Editing Hero of Alexandria (section)

== Life and career ==
Almost nothing is known about Hero's life, including his birthplace and background. The first extant mention of him is references to his works found in Book VIII of [[Pappus of Alexandria|Pappus]]'s ''Collection'' (4th century AD), and scholarly estimates for Hero's dates range from 150 BC to 250 AD.<ref>{{cite book |last=Heath |first=Thomas |author-link=Thomas Heath (classicist) |title=A History of Greek Mathematics |volume=2 |publisher=Oxford University Press |year=1921 |chapter=XVIII: Mensuration: Heron of Alexandria |at="Controversies as to Heron's Date", {{pgs|298–307}} |chapter-url=https://archive.org/details/historyofgreekm02heat/page/298/ }}</ref> [[Otto Neugebauer]] (1938) noted a lunar eclipse observed in Alexandria and Rome used as a hypothetical example in Hero's ''Dioptra'', and found that it best matched the details of an eclipse in 62 AD; [[A. G. Drachmann]] subsequently surmised that Hero personally observed the eclipse from Alexandria.<ref>{{cite journal |last=Keyser |first=Paul |title=Suetonius 'Nero' 41. 2 and the Date of Heron Mechanicus of Alexandria |journal=Classical Philology |volume=83 |number=3 |year=1988 |pages=218–220 }} {{pb}} {{cite journal |last=Neugebauer |first=Otto |year=1938 |title=Über eine Methode zur Distanzbestimmung Alexandria–Rom bei Heron |trans-title=On a method for determining the distance between Alexandria and Rome by Heron |language=de |journal=Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser |volume=26 |issue=2 }} {{pb}} {{cite journal |last=Drachmann |first=A. G. |author-link=A. G. Drachmann |title=Heron and Ptolemaios |journal=Centaurus |volume=1 |year=1950 |pages=117–131 }}</ref> 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.<ref>Heron's text is (translation by Masià): {{pb}}"Then, let it be necessary to measure, say, the path between Alexandria and Rome along a line – or rather along a great-circle arc on the earth – if it has been agreed that the circumference of the earth is 252,000 stades – as Eratosthenes, having worked rather more accurately than others, showed in his book entitled ''On the Measurement of the Earth''. Now, let <the> same lunar eclipse have been observed at Alexandria and Rome. If one is found in the records, we will use that, or, if not, it will be possible for us to state our own observations because lunar eclipses occur at 5 and 6 month intervals. Now let an eclipse be found <in the records> – this one, in the stated regions: in Alexandria in the 5th hour of the night, and the same one in the 3rd hour in Rome – obviously the same night. And let the night – that is, the day circle with respect to which the sun moves on the said night – be 9 (or 10) days from the vernal equinox in the direction of the winter solstice." {{pb}} {{cite journal |last=Sidoli |first=Nathan |year=2011 |title=Heron of Alexandria's Date |journal=Centaurus |volume=53 |pages=55–61 |doi=10.1111/j.1600-0498.2010.00203.x |url=http://individual.utoronto.ca/acephalous/Sidoli_2011.pdf }} {{pb}} {{cite journal |last=Masià |first=Ramon |title=On dating Hero of Alexandria |year=2015 |journal=Archive for History of Exact Sciences |volume=69 |number=3 |pages=231–255 |jstor=24569551 }}</ref>

