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 approximation to the square root of two, and approximates the length of the diagonal of a square of side length 30. Because the Babylonian sexagesimal notation did not indicate which digit had which place value, one alternative interpretation is that the number on the side of the square is 30/60 = 1/2. Under this alternative interpretation, the number on the diagonal is 30547/43200 ≈ 0.70711, a close numerical approximation of , the length of the diagonal of a square of side length 1/2, that is also off by less than one part in two million. David Fowler andInterpretation
Although YBC 7289 is frequently depicted (as in the photo) with the square oriented diagonally, the standard Babylonian conventions for drawing squares would have made the sides of the square vertical and horizontal, with the numbered side at the top. The small round shape of the tablet, and the large writing on it, suggests that it was a "hand tablet" of a type typically used for rough work by a student who would hold it in the palm of his hand. The student would likely have copied the sexagesimal value of the square root of 2 from another tablet, but an iterative procedure for computing this value can be found in another Babylonian tablet, BM 96957 + VAT 6598. The mathematical significance of this tablet was first recognized by Otto E. Neugebauer and Abraham Sachs in 1945. The tablet "demonstrates the greatest known computational accuracy obtained anywhere in the ancient world", the equivalent of six decimal digits of accuracy. Other Babylonian tablets include the computations of areas ofProvenance and curation
It is unknown where in Mesopotamia YBC 7289 comes from, but its shape and writing style make it likely that it was created in southern Mesopotamia, sometime between 1800BC and 1600BC.See also
*References
{{reflist, 30em, refs= {{citation , last = Robson , first = Eleanor , author-link = Eleanor Robson , editor-last = Katz , editor-first = Victor J. , page = 143 , publisher = Princeton University Press , contribution = Mesopotamian Mathematics , title = The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook , url = https://books.google.com/books?id=3ullzl036UEC , year = 2007, isbn = 978-0-691-11485-9 {{citation , last = Friberg , first = Jöran , editor1-first = Jöran , editor1-last = Friberg , doi = 10.1007/978-0-387-48977-3 , isbn = 978-0-387-34543-7 , mr = 2333050 , page = 211 , publisher = Springer, New York , series = Sources and Studies in the History of Mathematics and Physical Sciences , title = A remarkable collection of Babylonian mathematical texts , year = 2007 {{citation , last1 = Fowler , first1 = David , author1-link = David Fowler (mathematician) , last2 = Robson , first2 = Eleanor , author2-link = Eleanor Robson , doi = 10.1006/hmat.1998.2209 , issue = 4 , journal = Historia Mathematica , mr = 1662496 , pages = 366–378 , title = Square root approximations in old Babylonian mathematics: YBC 7289 in context , volume = 25 , year = 1998 {{citation , last1 = Neugebauer , first1 = O. , author1-link = Otto E. Neugebauer , last2 = Sachs , first2 = A. J. , author2-link = Abraham Sachs , mr = 0016320 , page = 43 , publisher = American Oriental Society and the American Schools of Oriental Research, New Haven, Conn. , series = American Oriental Series , title = Mathematical Cuneiform Texts , year = 1945 {{citation , last = Neugebauer , first = O. , author-link = Otto E. Neugebauer , mr = 0465672 , pages = 22–23 , publisher = Springer-Verlag, New York-Heidelberg , title = A History of Ancient Mathematical Astronomy, Part One , url = https://books.google.com/books?id=6tkqBAAAQBAJ&pg=PA22 , year = 1975, isbn = 978-3-642-61910-6 {{citation, url=https://books.google.com/books?id=8eaHxE9jUrwC&pg=PA57, page=57, title=A Survey of the Almagest, series=Sources and Studies in the History of Mathematics and Physical Sciences, first=Olaf, last=Pedersen, editor-first=Alexander, editor-last=Jones, publisher=Springer, year=2011, isbn=978-0-387-84826-6 {{citation , last = Rudman , first = Peter S. , isbn = 978-1-59102-477-4 , mr = 2329364 , page = 241 , publisher = Prometheus Books, Amherst, NY , title = How mathematics happened: the first 50,000 years , url = https://books.google.com/books?id=BtcQq4RUfkUC&pg=PA241 , year = 2007 {{citation , last1 = Beery , first1 = Janet L. , author1-link = Janet Beery , last2 = Swetz , first2 = Frank J. , date = July 2012 , doi = 10.4169/loci003889 , journal = Convergence , publisher = Mathematical Association of America , title = The best known old Babylonian tablet? {{citation, title=A 3,800-year journey from classroom to classroom, first=Patrick, last=Lynch, magazine=Yale News, date=April 11, 2016, url=https://news.yale.edu/2016/04/11/3800-year-journey-classroom-classroom, access-date=2017-10-25 {{citation, title=A 3D-print of ancient history: one of the most famous mathematical texts from Mesopotamia, date=January 16, 2016, url=http://ipch.yale.edu/news/3d-print-ancient-history-one-most-famous-mathematical-texts-mesopotamia, publisher=Yale Institute for the Preservation of Cultural Heritage, access-date=2017-10-25 {{citation , title=Mesopotamian tablet YBC 7289 , last=Kwan , first=Alistair , date=April 20, 2019 , publisher=University of Auckland , doi = 10.17608/k6.auckland.6114425.v1 Babylonian mathematics Mathematics manuscripts Clay tablets 18th-century BC works