Editing Mathematical table (section)

==History and use==
The first tables of [[trigonometric functions]] known to be made were by [[Hipparchus]] (c.190  &ndash; c.120 BCE) and [[Menelaus of Alexandria|Menelaus]] (c.70–140 CE), but both have been lost. Along with the [[Ptolemy's table of chords|surviving table of Ptolemy]] (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the [[sine]] function.<ref name="mcs"/> The [[Āryabhaṭa's sine table|table produced by the Indian mathematician Āryabhaṭa]] (476–550 CE) is considered the first sine table ever constructed.<ref name="mcs">{{cite web|url=http://www-history.mcs.st-andrews.ac.uk/HistTopics/Trigonometric_functions.html |title=The trigonometric functions|last=J J O'Connor and E F Robertson|date=June 1996 |access-date=4 March 2010}}</ref> 
Āryabhaṭa's table remained the standard sine table of ancient India. There were continuous attempts to improve the accuracy of this table, culminating in the discovery of the [[Madhava series|power series expansions]] of the sine and cosine functions by [[Madhava of Sangamagrama]] (c.1350 – c.1425), and the tabulation of a [[Madhava's sine table|sine table by Madhava]] with values accurate to seven or eight decimal places.

[[Image:Four-Place Mathematical Tables cover.jpg|thumb|right|upright=0.60|These mathematical tables from 1925 were distributed by the [[College Entrance Examination Board]] to students taking the mathematics portions of the tests]]

Tables of [[common logarithm]]s were used until the invention of computers and electronic calculators to do rapid multiplications, divisions, and exponentiations, including the extraction of ''n''th roots.

Mechanical special-purpose computers known as [[difference engine]]s were proposed in the 19th century to tabulate polynomial approximations of logarithmic functions &ndash; that is, to compute large logarithmic tables. This was motivated mainly by errors in logarithmic tables made by the [[human computer]]s of the time. Early digital computers were developed during World War II in part to produce specialized mathematical tables for aiming [[artillery]]. From 1972 onwards, with the launch and growing use of [[HP-35|scientific calculator]]s, most mathematical tables went out of use.

One of the last major efforts to construct such tables was the [[Mathematical Tables Project]] that was started in the [[United States]] in 1938 as a project of the Works Progress Administration (WPA),  employing 450 out-of-work clerks to tabulate higher mathematical functions.  It lasted through World War II.<ref>{{cite journal|last=Grier|first=David Alan|title=The Math Tables Project of the Work Projects Administration: The Reluctant Start of the Computing Era|journal=IEEE Ann. Hist. Comput.|year=1998|volume=20|issue=3|pages=33–50|doi=10.1109/85.707573|issn=1058-6180}}</ref>

Tables of [[special functions]] are still used.  For example, the use of tables of values of the [[cumulative distribution function]] of the [[normal distribution]] – so-called [[standard normal table]]s – remains commonplace today, especially in schools, although the use of [[scientific calculator|scientific]] and [[graphing calculator]]s as well as [[spreadsheet]] and dedicated statistical software on personal computers is making such tables redundant.

Creating tables stored in [[random-access memory]] is a common [[code optimization]] technique in computer programming, where the use of such tables  speeds up calculations in those cases where a [[Lookup table|table lookup]] is faster than the corresponding calculations (particularly if the computer in question doesn't have a hardware implementation of the calculations). In essence, one [[Space–time tradeoff|trades computing speed for the computer memory space]] required to store the tables.