Editing Heron's formula (section)

== History ==

The formula is credited to [[Hero of Alexandria|Heron (or Hero) of Alexandria]] ({{fl.}} 60 AD),<ref>{{cite journal
 | last1 = Id | first1 = Yusuf
 | last2 = Kennedy | first2 = E. S.
 | journal = [[The Mathematics Teacher]]
 | jstor = 27958225
 | mr = 256819
 | pages = 585–587
 | title = A medieval proof of Heron's formula
 | volume = 62
 | year = 1969| issue = 7
 | doi = 10.5951/MT.62.7.0585
 }}</ref> and a proof can be found in his book ''Metrica''. Mathematical historian [[Thomas Heath (classicist)|Thomas Heath]] suggested that [[Archimedes]] knew the formula over two centuries earlier,<ref>{{cite book
| author=Heath, Thomas L.
| title=A History of Greek Mathematics
| volume=II
| publisher=Oxford University Press
| year=1921
| pages=321–323}}</ref> and since ''Metrica'' is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work.<ref>{{MathWorld |urlname=HeronsFormula |title=Heron's Formula}}</ref>

A formula equivalent to Heron's was discovered by Chinese mathematician Qin Jiushao:

<math display=block>
A = \frac1{2}\sqrt{a^2 c^2 - \left(\frac{a^2 + c^2 - b^2}{2}\right)^2},
</math>

published in ''[[Mathematical Treatise in Nine Sections]]'' ([[Qin Jiushao]], 1247).<ref>{{Cite book |title=數學九章 (四庫全書本) |lang=zh |last=秦 |first=九韶 |year=1773 |chapter=卷三上, 三斜求积 |chapter-url=https://zh.wikisource.org/zh-hant/%E6%95%B8%E5%AD%B8%E4%B9%9D%E7%AB%A0_(%E5%9B%9B%E5%BA%AB%E5%85%A8%E6%9B%B8%E6%9C%AC)/%E5%85%A8%E8%A6%BD#%E4%B8%89%E6%96%9C%E6%B1%82%E7%A9%8D}}</ref>