Editing History of mathematics (section)

==Roman==
{{further|Roman abacus|Roman numerals}}
[[File:Aquinqum BHM IMG 0662 land surveyor equipment.jpg|thumb|Equipment used by an [[Ancient Rome|ancient Roman]] land [[surveyor]] (''[[gromatici]]''), found at the site of [[Aquincum]], modern [[Budapest]], [[Hungary]]]]
Although [[Greeks|ethnic Greek]] mathematicians continued under the rule of the late [[Roman Republic]] and subsequent [[Roman Empire]], there were no noteworthy [[Latins (Italic tribe)|native Latin]] mathematicians in comparison.<ref>{{Harv|Goodman|2016|p=119}}</ref><ref>{{Harv|Cuomo|2001|pp=194, 204–06}}</ref> [[Ancient Rome|Ancient Romans]] such as [[Cicero]] (106–43 BC), an influential Roman statesman who studied mathematics in Greece, believed that Roman [[surveyor]]s and [[Mental calculator|calculators]] were far more interested in [[applied mathematics]] than the [[theoretical mathematics]] and geometry that were prized by the Greeks.<ref>{{Harv|Cuomo|2001|pp=192–95}}</ref> It is unclear if the Romans first derived [[Roman numerals|their numerical system]] directly from [[Greek numerals|the Greek precedent]] or from [[Etruscan numerals]] used by the [[Etruscan civilization]] centered in what is now [[Tuscany]], [[central Italy]].<ref>{{Harv|Goodman|2016|pp=120–21}}</ref>

Using calculation, Romans were adept at both instigating and detecting financial [[fraud]], as well as [[List of Roman taxes|managing taxes]] for the [[treasury]].<ref>{{Harv|Cuomo|2001|p=196}}</ref> [[Siculus Flaccus]], one of the Roman ''[[gromatici]]'' (i.e. land surveyor), wrote the ''Categories of Fields'', which aided Roman surveyors in measuring the [[surface area]]s of allotted lands and territories.<ref>{{Harv|Cuomo|2001|pp=207–08}}</ref> Aside from managing trade and taxes, the Romans also regularly applied mathematics to solve problems in [[Roman engineering|engineering]], including the erection of [[Roman architecture|architecture]] such as [[Roman bridge|bridges]], [[Roman roads|road-building]], and [[Roman military engineering|preparation for military campaigns]].<ref>{{Harv|Goodman|2016|pp=119–20}}</ref> [[Roman art|Arts and crafts]] such as [[Roman mosaic]]s, inspired by previous [[Mosaics of Delos|Greek designs]], created illusionist geometric patterns and rich, detailed scenes that required precise measurements for each [[tessera]] tile, the [[opus tessellatum]] pieces on average measuring eight millimeters square and the finer [[opus vermiculatum]] pieces having an average surface of four millimeters square.<ref>{{Harv|Tang|2005|pp=14–15, 45}}</ref><ref>{{Harv|Joyce|1979|p=256}}</ref>

The creation of the [[Roman calendar]] also necessitated basic mathematics. The first calendar allegedly dates back to 8th century BC during the [[Roman Kingdom]] and included 356 days plus a [[leap year]] every other year.<ref>{{Harv|Gullberg|1997|p=17}}</ref> In contrast, the [[lunar calendar]] of the Republican era contained 355 days, roughly ten-and-one-fourth days shorter than the [[solar year]], a discrepancy that was solved by adding an extra month into the calendar after the 23rd of February.<ref>{{Harv|Gullberg|1997|pp=17–18}}</ref> This calendar was supplanted by the [[Julian calendar]], a [[solar calendar]] organized by [[Julius Caesar]] (100–44 BC) and devised by [[Sosigenes of Alexandria]] to include a [[leap day]] every four years in a 365-day cycle.<ref>{{Harv|Gullberg|1997|p=18}}</ref> This calendar, which contained an error of 11 minutes and 14 seconds, was later corrected by the [[Gregorian calendar]] organized by [[Pope Gregory XIII]] ({{reign|1572|1585}}), virtually the same solar calendar used in modern times as the international standard calendar.<ref>{{Harv|Gullberg|1997|pp=18–19}}</ref>

At roughly the same time, [[Science and technology of the Han dynasty|the Han Chinese]] and the Romans both invented the wheeled [[odometer]] device for measuring [[distance]]s traveled, the Roman model first described by the Roman civil engineer and architect [[Vitruvius]] ({{circa|80 BC|15 BC}}).<ref>{{Harv|Needham|Wang|2000|pp=281–85}}</ref> The device was used at least until the reign of emperor [[Commodus]] ({{reign|177|192 AD}}), but its design seems to have been lost until experiments were made during the 15th century in Western Europe.<ref>{{Harv|Needham|Wang|2000|p=285}}</ref> Perhaps relying on similar gear-work and [[Roman technology|technology]] found in the [[Antikythera mechanism]], the odometer of Vitruvius featured chariot wheels measuring 4 feet (1.2&nbsp;m) in diameter turning four-hundred times in one [[Roman mile]] (roughly 4590&nbsp;ft/1400&nbsp;m). With each revolution, a pin-and-axle device engaged a 400-tooth [[cogwheel]] that turned a second gear responsible for dropping pebbles into a box, each pebble representing one mile traversed.<ref>{{Harv|Sleeswyk|1981|pp=188–200}}</ref>