Hero of Alexandria (/ˈhɪəroʊ/; Greek: Ἥρων[1] ὁ Ἀλεξανδρεύς, Heron ho Alexandreus; also known as Heron of Alexandria /ˈhɛrən/; c. 10 AD – c. 70 AD) was a Greco-Egyptian 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]

Inventions

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.[14]

Hero's wind-powered organ (reconstruction)

The first vending machine was also one of his constructions; when a coin was introduced via a slot on the top of the machine, a set amount of holy water was dispensed. 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.[15]

A wind-wheel operating an organ, marking the first instance in history of wind powering a machine.[4][5]

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.[16]

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 1000 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 programmable cart that was powered by a falling weight. The "program" consisted of strings wrapped around the drive axle.[17]

Mathematics

Hero described a method for iteratively computing the square root of a number.[18] 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.[19] 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. "No one discovery forms the basis for 3D geometry. However Heron of Alexandria is one of the major contributors" Herons work, Metrica discusses the properties of regular polygons, circles, and conic sections, and thus opened up the exploration and understanding of the third dimension. Heron, father of 3D[20] can be attributed to him.

Cultural references

A 1979 Soviet animated short film focuses on Hero's invention of the aeolipile,[20] showing him as a plain craftsman who invented the turbine accidentally[21]

A 2007 The History Channel television show Ancient Discoveries includes recreations of most of Hero's devices

A 2010 The History Channel television show Ancient Aliens episode "Alien Tech" includes a discussion of Hero's steam engine

A 2014 The History Channel television show Ancient Impossible episode "Ancient Einstein"

Bibliography

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:

Pneumatica (Πνευματικά), a description of machines working on air, steam or water pressure, including the hydraulis or water organ[22]

Automata, a description of machines which enable wonders in banquets and possibly also theatrical contexts by mechanical or pneumatical means (e.g. automatic opening or closing of temple doors, statues that pour wine and milk, etc.)[23]

Mechanica, preserved only in Arabic, written for architects, containing means to lift heavy objects

Metrica, a description of how to calculate surfaces and volumes of diverse objects

On the Dioptra, a collection of methods to measure lengths, a work in which the odometer and the dioptra, an apparatus which resembles the theodolite, are described

Belopoeica, a description of war machines

Catoptrica, about the progression of light, reflection and the use of mirrors

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

Geometrica, a collection of equations based on the first chapter of Metrica

Stereometrica, examples of three-dimensional calculations based on the second chapter of Metrica

Mensurae, tools which can be used to conduct measurements based on Stereometrica and Metrica

Cheiroballistra, about catapults

Definitiones, containing definitions of terms for geometry

Works that are preserved only in fragments:

Geodesia

Geoponica

See also

iconMathematics portal iconPhysics portal Technology portal

Heronian triangle

Heronian mean

References

Genitive: Ἥρωνος.

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"

Marie Boas, "Hero's Pneumatica: A Study of Its Transmission and Influence", Isis, Vol. 40, No. 1 (Feb., 1949), p. 38 and supra

A.G. Drachmann, "Heron's Windmill", Centaurus, 7 (1961), pp. 145–151

Dietrich Lohrmann, "Von der östlichen zur westlichen Windmühle", Archiv für Kulturgeschichte, Vol. 77, Issue 1 (1995), pp. 1–30 (10f.)

Ceccarelli, Marco (2007). Distinguished Figures in Mechanism and Machine Science: Their Contributions and Legacies. Springer. p. 230. ISBN 978-1-4020-6366-4.

George Sarton (1936). "The Unity and Diversity of the Mediterranean World", Osiris 2, p. 406-463 [429]

John H. Lienhard (1995). "Hero of Alexandria". The Engines of Our Ingenuity. Episode 1038. NPR. KUHF-FM Houston.

T. D. De Marco (1974). "Gas-Turbine Standby-Power Generation for Water-Treatment Plants", Journal American Water Works Association 66 (2), p. 133-138.

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."

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.

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.

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.

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"

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

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"

* 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

The above citation embeds a video using Flash Player, which fewer devices support over time. The same video is also available at this URL: https://www.youtube.com/watch?v=xyQIo9iS_z0

Heath, Thomas (1921). A History of Greek Mathematics, Vol. 2. Oxford: Clarendon Press. pp. 323–324.

Smyly, J. Gilbart (1920). "Heron's Formula for Cube Root". Hermathena. Trinity College Dublin. 19 (42): 64–67. JSTOR 23037103.

Peddie, Jon. (2013). The history of visual magic in computers : how beautiful images are made in CAD, 3D, VR and AR. London: Springer. pp. 25–26. ISBN 978-1-4471-4932-3. OCLC 849634980.

"Russian animation in letters and figures | Films | "GERON"". animator.ru.

McKinnon, Jamies W. (2001). "Hero of Alexandria and Hydraulis". In Root, Deane L. (ed.). The New Grove Dictionary of Music and Musicians. Oxford University Press.

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.

O'Connor, J.J. & E.F. Robertson. "Heron biography". The MacTutor History of Mathematics archive. Retrieved 2006-06-18.

Further reading

Drachmann, Aage Gerhardt (1963). The Mechanical Technology of Greek and Roman Antiquity: A Study of the Literary Sources. Madison, WI: University of Wisconsin Press.

Landels, J.G. (2000). Engineering in the ancient world (2nd ed.). Berkeley: University of California Press. ISBN 0-520-22782-4.

Marsden, E.W. (1969). Greek and Roman Artillery: Technical Treatises. Oxford: Clarendon Press.

Schellenberg, H.M.: Anmerkungen zu Hero von Alexandria und seinem Werk über den Geschützbau, in: Schellenberg, H.M./ Hirschmann, V.E./ Krieckhaus, A.(edd.): A Roman Miscellany. Essays in Honour of Anthony R. Birley on his Seventieth Birthday, Gdansk 2008, 92-130 (with a huge bibliography of over 300 titles and discussion of the communis opinio on Hero).

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Ancient Greek and Hellenistic mathematics (Euclidean geometry)

Mathematicians

(timeline)

Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises

Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner

Problems

Angle trisection Doubling the cube Squaring the circle Problem of Apollonius

Concepts/definitions

Circles of Apollonius

Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center

Results

In Elements

Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon

Apollonius

Apollonius's theorem

Other

Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Cyrene Library of Alexandria Platonic Academy

Other

Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

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