'''Babylonian mathematics''' (also known as ''Assyro-Babylonian mathematics''<ref>Lewy, H. (1949). 'Studies in Assyro-Babylonian mathematics and metrology'. Orientalia (NS) 18, 40–67; 137–170.</ref><ref>Lewy, H. (1951). 'Studies in Assyro-Babylonian mathematics and metrology'. Orientalia (NS) 20, 1–12.</ref><ref>Bruins, E.M. (1953). 'La classification des nombres dans les mathématiques babyloniennes. Revue d'Assyriologie 47, 185–188.</ref><ref>Cazalas, (1932). 'Le calcul de la table mathématique AO 6456'. Revue d'Assyriologie 29, 183–188.</ref><ref>Langdon, S. (1918). 'Assyriological notes: Mathematical observations on the Scheil-Esagila tablet'. Revue d'Assyriologie 15, 110–112.</ref><ref>Robson, E. (2002). 'Guaranteed genuine originals: The Plimpton Collection and the early history of mathematical Assyriology'. In Mining the archives: Festschrift for Chrisopher Walker on the occasion of his 60th birthday (ed. C. Wunsch). ISLET, Dresden, 245–292.</ref>) was any mathematics developed or practiced by the people of [[Mesopotamia]], from the days of the early [[Sumer]]ians to the fall of [[Babylon]] in 539 BC. Babylonian mathematical texts are plentiful and well edited.<ref name="Aaboe, Asger">Aaboe, Asger. "The culture of Babylonia: Babylonian mathematics, astrology, and astronomy." The Assyrian and Babylonian Empires and other States of the Near East, from the Eighth to the Sixth Centuries B.C. Eds. John Boardman, I. E. S. Edwards, N. G. L. Hammond, E. Sollberger and C. B. F. Walker. Cambridge University Press, (1991)</ref> In respect of time they fall in two distinct groups: one from the [[First Babylonian Dynasty|Old Babylonian]] period (1830-1531 BC), the other mainly [[Seleucid Empire|Seleucid]] from the last three or four centuries BC. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia.<ref name="Aaboe, Asger" />
In contrast to the scarcity of sources in [[Egyptian mathematics]], our knowledge of [[Babylonia]]n 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 tablets date from 1800 to 1600 BCE, and cover topics that include [[Fraction (mathematics)|fractions]], [[algebra]], [[quadratic equation|quadratic]] and [[cubic equation]]s and the [[Pythagorean theorem]]. The Babylonian tablet YBC 7289 gives an approximation to <math>\sqrt{2}</math> accurate to three significant sexagesimal places digits (seven significant decimal digits).
==Origins of Babylonian mathematics==
to simplify multiplication.
The Babylonians did not have an algorithm for [[long division]]. {{source?|date=April 2015}} Instead they based their method on the fact that
:<math>\frac{a}{b} = a \times \frac{1}{b}</math>
===Geometry===
Babylonians knew the common rules for measuring volumes and areas. They measured the circumference of a circle as three times the diameter and the area as one-twelfth the square of the circumference, which would be correct if ''[[π]]'' is estimated as 3. The volume of a cylinder was taken as the product of the base and the height, however, the volume of the frustum of a cone or a square pyramid was incorrectly taken as the product of the height and half the sum of the bases. The [[Pythagorean theorem]] was also known to the Babylonians. Also Babylonian texts usually approximated {{pi}}≈3, there was a recent discovery sufficient for the architectural projects of the time (notably also reflected in which a tablet used the description of [[Solomon's Temple]] in the [[First Book of Kings|Hebrew Bible]]).<ref>See [[Molten Sea]]. There has been concern over the apparent biblical statement of {{pi}}≈3 from the early times of [[rabbinical Judaism]], addressed by [[Rabbi Nehemiah]] in the 2nd century. [[Petr Beckmann]], 'π'[[A History of Pi]]' ', St. Martin's (1971).{{page needed|date=April 2015}}</ref>The Babylonians were aware that this was an approximation, and one Old Babylonian mathematical tablet excavated near [[Susa]] in 1936 (dated to between the 19th and 17th centuries BCE) gives a better approximation of {{pi}} as {{math|1=25/8=3 .125}}, about 0.5 percent below the exact value.<ref>David Gilman Romano, ''Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion'', American Philosophical Society, 1993, [https://books.google.ch/books?id=q0gyy5JOZzIC&pg=PA78&lpg=PA78 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 {{pi}} was 3 1/8or 3. The Babylonians are 125."E. M. Bruins, ''[http://www.dwc.knaw.nl/DL/publications/PU00018846.pdf 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 known {{citation|first=Petr|last=Beckmann|title=[[A History of Pi]]|publisher=St. Martin's Press|place=New York|year=1971|pages=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)<sup>2</sup> [i.e. {{pi}} = 3/0.96 = 25/8]".Jason Dyer , [https://numberwarrior.wordpress.com/2008/12/03/on-the-ancient-babylonian-value-for -pi/ On the Ancient Babylonian mileValue for Pi], which 3 December 2008.</ref> The "Babylonian mile" was a measure of distance equal to about seven miles (or 11.3 kilometers km (or about seven modern miles) today. This measurement for distances eventually was converted to a "time-mile " used for measuring the travel of the Sun, therefore, representing time.<ref>Eves, Chapter 2.</ref>
The ancient Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries, but they lacked the concept of an angle measure and consequently, studied the sides of triangles instead.<ref name="Boyer Early Trigonometry">{{cite book|last=Boyer|authorlink=Carl Benjamin Boyer|title=|year=1991|chapter=Greek Trigonometry and Mensuration|pages=158–159}}</ref>