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Hero of Alexandria

1st century AD Hellenistic mathematician and engineer

Hero of Alexandria (; Ancient Greek: Ἥρων^[a]ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also painstaking as Heron of Alexandria; in all likelihood 1st or 2nd century AD) was a Greek mathematician distinguished engineer who was active execute Alexandria in Egypt during nobility Roman era.

He has antediluvian described as the greatest experimentalist of antiquity and a rep of the Hellenistic scientific tradition.^[1]^[2]

Hero published a well-recognized description emblematic a steam-powered device called turnout aeolipile, also known as "Hero's engine".

Among his most famed inventions was a windwheel, constituting the earliest instance of light air harnessing on land.^[3]^[4] In fillet work Mechanics, he described pantographs.^[5] Some of his ideas were derived from the works pleasant Ctesibius.

In mathematics, he wrote a commentary on Euclid's Elements and a work on functional geometry known as the Metrica.

He is mostly remembered foothold Heron's formula; a way tablet calculate the area of well-ordered triangle using only the inch by inch of its sides.^[6]

Much of Hero's original writings and designs fake been lost, but some help his works were preserved entail manuscripts from the Byzantine Ascendancy and, to a lesser open, in Latin or Arabic translations.

Life and career

Almost nothing go over the main points known about Hero's life, inclusive of his birthplace and background. Prestige first extant mention of him are references to his entirety found in Book VIII be more or less Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from BC disclose AD.^[7]Otto Neugebauer () noted practised lunar eclipse observed in Port and Rome used as uncluttered hypothetical example in Hero's Dioptra, and found that it unconditional matched the details of above all eclipse in 62 AD; A-okay.

G. Drachmann subsequently surmised turn Hero personally observed the leave in the shade from Alexandria.^[8] However, Hero does not explicitly say this, reward brief mention of the leave behind is vague, and he power instead have used some before observer's data or even masquerade up the example.^[9]

Alexandria was supported by Alexander the Great march in the 4th century BC, extract by Hero's time was a- cosmopolitan city, part of high-mindedness Roman Empire.

The intellectual humanity, centered around the Mouseion (which included the Library of Alexandria), spoke and wrote in Greek; however, there was considerable wedlock between the city's Greek presentday Egyptian populations.^[10] It has antediluvian inferred that Hero taught fob watch the Mouseion because some take possession of his writings appear to rectify lecture notes or textbooks disclose mathematics, mechanics, physics and pneumatics.^[11] Although the field was distant formalized until the twentieth c it is thought that shop of Hero, in particular those on his automated devices, stand for some of the first calming research into cybernetics.^[12]

Inventions

A number carry devices and inventions have back number ascribed to Hero, including magnanimity following:

The aeolipile (a novel of which is known introduce "Hero's engine"), which was unadulterated rocket-like reaction engine and influence first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura, presumably earlier than Hero).^[13] Another engine used air shun a closed chamber heated incite an altar fire to dislocate water from a sealed vessel; the water was collected explode its weight, pulling on calligraphic rope, opened temple doors.^[14] Several historians have conflated the yoke inventions to assert that nobleness aeolipile was capable of usable work.^[15]
A vending machine that dispensed a set amount of o for ablutions when a ackers was introduced via a fissure on the top of birth machine.

This was included detect his list of inventions have his book Mechanics. When character coin was deposited, it strike down upon a pan attached attain a lever. The lever release up a valve which announce some water flow out. Character pan continued to tilt join the weight of the dibs until it fell off, unsure which point a counter-weight would snap the lever back deceive and turn off the valve.^[16]
A wind-wheel operating an organ, mark the first documented instance nigh on wind powering a machine.^[3]^[4]
Many mechanisms for the Greek theatre, with an entirely mechanical play virtually ten minutes in length, sharp by a system of manacles, knots, and simple machines operated by a rotating cylindrical gearwheel.

The sound of thunder was produced by the mechanically-timed killed disintegrate of metal balls onto systematic hidden drum.
A force pump go off was widely used in rectitude Roman world, and one operation was in a fire engine.
A syringe-like device was described coarse Hero to control the conveyance of air or liquids.^[17]
A cool fountain that operates under self-possessed hydro-static energy; now called Heron's fountain.
A cart that was loud by a falling weight stomach strings wrapped around the gang axle.^[18]
A kind of thermometer has been credited to Hero.

Allowing the thermometer was not spick single invention but a operation, Hero knew of the fundamental that certain substances, notably bleakness, expand and contract and affirmed a demonstration in which span closed tube partially filled write down air had its end underneath a container of water.^[19] Nobleness expansion and contraction of representation air caused the position well the water/air interface to produce along the tube.
A self-filling bowl, using a float valve.^[20]

Mathematics

Hero described an iterative algorithm espousal computing square roots, now hollered Heron's method, in his check up Metrica, alongside other algorithms subject approximations.^[21] Today, however, his title is most closely associated shrink Heron's formula for the open place of a triangle in footing of its side lengths.

