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03 - Babylonian mathematics and Numeration.pptx
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- 2. i n tr o d u c t i o n “Babylonian” refer to those peoples who occupied the alluvial plain between the the Tigris and the Euphrates. The Greeks called this land “Mesopotamia,” meaning “the land between the rivers.”
- 3. Let’s delve into ancient Mesopotamia After3000 B.C. the Babylonians developed a system of writing from “pictographs”—a kind of picture writing much like hieroglyphics.
- 4. 01 The Cuneiform 02 Deciphering the cuneiform 03 Babylonian positional numbersystem Babylonian Numeral
- 5. Cuneiform is from theword “cuneus” meaning “wedge”. Cuneiform script was a natural consequence of the choice of clay as a writing medium. Only within the last two centuries has anyone known what the many extant cuneiform writings meant, and indeed whether they were writing or simply decoration. The Cuneiform This Photo by Unknown Author is licensed under CC BY This Photo by Unknown Author is licensed under CC BY-SA
- 6. Deciphering the Cuneiform • GeorgFriedrich Grotefend (1775- 1853) – took the initial step in deciphering the Babylonian clay tablets • Champollion – won an international reputation on deciphering cuneiform
- 7. The Babylonians werethe only pre-Grecian people who made even a partial use of a positional number system. Such systems are based on the notion of place value, in which the value of a symbol depends on the position it occupies in the numerical representation. Their immense advantage over other systems is that a limited set of symbols suffices to express numbers, no matter how large or small. The Babylonian scale of enumeration was not decimal, but sexagesimal (60 as a base), so that every place a “digit” is moved to the left increases its value by a factor of 60. This Photo by Unknown Author is licensed under CC BY
- 8. Thank You For Liste ni ng!
- 9. Notable Facts • Babylonianmathematics emerged primarily from Mesopotamia, notably among the Sumerians and Akkadians. • It relied heavily on clay tablets, with no long treatises like the Egyptian Rhind Papyrus. • The sexagesimal (base-60) positional number system enabled efficient computation, especially with fractions. • Babylonian mathematicians produced numerous reciprocal tables, crucial for division and solving equations. • They developed sophisticated algebraic techniques, including methods to solve quadratic and even cubic equations. • Quadratic equations were often solved using formulas akin to the quadratic formula we use today. • Negative solutions were ignored, and only positive, practical answers were sought. • Problems were highly algebraic and practical, involving fields, reeds, and weights. • They used false position, transformations, and geometric reasoning to solve word problems. • Overall, Babylonian mathematics was both empirical and advanced, foreshadowing later algebraic methods.
- 10. Plimpton 322 • Plimpton322 is a Babylonian clay tablet dated between 1900–1600 B.C., deciphered in 1945. • It contains a table of numbers that demonstrate knowledge of Pythagorean triples well before Pythagoras. • The tablet features three preserved columns: line number, width (shorter leg), and diagonal (hypotenuse). • Many entries correspond to the equation x^2+y^2=z^2, verifying the Babylonians’ grasp of right triangle properties. • The tablet's mathematical sophistication supports claims that Babylonians developed key geometric concepts independently
Editor's Notes
- #2 Besides the Egyptian, another culture of antiquity that exerted a marked influence on the development of mathematics was the Babylonian. Here the term “Babylonian” is used without chronological restrictions to refer to those peoples who, many thousands of years ago, occupied the alluvial plain between the twin rivers, the Tigris and the Euphrates. The Greeks called this land “Mesopotamia,” meaning “the land between the rivers.”
- #3 Shortly after 3000 B.C., the Babylonians developed a system of writing from “pictographs”—a kind of picture writing much like hieroglyphics. But the materials chosen for writing imposed special limitations of their own, which soon robbed the pictographs of any resemblance to the objects, they stood for.
- #6 Because there were no colossal temples or monuments to capture the archeological imagination (the land is practically devoid of building stone), excavation came later to this part of the ancient world than to Egypt. It is estimated that today there are at least 400,000 Babylonian clay tablets, generally the size of a hand, scattered among the museums of various countries. Of these, some 400 tablets or tablet fragments have been identified as having mathematical content. Their decipherment and interpretation have gone slowly, owing to the variety of dialects and natural modifications in the language over the intervening several thousand years. The initial step was taken by an obscure German schoolteacher, Georg Friedrich Grotefend (1775–1853), of Göttingen, who although well versed in classical Greek, was ignorant of Oriental languages. While drinking with friends, Grotefend wagered that he could decipher a certain cuneiform inscription from Persepolis if they would supply him with the previously published literature on the subject. By an inspired guess he found the key to reading Persian cuneiform. The prevailing arrangement of the characters was such that the points of the wedges headed either downward or to the right, and the angles formed by the broad wedges consistently opened to the right. He assumed that the language’s characters were alphabetic; he then began picking out those characters that occurred with the greatest frequency and postulated that these were vowels. The most recurrent sign group was assumed to represent the word for “king.” These suppositions allowed Grotefend to decipher the title “King of Kings” and the names Darius, Xerxes, and Hystapes. Thereafter, he was able to isolate a great many individual characters and to read 12 of them correctly. Grotefend thus produced a translation that, although it contained numerous errors, gave an adequate idea of the contents. In 1802, when Grotefend was only 27 years old, he had his investigations presented to the Academy of Science in Gottingen (Grotefend was not allowed to read his own paper). But the achievements of this little-known scholar, who neither belonged to the faculty of the university nor was even an Orientalist by profession, only evoked ridicule from the learned body. Buried in an obscure publication, Grotefend’s brilliant discovery fell into oblivion, and decades later cuneiform script had to be deciphered anew. It is one of the whims of history that Champollion, the original translator of hieroglyphics, won an international reputation, while Georg Grotefend is almost entirely ignored.