Heron of Alexandria
17th-century German depiction of Hero
Bornc. 10 AD
Diedc. 70 AD (aged around 60)
CitizenshipAlexandria, Roman Egypt
Known forAeolipile
Heron's fountain
Heron's formula
Vending machine
Scientific career
Pneumatic and hydraulic engineering

Hero of Alexandria (/ˈhɪər/; Greek: Ἥρων[1] ὁ Ἀλεξανδρεύς, Heron ho Alexandreus, also known as Heron of Alexandria /ˈhɛrən/; c. 10 AD – c. 70 AD), was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He is often considered the greatest experimenter of antiquity[2] and his work is representative of the Hellenistic scientific tradition.[3]

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.[4][5] He is said to have been a follower of the atomists. In his work Mechanics, he described pantographs.[6] Some of his ideas were derived from the works of Ctesibius.

In mathematics 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 Eastern Roman Empire and to a lesser extent, in Latin or Arabic translations.

Life and career

Hero's ethnicity may have been either Greek[2] or Hellenized Egyptian.[7][8][9][10] It is almost certain that Hero taught at the Musaeum which included the famous Library of Alexandria, because most of his writings appear as lecture notes for courses in mathematics, mechanics, physics and pneumatics. Although the field was not formalized until the twentieth century, it is thought that the work of Hero, in particular his automated devices, represented some of the first formal research into cybernetics.[11]


Hero's aeolipile
Hero's aeolipile

Hero described[12] 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.[13] Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work, which is not entirely false, air containing a trace of water vapor. However, this engine is far from a pure aeolipile.[14]

Hero's wind-powered organ (reconstruction)
Hero's wind-powered organ (reconstruction)


Hero described a method for iteratively computing the square root of a number.[19] 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.[20] 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.

Cultural references


The book About automata by Hero of Alexandria (1589 edition)
The book About automata by Hero of Alexandria (1589 edition)

The most comprehensive edition of Hero's works was published in five volumes in Leipzig by the publishing house Teubner in 1903.

Works known to have been written by Hero include:

Works that sometimes have been attributed to Hero, but are now thought most likely to have been written by someone else:[24]

Works that are preserved only in fragments:


See also


  1. ^ Genitive: Ἥρωνος.
  2. ^ a b Research Machines plc. (2004). The Hutchinson dictionary of scientific biography. Abingdon, Oxon: Helicon Publishing. p. 546. Hero of Alexandria (lived c. AD 60) Greek mathematician, engineer and the greatest experimentalist of antiquity
  3. ^ Marie Boas, "Hero's Pneumatica: A Study of Its Transmission and Influence", Isis, Vol. 40, No. 1 (Feb., 1949), p. 38 and supra
  4. ^ a b A.G. Drachmann, "Heron's Windmill", Centaurus, 7 (1961), pp. 145–151
  5. ^ a b Dietrich Lohrmann, "Von der östlichen zur westlichen Windmühle", Archiv für Kulturgeschichte, Vol. 77, Issue 1 (1995), pp. 1–30 (10f.)
  6. ^ Ceccarelli, Marco (2007). Distinguished Figures in Mechanism and Machine Science: Their Contributions and Legacies. Springer. p. 230. ISBN 978-1-4020-6366-4.
  7. ^ George Sarton (1936). "The Unity and Diversity of the Mediterranean World", Osiris 2, p. 406-463 [429]
  8. ^ John H. Lienhard (1995). "Hero of Alexandria". The Engines of Our Ingenuity. Episode 1038. NPR. KUHF-FM Houston.
  9. ^ T. D. De Marco (1974). "Gas-Turbine Standby-Power Generation for Water-Treatment Plants", Journal American Water Works Association 66 (2), p. 133-138.
  10. ^ Victor J. Katz (1998). A History of Mathematics: An Introduction, p. 184. Addison Wesley, ISBN 0-321-01618-1: "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."
  11. ^ Kelly, Kevin (1994). Out of control: the new biology of machines, social systems and the economic world. Boston: Addison-Wesley. ISBN 0-201-48340-8.
  12. ^ Hero (1899). "Pneumatika, Book ΙΙ, Chapter XI". Herons von Alexandria Druckwerke und Automatentheater (in Greek and German). Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. pp. 228–232.
  13. ^ Hero of Alexandria (1851). "Temple Doors opened by Fire on an Altar". Pneumatics of Hero of Alexandria. Bennet Woodcroft (trans.). London: Taylor Walton and Maberly (online edition from University of Rochester, Rochester, NY). Archived from the original on 2008-05-09. Retrieved 2008-04-23.
  14. ^ For example: Mokyr, Joel (2001). Twenty-five centuries of technological change. London: Routledge. p. 11. ISBN 0-415-26931-8. Among the devices credited to Hero are the aeolipile, a working steam engine used to open temple doors and Wood, Chris M.; McDonald, D. Gordon (1997). "History of propulsion devices and turbo machines". Global Warming. Cambridge, England: Cambridge University Press. p. 3. ISBN 0-521-49532-6. Two exhaust nozzles...were used to direct the steam with high velocity and rotate the sphere...By attaching ropes to the axial shaft Hero used the developed power to perform tasks such as opening temple doors
  15. ^ Humphrey, John W.; John P. Oleson; Andrew N. Sherwood (1998). Greek and Roman technology: A Sourcebook. Annotated translations of Greek and Latin texts and documents. Routledge Sourcebooks for the Ancient World. London and New York: Routledge. ISBN 978-0-415-06137-7., pp. 66–67
  16. ^ Woodcroft, Bennet (1851). The Pneumatics of Hero of Alexandria. London: Taylor Walton and Maberly. Bibcode:1851phal.book.....W. Archived from the original on 1997-06-29. Retrieved January 27, 2010. No. 57. Description of a Syringe
  17. ^ * Noel Sharkey (July 4, 2007), A programmable robot from AD 60, 2611, New Scientist, archived from the original on September 5, 2017, retrieved August 29, 2017
  18. ^ T.D. McGee (1988) Principles and Methods of Temperature Measurement ISBN 0-471-62767-4
  19. ^ Heath, Thomas (1921). A History of Greek Mathematics, Vol. 2. Oxford: Clarendon Press. pp. 323–324.
  20. ^ Smyly, J. Gilbart (1920). "Heron's Formula for Cube Root". Hermathena. Trinity College Dublin. 19 (42): 64–67. JSTOR 23037103.
  21. ^ "Russian animation in letters and figures | Films | "GERON"". animator.ru.
  22. ^ McKinnon, Jamies W. (2001). "Hero of Alexandria and Hydraulis". In Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary of Music and Musicians (2nd ed.). London: Macmillan.
  23. ^ On the main translations of the treatise, including Bernardino Baldi's 1589 translation into Italian, see now the discussion in Francesco Grillo (2019). Hero of Alexandria's Automata. A Critical Edition and Translation, Including a Commentary on Book One, PhD thesis, Univ. of Glasgow, pp. xxviii-xli.
  24. ^ O'Connor, J.J. & E.F. Robertson. "Heron biography". The MacTutor History of Mathematics archive. Retrieved 2006-06-18.

Further reading

Greek Wikisource has original text related to this article: Ἥρων ὁ Ἀλεξανδρεύς
Wikisource has the text of the 1911 Encyclopædia Britannica article "Hero of Alexandria".