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Db2-146
IM 67118, also known as Db2-146, is an First Babylonian dynasty, Old Babylonian clay tablet in the collection of the National Museum of Iraq that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal. In the last part of the text the solution is proved correct by means of the Pythagorean theorem. The steps of the solution are believed to represent cut-and-paste geometry operations involving a diagram from which, it has been suggested, ancient Mesopotamians might, at an earlier time, have derived the Pythagorean theorem. Description The tablet was excavated in 1962 at Tell al-Dhiba'i, Tell edh-Dhiba'i, an Old Babylonian settlement near modern Baghdad that was once part of the kingdom of Eshnunna, and was published by Taha Baqir in the same year. It dates to approximately 1770 BCE (according to the middle chronology), during the reign of Ibal-pi-el II, who ruled Eshnunna at the same time that Hammurabi ruled Babylon. The tablet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Babylonian Mathematics
Babylonian mathematics (also known as ''Assyro-Babylonian mathematics'') are the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. With respect to time they fall in two distinct groups: one from the Old Babylonian period (1830–1531 BC), the other mainly Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for nearly two millennia. In contrast to the scarcity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and the hypotenuse ''c'', often called the Pythagorean equation: :a^2 + b^2 = c^2 , The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jens Høyrup
Jens Egede Høyrup, born 1943 in Copenhagen, is a Danish historian of mathematics, specializing in pre-modern and early modern mathematics, ancient Mesopotamian mathematics in particular. He is especially known for his interpretation of what has often been referred to as Old Babylonian "algebra" as consisting of concrete, geometric manipulations. Career Høyrup studied physics and mathematics at the University of Copenhagen, Niels Bohr Institute from 1962 to 1969 (also, in 1965/66, at the Institut Henri Poincaré in Paris), with a focus on theoretical physics. In 1969 he completed his studies (as Danish ''cand. Scient.'') with a thesis on theoretical elementary particle physics and was assistant lecturer (Danish ''adjunkt'') in physics at the Danish Academy for Engineering from 1971 to 1973. Starting in 1973 he was senior lecturer (Danish ''lektor'') and in 1989 reader (Danish ''docent'') for the history and philosophy of science at Roskilde University, most recently in the Secti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale Babylonian Collection
Comprising some 45,000 items, the Yale Babylonian Collection is an independent branch of the Yale University Library housed on the Yale University campus in Sterling Memorial Library at New Haven, Connecticut, United States. In 2017, the collection was affiliated to the Peabody Museum of Natural History. Established by the donation of a collection of cuneiform tablets by J. P. Morgan in 1909, the Collection is now home to one of the largest collections of ancient Near Eastern writing in America and ranks among the best repositories of its kind in the world. Beyond the ongoing study and conservation of its own holdings, the Yale Babylonian Collection stands as an important center for innovative research in Assyriology and other related fields. Since 2019 all cuneiform artifacts as well as cylinder and stamp seals are being digitized. These digital assets will be freely available in a number of online repositories. The collection contains over 1,300 private and official letters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuneiform Digital Library Initiative
The Cuneiform Digital Library Initiative (CDLI) is an international digital library project aimed at putting text and images of an estimated 500,000 recovered cuneiform tablets created from between roughly 3350 BC and the end of the pre-Christian era online. Directors of the project are Robert K. Englund from University of California, Los Angeles and Jürgen Renn of the Max Planck Institute for the History of Science. Co-principal investigators are Jacob Dahl at Oxford University, Bertrand Lafront at the Centre national de la recherche scientifique, Nanterre and Émilie Pagé-Perron, University of Toronto. Preceding leadership comprised co-director Peter Damerow (1939-2011) from the Max Planck Institute for the History of Science and Pennsylvania Sumerian Dictionary leader Stephen J. Tinney who was co-principal investigator. In 2004 Englund received the Richard W. Lyman Award from the National Humanities Center for his work on the initiative. The project began in 1998 but it was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YBC 7289
YBC 7289 is a Babylonian clay tablet notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square. This number is given to the equivalent of six decimal digits, "the greatest known computational accuracy ... in the ancient world". The tablet is believed to be the work of a student in southern Mesopotamia from some time between 1800 and 1600 BC. It was donated to the Yale Babylonian Collection by J. P. Morgan. Content The tablet depicts a square with its two diagonals. One side of the square is labeled with the sexagesimal number 30. The diagonal of the square is labeled with two sexagesimal numbers. The first of these two, 1;24,51,10 represents the number 305470/216000 ≈ 1.414213, a numerical approximation of the square root of two that is off by less than one part in two million. The second of the two numbers is 42;25,35 = 30547/720 ≈ 42.426. This number is the result of multiplying 30 by the given appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plimpton 322
Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers , , and satisfying . From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem. At the same time, one should recall the tablet's author was a scribe, rather than a professional mathematician; it has been suggested that one of his goals may have been to produce examples for school problems. There has been significant scholarly debate on the nature and purpose of the tablet. For readable popular treatments of this tablet see rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism. The t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zhoubi Suanjing
The ''Zhoubi Suanjing'' () is one of the oldest Chinese mathematical texts. "Zhou" refers to the ancient Zhou dynasty (1046–256 BCE); "Bì" literally means "thigh", but in the book refers to the gnomon of a sundial. The book is dedicated to astronomical observation and calculation. ''Suan Jing'' or "classic of arithmetics" were appended in later time to honor the achievement of the book in mathematics. This book dates from the period of the Zhou dynasty, yet its compilation and addition of materials continued into the Han dynasty (202 BCE–220 CE). It is an anonymous collection of 246 problems encountered by the Duke of Zhou and his astronomer and mathematician, Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm. The book also makes use of the Pythagorean Theorem on various occasions and might also contain a geometric proof of the theorem for the case of the 3-4-5 triangle (but the procedure works for a general right triangle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logograms
In a written language, a logogram, logograph, or lexigraph is a written character that represents a word or morpheme. Chinese characters (pronounced ''hanzi'' in Mandarin, ''kanji'' in Japanese, ''hanja'' in Korean) are generally logograms, as are many hieroglyphic and cuneiform characters. The use of logograms in writing is called ''logography'', and a writing system that is based on logograms is called a ''logography'' or ''logographic system''. All known logographies have some phonetic component, generally based on the rebus principle. Alphabets and syllabaries are distinct from logographies in that they use individual written characters to represent sounds directly. Such characters are called '' phonograms'' in linguistics. Unlike logograms, phonograms do not have any inherent meaning. Writing language in this way is called ''phonemic writing'' or ''orthographic writing''. Etymology Doulgas Harper's Online Etymology Dictionary states that the term 'logogram' was derived f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumerian Language
Sumerian is the language of ancient Sumer. It is one of the oldest attested languages, dating back to at least 3000 BC. It is accepted to be a local language isolate and to have been spoken in ancient Mesopotamia, in the area that is modern-day Iraq. Akkadian, a Semitic language, gradually replaced Sumerian as a spoken language in the area around 2000 BC (the exact date is debated), but Sumerian continued to be used as a sacred, ceremonial, literary and scientific language in Akkadian-speaking Mesopotamian states such as Assyria and Babylonia until the 1st century AD. Thereafter it seems to have fallen into obscurity until the 19th century, when Assyriologists began deciphering the cuneiform inscriptions and excavated tablets that had been left by its speakers. Stages The history of written Sumerian can be divided into several periods: *Archaic Sumerian – 31st–26th century BC *Old or Classical Sumerian – 26th–23rd century BC *Neo-Sumerian – 23rd–21 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
