Related papers: Volumes of Solid Objects in Elamite Mathematics
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…
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…
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.
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,…
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…
The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article reviews all known ways to compute volumes in the…
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}…
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…
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…
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.
The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.
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…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
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…
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…
We present a method to compute the volume of a solid of revolution as a double integral in a very simple way. Then, we see that the classical methods (disks and shells) are recovered if this double integral is computed by each of the two…
We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differential equations. Our approach rests on…
The Great Pyramids of Egypt hide mathematic information unknown up to date. The measurements of the three Great Pyramids of Egypt at Giza show that Egyptians knew how to calculate the circumference, the volume and the area of the sphere…
The volume of a Meissner polyhedron is computed in terms of the lengths of its dual edges. This allows to reformulate the Meissner conjecture regarding constant width bodies with minimal volume as a series of explicit finite dimensional…
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…