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 around the [[Mouseion]] (which included the [[Library of Alexandria]]), spoke and wrote in Greek; however, there was considerable intermarriage between the city's Greek and Egyptian populations.<ref>{{cite book |last=Katz |first=Victor J. |author-link=Victor Katz |year=1998 |title=A History of Mathematics: An Introduction |page=184 |publisher=Addison Wesley |isbn=0-321-01618-1 |quote=But what we really want to know is to what extent the Alexandrian mathematicians of the period from the first to the fifth centuries C.E. were Greek. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. And most modern studies conclude that the Greek community coexisted [...] So should we assume that Ptolemy and Diophantus, Pappus and Hypatia were ethnically Greek, that their ancestors had come from Greece at some point in the past but had remained effectively isolated from the Egyptians? It is, of course, impossible to answer this question definitively. But research in papyri dating from the early centuries of the common era demonstrates that a significant amount of intermarriage took place between the Greek and Egyptian communities [...] And it is known that Greek marriage contracts increasingly came to resemble Egyptian ones. In addition, even from the founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles. Of course, it was essential in such cases for the Egyptians to become "Hellenized", to adopt Greek habits and the Greek language. Given that the Alexandrian mathematicians mentioned here were active several hundred years after the founding of the city, it would seem at least equally possible that they were ethnically Egyptian as that they remained ethnically Greek. In any case, it is unreasonable to portray them with purely European features when no physical descriptions exist.}}</ref> It has been inferred that Hero taught at the Mouseion because some of his writings appear to be lecture notes or textbooks in [[mathematics]], [[mechanics]], [[physics]] and [[pneumatics]].{{r|mactutor}} 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]].<ref name="Kelly">{{cite book |last= Kelly|first=Kevin|title = Out of control: the new biology of machines, social systems and the economic world|publisher = Addison-Wesley|location=Boston|date= 1994|isbn=0-201-48340-8|url = https://archive.org/details/outofcontrolnewb00kell}}</ref>

=== Inventions ===
[[Image:Aeolipile illustration.png|thumb|upright|Hero's aeolipile]]
A number of devices and inventions have been ascribed to Hero, including the following:

* The ''[[aeolipile]]'' (a version of which is known as "Hero's engine"), which was a [[rocket engine|rocket-like reaction engine]] and the first-recorded [[steam engine]] (although [[Vitruvius]] mentioned the aeolipile in ''[[De Architectura]]'', presumably earlier than Hero).<ref>{{cite book|title=Herons von Alexandria Druckwerke und Automatentheater|author-last=Hero|author-link=Hero of Alexandria|others=Wilhelm Schmidt (translator)|place=Leipzig|publisher=B.G. Teubner|date=1899|language =el, de|chapter-url=https://archive.org/stream/heronsvonalexandhero#page/228/mode/2up|pages=228–232|chapter=Pneumatika, Book ΙΙ, Chapter XI}}</ref> 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.<ref>{{cite web |last=Hero of Alexandria |translator=Bennet Woodcroft (trans.) |year=1851 |title=Temple Doors opened by Fire on an Altar |work=Pneumatics of Hero of Alexandria |publisher=London: Taylor Walton and Maberly (online edition from University of Rochester, Rochester, NY) |url=http://www.history.rochester.edu/steam/hero/section37.html |access-date=2008-04-23 |url-status=dead |archive-url=https://web.archive.org/web/20080509122356/http://www.history.rochester.edu/steam/hero/section37.html |archive-date = 2008-05-09 }}</ref> Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work.<ref>For example: {{cite book |last=Mokyr |first=Joel |author-link = Joel Mokyr |year=2001 |title=Twenty-five centuries of technological change |location=London |publisher=Routledge |page=11 |isbn=0-415-26931-8 |quote=Among the devices credited to Hero are the aeolipile, a working steam engine used to open temple doors}} and {{cite book |last=Wood |first=Chris M. |last2=McDonald |first2=D. Gordon |year=1997 |title=Global Warming |publisher = Cambridge University Press |page=3 |chapter=History of propulsion devices and turbo machines |isbn=0-521-49532-6 |quote=Two exhaust nozzles{{nbsp}}... were used to direct the steam with high velocity and rotate the sphere{{nbsp}}... By attaching ropes to the axial shaft Hero used the developed power to perform tasks such as opening temple doors }}</ref>
* A [[vending machine]] that dispensed a set amount of water for ablutions when a coin was introduced via a slot on the top of the machine. This was included in his list of inventions in his book ''Mechanics''. 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.<ref>{{Cite book |last1=Humphrey |first1=John W. |last2=Oleson |first2=John P. |last3=Sherwood |first3=Andrew N. |year=1998 |title=Greek and Roman technology: A Sourcebook |location=London |publisher=Routledge |pages=66–67 |isbn=978-0-415-06137-7 }}</ref>
* A wind-wheel operating an organ, marking the first documented instance of wind powering a machine.<ref name=drachmann>{{cite journal |last=Drachmann |first=A. G. |author-link=A. G. Drachmann |year=1961 |title=Heron's Windmill |journal=Centaurus |volume=7 |pages=145–151 }}</ref><ref name=lohrmann>{{cite journal |last=Lohrmann |first=Dietrich |year=1995 |title=Von der östlichen zur westlichen Windmühle |journal=Archiv für Kulturgeschichte |volume=77 |issue=1 |pages=1–30 (10f.) }}</ref>
* Many mechanisms for the Greek [[theater|theatre]], including an entirely mechanical play almost ten minutes in length, powered by a 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.
* A [[force pump]] that was widely used in the [[Ancient Rome|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.<ref>{{cite book|last1=Woodcroft|first1=Bennet|title=The Pneumatics of Hero of Alexandria|date=1851|publisher=Taylor Walton and Maberly|location=London|url=http://www.history.rochester.edu/steam/hero/section57.html|archive-url=https://web.archive.org/web/19970629025336/http://www.history.rochester.edu/steam/hero/section57.html|url-status=dead|archive-date=1997-06-29|access-date=January 27, 2010|quote=No. 57. Description of a Syringe|bibcode=1851phal.book.....W}}</ref>
* 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.<ref>{{cite news |last1=Sharkey |first1=Noel |title=The programmable robot of ancient Greece |url=https://www.newscientist.com/article/mg19526111-600-the-programmable-robot-of-ancient-greece/ |work=New Scientist |issue=2611 |date=7 July 2007 |url-access=subscription}} {{pb}} {{cite web|title=A programmable robot from AD 60: Noel Sharkey traces the technology way back to ancient Alexandria |first=Ben |last=Crystall |website=New Scientist blog |url=https://www.newscientist.com/blog/technology/2007/07/programmable-robot-from-60ad.html|date=July 4, 2007 |access-date=August 29, 2017 |archive-url=https://web.archive.org/web/20170905101636/https://www.newscientist.com/blog/technology/2007/07/programmable-robot-from-60ad.html|archive-date=September 5, 2017|url-status=dead}} (Video also available [https://www.youtube.com/watch?v=xyQIo9iS_z0 from YouTube])</ref>
* A kind of [[thermometer]] has been credited to Hero. Although the thermometer was [[Timeline of temperature and pressure measurement technology|not a single invention 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.<ref>T.D. McGee (1988) ''Principles and Methods of Temperature Measurement'' {{ISBN|0-471-62767-4}}</ref> 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]].<ref>{{Cite web|url=https://engines.egr.uh.edu/episode/1038|title=Hero of Alexandria &#124; The Engines of Our Ingenuity|website=engines.egr.uh.edu}}</ref>

