Hero of Alexandria

Hero of Alexandria (Ἥρων ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity and his work is representative of the Hellenistic scientific tradition.

Hero published a well-recognized description of a steam-powered device called an aeolipile (sometimes called a "Hero engine"). Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. In his work Mechanics, he described pantographs. Some of his ideas were derived from the works of Ctesibius.

In mathematics, he wrote a commentary on Euclid's Elements and a work on applied geometry known as the Metrica. He is mostly remembered for Heron's formula, a way to calculate the area of a triangle using only the lengths of its sides.

Much of Hero's original writings and designs have been lost, but some of his works were preserved including in manuscripts from the Byzantine Empire and to a lesser extent, in Latin or Arabic translations.

Life and career
Almost nothing is known about Hero's life, including his ethnicity – which may have been Greek or Hellenized Egyptian – parents' names or occupations, birthplace, or dates. The first mention of him in extant secondary sources is a quotation of Mechanics by Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from 150 BC to 250 AD. Otto Neugebauer (1938) noted a lunar eclipse observed in Alexandria and Rome used as a hypothetical example in Hero's Dioptra, found that it best matched the details of an eclipse in 62 AD, and Aage Gerhardt Drachmann surmised that Hero personally observed the eclipse from Alexandria; however, Hero does not explicitly say this, his brief mention of the eclipse is vague, and he might instead have used some earlier observer's data or even made up the example.

Alexandria was founded by Alexander the Great in the 4th century BC, and by Hero's time was a cosmopolitan city, part of the Roman Empire. The intellectual community, centered on the institution of the Musaeum (which included the Library of Alexandria), spoke and wrote in Greek; however, there was significant intermarriage between the city's Greek and Egyptian populations. It is assumed that Hero taught at the Musaeum because his writings appear to be lecture notes for courses or textbooks in mathematics, mechanics, physics and pneumatics. Although the field was not formalized until the twentieth century, it is thought that works of Hero, in particular those on his automated devices, represented some of the first formal research into cybernetics.

Inventions
Hero described the construction of the aeolipile (a version of which is known as Hero's engine) which was a rocket-like reaction engine and the first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura some 100 years earlier than Hero). It was described almost two millennia before the industrial revolution. Another engine used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors. Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work.
 * The first vending machine was also one of his constructions; when a coin was introduced via a slot on the top of the machine, it dispensed a set amount of water for ablutions. This was included in his list of inventions in his book Mechanics and Optics. When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve.
 * A wind-wheel operating an organ, marking the first instance in history of wind powering a machine.
 * Hero also invented many mechanisms for the Greek theatre, including an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel. The sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum.
 * The force pump was widely used in the Roman world, and one application was in a fire engine.
 * A syringe-like device was described by Hero to control the delivery of air or liquids.
 * In optics, Hero formulated the principle of the shortest path of light: If a ray of light propagates from point A to point B within the same medium, the path-length followed is the shortest possible. It was nearly 1,000 years later that Alhacen expanded the principle to both reflection and refraction, and the principle was later stated in this form by Pierre de Fermat in 1662; the most modern form is that the optical path is stationary.
 * A stand-alone fountain that operates under self-contained hydro-static energy; now called Heron's fountain.
 * A cart that was powered by a falling weight and strings wrapped around the drive axle.
 * Various authors have credited the invention of the thermometer to Hero. The thermometer was not a single invention, however, but a development. Hero knew of the principle that certain substances, notably air, expand and contract and described a demonstration in which a closed tube partially filled with air had its end in a container of water. The expansion and contraction of the air caused the position of the water/air interface to move along the tube.
 * A self-filling wine bowl, using a float valve.

Mathematics
Hero described a method, now known as Heron's method, for iteratively computing the square root of a number. Today, however, his name is most closely associated with Heron's formula for finding the area of a triangle from its side lengths. He also devised a method for calculating cube roots. He also designed a shortest path algorithm, that is, given two points A and B on one side of a line, find C a point on the straight line that minimizes AC+BC.

In solid geometry, the Heronian mean may be used in finding the volume of a frustum of a pyramid or cone.