Friberg, Jöran (2007). "A9.2. An Explicit Late Babylonian Multiplication Algorithm". A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection, Cuneiform Texts I. Sources and Studies in the History of Mathematics and Physical Sciences. Springer. pp. 456–460. doi:10.1007/978-0-387-48977-3. ISBN978-0-387-34543-7. MR2333050. The quote "the only one of its kind known" is from the book's introduction, p. x. The quote "slanting column of partial products" is from p. 456.
The standard sexagesimal notation using semicolon–commas was introduced by Otto Neugebauer in the 1930s. Neugebauer, Otto; Sachs, Abraham Joseph; Götze, Albrecht (1945). Mathematical Cuneiform Texts. American Oriental Series. Vol. 29. New Haven: American Oriental Society and the American Schools of Oriental Research. p. 2.
David Gilman Romano, Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion, American Philosophical Society, 1993, p. 78.
"A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of 3+1⁄8 or 3.125."
E. M. Bruins, Quelques textes mathématiques de la Mission de Suse, 1950.
E. M. Bruins and M. Rutten, Textes mathématiques de Suse, Mémoires de la Mission archéologique en Iran vol. XXXIV (1961).
See also Beckmann, Petr (1971). A History of Pi. New York: St. Martin's Press. pp. 12, 21–22.
"in 1936, a tablet was excavated some 200 miles from Babylon. [...] The mentioned tablet, whose translation was partially published only in 1950, [...] states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60 + 36/(60)2 [i.e. π = 3/0.96 = 25/8]".
Jason Dyer, On the Ancient Babylonian Value for Pi, 3 December 2008.
Høyrup, Jens (2018). "Computational techniques and computational aids in ancient Mesopotamia". In Volkov, Alexei; Freiman, Viktor (eds.). Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Mathematics Education in the Digital Era. Vol. 11. Springer. pp. 49–63. doi:10.1007/978-3-319-73396-8_3. ISBN9783319733968.
Friberg, Jöran (2007). "A9.2. An Explicit Late Babylonian Multiplication Algorithm". A Remarkable Collection of Babylonian Mathematical Texts: Manuscripts in the Schøyen Collection, Cuneiform Texts I. Sources and Studies in the History of Mathematics and Physical Sciences. Springer. pp. 456–460. doi:10.1007/978-0-387-48977-3. ISBN978-0-387-34543-7. MR2333050. The quote "the only one of its kind known" is from the book's introduction, p. x. The quote "slanting column of partial products" is from p. 456.
Allen, Arnold (January 1999). "Reviews: Mathematics: From the Birth of Numbers. By Jan Gullberg". The American Mathematical Monthly. 106 (1): 77–85. doi:10.2307/2589607. JSTOR2589607.
Allen, Arnold (January 1999). "Reviews: Mathematics: From the Birth of Numbers. By Jan Gullberg". The American Mathematical Monthly. 106 (1): 77–85. doi:10.2307/2589607. JSTOR2589607.
David Gilman Romano, Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion, American Philosophical Society, 1993, p. 78.
"A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of 3+1⁄8 or 3.125."
E. M. Bruins, Quelques textes mathématiques de la Mission de Suse, 1950.
E. M. Bruins and M. Rutten, Textes mathématiques de Suse, Mémoires de la Mission archéologique en Iran vol. XXXIV (1961).
See also Beckmann, Petr (1971). A History of Pi. New York: St. Martin's Press. pp. 12, 21–22.
"in 1936, a tablet was excavated some 200 miles from Babylon. [...] The mentioned tablet, whose translation was partially published only in 1950, [...] states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60 + 36/(60)2 [i.e. π = 3/0.96 = 25/8]".
Jason Dyer, On the Ancient Babylonian Value for Pi, 3 December 2008.
David Gilman Romano, Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion, American Philosophical Society, 1993, p. 78.
"A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of 3+1⁄8 or 3.125."
E. M. Bruins, Quelques textes mathématiques de la Mission de Suse, 1950.
E. M. Bruins and M. Rutten, Textes mathématiques de Suse, Mémoires de la Mission archéologique en Iran vol. XXXIV (1961).
See also Beckmann, Petr (1971). A History of Pi. New York: St. Martin's Press. pp. 12, 21–22.
"in 1936, a tablet was excavated some 200 miles from Babylon. [...] The mentioned tablet, whose translation was partially published only in 1950, [...] states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60 + 36/(60)2 [i.e. π = 3/0.96 = 25/8]".
Jason Dyer, On the Ancient Babylonian Value for Pi, 3 December 2008.
Høyrup, p. 406. "To judge from this evidence alone it is therefore likely that the Pythagorean rule was discovered within the lay surveyors' environment, possibly as a spin-off from the problem treated in Db2-146, somewhere between 2300 and 1825 BC." (Db2-146 is an Old Babylonian clay tablet from Eshnunna concerning the computation of the sides of a rectangle given its area and diagonal.) Høyrup, Jens. "Pythagorean 'Rule' and 'Theorem' – Mirror of the Relation Between Babylonian and Greek Mathematics". In Renger, Johannes (ed.). Babylon: Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. März 1998 in Berlin(PDF). Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. pp. 393–407.