=== Mathematics ===
Hero described an iterative algorithm for computing [[square root]]s, now called [[Heron's method]], in his work ''Metrica'', alongside other algorithms and approximations.<ref>{{cite book |last=Heath |first=Thomas |year=1921 |title= A History of Greek Mathematics |volume=2 |publisher=Clarendon Press |location = Oxford |at=[https://archive.org/details/ahistorygreekma00heatgoog/page/n340 {{pgs{{!}}323–324}}] |url=https://archive.org/details/ahistorygreekma00heatgoog}}</ref> Today, however, his name is most closely associated with [[Heron's formula]] for the area of a triangle in terms of its side lengths. Hero also reported on a method for calculating cube roots.<ref>{{cite journal |last=Smyly |first=J. Gilbart |title=Heron's Formula for Cube Root |journal=Hermathena |year=1920 |volume=19 |issue=42 |pages=64–67 |jstor=23037103}}</ref> In [[solid geometry]], the [[Heronian mean]] may be used in finding the [[volume]] of a [[frustum]] of a [[pyramid]] or [[cone (geometry)|cone]].

Hero also described a shortest path algorithm, that is, given two points A and B on one side of a line, find a point C on the straight line that minimizes AC + BC. This led him to formulate the [[Fermat's principle|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. In the Middle Ages, [[Ibn al-Haytham]] 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 point|stationary]].