Editing Mesopotamia (section)

===Mathematics===
{{Main|Babylonian mathematics}}

[[File:Clay tablet, mathematical, geometric-algebraic, similar to the Euclidean geometry. From Tell Harmal, Iraq. 2003-1595 BCE. Iraq Museum.jpg|thumb|A [[clay tablet]], mathematical, geometric-algebraic, similar to the Euclidean geometry. From [[Shaduppum]] Iraq. 2003–1595 BC. [[Iraq Museum]].]]
Mesopotamian mathematics and science was based on a [[sexagesimal]] (base 60) [[numeral system]]. This is the source of the 60-minute hour, the 24-hour day, and the 360-[[degree (angle)|degree]] circle. The [[Sumerian calendar]] was lunisolar, with three seven-day weeks of a lunar month. This form of mathematics was instrumental in early [[History of cartography|map-making]]. The Babylonians also had theorems on how to measure the area of  shapes and solids. 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 {{pi}} were fixed at 3.<ref name="Holt, Rinehart and Winston">{{cite book |url=https://archive.org/details/introductiontohi00eves_0 |url-access=registration |page=[https://archive.org/details/introductiontohi00eves_0/page/31 31] |title=An Introduction to the History of Mathematics |publisher=Holt, Rinehart and Winston |last1=Eves |first1=Howard |year=1969 |isbn=9780030745508 }}</ref>

The volume of a cylinder was taken as the product of the area 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. Also, there was a recent discovery in which a tablet used {{pi}} as 25/8 (3.125 instead of 3.14159~). The Babylonians are also known for the Babylonian mile, which was a measure of distance equal to about seven modern miles (11&nbsp;km). This measurement for distances eventually was converted to a time-mile used for measuring the travel of the Sun, therefore, representing time.<ref name="Holt, Rinehart and Winston"/>

==== Algebra ====
{{Main|Algebra|Square root of 2}}
The roots of algebra can be traced to the ancient Babylonia<ref>{{cite book |last=Struik |first=Dirk J. |url=https://archive.org/details/concisehistoryof0000stru_m6j1 |title=A Concise History of Mathematics |publisher=Dover Publications |year=1987 |isbn=978-0-486-60255-4 |location=New York |url-access=registration}}</ref> who developed an advanced arithmetical system with which they were able to do calculations in an [[algorithm]]ic fashion.

The [[Babylonia]]n clay tablet [[YBC 7289]] ({{circa|1800}}–1600 BC) gives an approximation of {{math|{{sqrt|2}}}} in four [[sexagesimal]] figures, {{nowrap|1 24 51 10}}, which is accurate to about six [[decimal]] digits,<ref>Fowler and Robson, p. 368. [http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html Photograph, illustration, and description of the ''root(2)'' tablet from the Yale Babylonian Collection]. {{webarchive|url=https://web.archive.org/web/20120813054036/http://it.stlawu.edu/%7Edmelvill/mesomath/tablets/YBC7289.html|date=2012-08-13}}. [http://www.math.ubc.ca/%7Ecass/Euclid/ybc/ybc.html High resolution photographs, descriptions, and analysis of the ''root(2)'' tablet (YBC 7289) from the Yale Babylonian Collection]. {{Webarchive|url=https://web.archive.org/web/20200712173830/http://www.math.ubc.ca/~cass/Euclid/ybc/ybc.html|date=12 July 2020}}.</ref> and is the closest possible three-place sexagesimal representation of {{math|{{sqrt|2}}}}:

: <math>1 + \frac{24}{60} + \frac{51}{60^2} + \frac{10}{60^3} = \frac{305470}{216000} = 1.41421\overline{296}.</math>

The Babylonians were not interested in exact solutions, but rather approximations, and so they would commonly use [[linear interpolation]] to approximate intermediate values.<ref name="Boyer Babylon p30">{{Harvnb|Boyer|1991|loc="Mesopotamia" p. 30}}: "Babylonian mathematicians did not hesitate to interpolate by proportional parts to approximate intermediate values. Linear interpolation seems to have been a commonplace procedure in ancient Mesopotamia, and the positional notation lent itself conveniently to the rile of three. [...] a table essential in Babylonian algebra; this subject reached a considerably higher level in Mesopotamia than in Egypt. Many problem texts from the Old Babylonian period show that the solution of the complete three-term quadratic equation afforded the Babylonians no serious difficulty, for flexible algebraic operations had been developed. They could transpose terms in equations by adding equals to equals, and they could [[Multiplication|multiply]] both sides by like quantities to remove [[fraction]]s or to eliminate factors. By adding <math>4ab</math> to <math>(a - b)^2</math> they could obtain <math>(a + b)^2</math> for they were familiar with many simple forms of factoring. [...]Egyptian algebra had been much concerned with linear equations, but the Babylonians evidently found these too elementary for much attention. [...] In another problem in an Old Babylonian text we find two simultaneous linear equations in two unknown quantities, called respectively the "first silver ring" and the "second silver ring.""</ref> One of the most famous tablets is the [[Plimpton 322|Plimpton 322 tablet]], created around 1900–1600&nbsp;BC, which gives a table of [[Pythagorean triples]] and represents some of the most advanced mathematics prior to Greek mathematics.<ref>{{cite web|author=Joyce, David E. |year=1995 |title=Plimpton 322 |url=http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.html |quote=The clay tablet with the catalog number 322 in the G. A. Plimpton Collection at Columbia University may be the most well known mathematical tablet, certainly the most photographed one, but it deserves even greater renown. It was scribed in the Old Babylonian period between −1900 and −1600 and shows the most advanced mathematics before the development of Greek mathematics. |access-date=3 June 2022 |archive-date=8 March 2011 |archive-url=https://web.archive.org/web/20110308060531/http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.html |url-status=live }}</ref>