// minds behind maths

Hero of Alexandria

c. 10 – c. 70 AD · Geometry, engineering

Hero (or Heron) of Alexandria was a Greek mathematician and engineer of the first century AD. The area formula that bears his name — giving a triangle's area from its three side lengths alone, with no angle or height required — is proved in his work Metrica, though the result was probably known earlier and the historian Thomas Heath suggested Archimedes knew it two centuries before. An equivalent formula was found independently by the Chinese mathematician Qin Jiushao in 1247. The formula can be proved geometrically, with trigonometry via the law of cosines, or algebraically using the Pythagorean theorem.

Source: Wikipedia — Heron's formula

Formulas that trace back to Hero of Alexandria

Heron's formula Area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
Heron's formula via the Pythagorean theorem d = (a²−b²+c²)/(2c), h = √(a²−d²), Area = ½·c·h = √(s(s−a)(s−b)(s−c))