published by Neugebauer and Sachs in 1945, the Old Babylonian tablet known as Plimpton 322 has been the subject of numerous studies leading to different and often conflicting interpretations of it. Overall, the tablet is…
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise measurements on the sky or a circle,…
Multiplication and exponentiation can be defined by equations in which one of the operands is written as the sum of powers of two. When these powers are non-negative integers, the operand is integer; without this restriction it is a…
The main source of information regarding ancient Mesopotamian history and culture are clay cuneiform tablets. Despite being an invaluable resource, many tablets are fragmented leading to missing information. Currently these missing parts…
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…
One of the greatest achievements of Greek mathematics is the proof that the square root of 2 is irrational. It has not been thought that the Babylonians appreciated the concept of irrationality and certainly that they did not prove that the…
The Babylonian graph B has the positive integers as vertices and connects two if they define a Pythagorean triple. Triangular subgraphs correspond to Euler bricks. What are the properties of this graph? Are there tetrahedral subgraphs…
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…
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.
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
We investigate ``shell structure'' from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the…
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…
We discuss the babylonian method of extracting the root square of a number, from the point of view of modern mathematics. We also speculate that the babylonian mathematics was rich enough for a generalization of this method, despite the…
In the present paper I shall clarify the Babylonian method by which many large tables of reciprocals could be constructed.
The symbolic representation of a number should be considered as a data structure, and the choice of data structure depends on the arithmetic operations that are to be performed. Numbers are almost universally represented using position…