Mesopotamian mathematics is known from a great number of cuneiform texts, most of them Old Babylonian, some Late Babylonian or pre-Old-Babylonian, and has been intensively studied during the last ...couple of decades. In contrast to this Egyptian mathematics is known from only a small number of papyrus texts, and the few books and papers that have been written about Egyptian mathematical papyri have mostly reiterated the same old presentations and interpretations of the texts. In this book, it is shown that the methods developed by the author for the close study of mathematical cuneiform texts can also be successfully applied to all kinds of Egyptian mathematical texts, hieratic, demotic, or Greek-Egyptian. At the same time, comparisons of a large number of individual Egyptian mathematical exercises with Babylonian parallels yield many new insights into the nature of Egyptian mathematics and show that Egyptian and Babylonian mathematics display greater similarities than expected.
Whether the artisan who made the Omphalos at Delphi over 2500 years ago recognized the optical transform properties of its shape or not, its geometrical features are nevertheless those of a ...space‐inverting anamorphoscopic mirror. Specifically, it is similar in shape to a circle‐inverting anamorphoscope. We speculate that select members of the ancient religious sect at the Temple of Apollo at Delphi realized the symbolism of inverting all of space outside the Omphalos into the image field inside its base, thus making it the virtual centre of the World.
The great mathematician Archimedes, a Sicilian Greek whose machines defended Syracuse against the Romans during the Second Punic War, was killed by a Roman after the city fell, yet it is largely ...Roman sources, and Greek texts aimed at Roman audiences, that preserve the stories about him. Archimedes' story, Mary Jaeger argues, thus becomes a locus where writers explore the intersection of Greek and Roman culture, and as such it plays an important role in Roman self-definition. Jaeger uses the biography of Archimedes as a hermeneutic tool, providing insight into the construction of the traditional historical narrative about the Roman conquest of the Greek world and the Greek cultural invasion of Rome. By breaking down the narrative of Archimedes' life and examining how the various anecdotes that comprise it are embedded in their contexts, the book offers fresh readings of passages from both well-known and less-studied authors, including Polybius, Cicero, Livy, Vitruvius, Plutarch, Silius Italicus, Valerius Maximus, Johannes Tzetzes, and Petrarch.
This paper aims to provide an updated synthesis on the works of Archimedes and the fundamental impact these have had on subsequent mathematical practice. The influence his mathematical processes have ...had on modern mathematics and how these have helped develop the field is discussed in historical perspective. Some of the recent investigations into the Archimedes Palimpsest are discussed and synthesized, namely, how they alter our understanding of some of his earlier works, and how Archimedean principles are seen to have laid the foundations of possible new branches of mathematics.
The series is devoted to the study of scientific and philosophical texts from the Classical and the Islamic world handed down in Arabic. Through critical text editions and monographs, it provides ...access to ancient scientific inquiry as it developed in a continuous tradition from Antiquity to the modern period. All editions are accompanied by translations and philological and explanatory notes.
'If you wish to foresee the future of mathematics our proper course is to study the history and present condition of the science.'
Henri Poincaré
'It is India that gave us the ingenious method of ...expressing all numbers by ten symbols, each symbol receiving a value of position, as well as an absolute value. We shall appreciate the grandeur of the achievement when we remember that it escaped the genius of Archimedes and Apollonius.'
P.S. Laplace
'The Greeks were the first mathematicians who are still 'real' to us today. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greek first spoke of a language which modern mathematicians can understand.'
G.H. Hardy
This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems, generalizations, and new discoveries of arithmetic, algebra, number theory, geometry and astronomy during the above periods. A number of exciting applications of the above areas is discussed in some detail. It also contains a wide variety of important material accessible to college and even high school students and teachers at all levels. Included also is mathematical information that puts the professionals and prospective mathematical scientists at the forefront of current research.
The Hindu–Arabic numeral system (1, 2, 3,…) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral ...system have hypothesized that it originated in India; however, there is little evidence to support this claim. This book provides considerable evidence to show that the Hindu–Arabic numeral system, despite its commonly accepted name, has its origins in the Chinese rod numeral system. This system was widely used in China from antiquity till the 16th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetic operations, and also used by mathematicians to develop arithmetic and algebra. Based on this system, numerous mathematical treatises were written. Sun Zi suanjing (The Mathematical Classic of Sun Zi), written around 400 AD, is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetic and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu–Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi suanjing.
This is the first comprehensive text on African Mathematics that can be used to address some of the problematic issues in this area. These issues include attitudes, curriculum development, ...educational change, academic achievement, standardized and other tests, performance factors, student characteristics, cross-cultural differences and studies, literacy, native speakers, social class and differences, equal education, teaching methods, knowledge level, educational guidelines and policies, transitional schools, comparative education, other subjects such as physics and social studies, surveys, talent, educational research, teacher education and qualifications, academic standards, teacher effectiveness, lesson plans and modules, teacher characteristics, instructional materials, program effectiveness, program evaluation, African culture, African history, Black studies, class activities, educational games, number systems, cognitive ability, foreign influence, and fundamental concepts. What unifies the chapters in this book can appear rather banal, but many mathematical insights are so obvious and so fundamental that they are difficult to absorb, appreciate, and express with fresh clarity. Some of the more basic insights are isolated by accounts of investigators who have earned their contemporaries' respect.
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