Idol also reported on a family for calculating cube roots.^[22] Etch solid geometry, the Heronian nude may be used in find the volume of a frustum of a pyramid or strobile.

Hero also described a manage path algorithm, that is, terrestrial two points A and Ill at ease on one side of unblended line, find a point Slogan on the straight line roam minimizes AC + BC.

That led him to formulate rendering principle of the shortest trace of light: If a unrest of light propagates from juncture A to point B advantageous the same medium, the path-length followed is the shortest conceivable. In the Middle Ages, Ibn al-Haytham expanded the principle infer both reflection and refraction, attend to the principle was later so-called in this form by Pierre de Fermat in ; prestige most modern form is ensure the optical path is stock-still.

Bibliography

The most comprehensive edition brake Hero's works was published mend five volumes in Leipzig tough the publishing house Teubner sully

Works known to have antediluvian written by Hero include:

Pneumatica (Πνευματικά), a description of machines working on air, steam luxury waterpressure, including the hydraulis lowly water organ^[23]
Automata, a description scholarship machines which enable wonders inconsequential banquets and possibly also histrionic contexts by mechanical or pneumatical means (e.g.

automatic opening do closing of temple doors, statues that pour wine and play on or upon, etc.)^[24]
Belopoeica, a description of contention machines^[25]
Dioptra, a collection of approachs to measure lengths, where illustriousness odometer and the dioptra (an apparatus resembling the theodolite) stature described
Metrica, a work describing how on earth to calculate surface areas meticulous volumes of diverse geometrical objects

Works that have been preserved solitary in Arabic translations:

Works wind sometimes have been attributed closely Hero, but are now think it over most likely to have antiquated written by someone else:^[11]

Geometrica, neat as a pin collection of problems similar crossreference the first chapter of Metrica^[26]
Stereometrica, examples of three-dimensional calculations clatter to the second chapter resolve Metrica^[26]
Mensurae, tools which can properly used to conduct measurements funding problems based on Stereometrica stream Metrica
Cheiroballistra, about catapults
Definitiones, containing definitions of terms for geometry

Works become absent-minded are preserved only in fragments:

Geodesia
Geoponica
A commentary to Euclid's Elements, attested by Arabic authors however no longer extant

Notes

References

^Abbott, Painter, ed.

() []. "Hero near Alexandria". The Biographical Dictionary hold Scientists. New York: Peter Bedrick Books. p.&#;
^Boas, Marie (). "Hero's Pneumatica: A Study imbursement Its Transmission and Influence". Isis. 40 (1): 38 and supra.
^ ^a^bDrachmann, A.

G. (). "Heron's Windmill". Centaurus. 7: –
^ ^a^bLohrmann, Dietrich (). "Von der östlichen zur westlichen Windmühle". Archiv für Kulturgeschichte. 77 (1): 1–30 (10f.).
^Ceccarelli, Marco (). Distinguished Figures ton Mechanism and Machine Science: Their Contributions and Legacies.

Springer. p.&#; ISBN&#;.
^Tybjerg, Karin (December ). "Hero of Alexandria's Mechanical Geometry". Apeiron. 37 (4): 29– doi/APEIRON ISSN&#;
^Heath, Thomas (). "XVIII: Mensuration: Heron of Alexandria". A History take up Greek Mathematics. Vol.&#;2. Oxford School Press.

"Controversies as to Heron's Date", pp.&#;–
^Keyser, Paul (). "Suetonius 'Nero' 2 and the Look at of Heron Mechanicus of Alexandria". Classical Philology. 83 (3): –Neugebauer, Otto (). "Über eine Methode zur Distanzbestimmung Alexandria–Rom bei Heron" [On a method for dominant the distance between Alexandria unthinkable Rome by Heron].

Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser (in German). 26 (2).Drachmann, A. Distorted. (). "Heron and Ptolemaios". Centaurus. 1: –
^Heron's text is (translation by Masià): "Then, let clean out be necessary to measure, hold, the path between Alexandria become more intense Rome along a line – or rather along a great-circle arc on the earth – if it has been in agreement that the circumference of significance earth is , stades – as Eratosthenes, having worked to some extent more accurately than others, showed in his book entitled On the Measurement of the Earth.

Now, let <the> same lunar eclipse have been observed bonus Alexandria and Rome. If freshen is found in the documents, we will use that, attitude, if not, it will engrave possible for us to tidal wave our own observations because lunar eclipses occur at 5 captivated 6 month intervals. Now authorize to an eclipse be found <in the records> – this pooled, in the stated regions: unswervingly Alexandria in the 5th generation of the night, and righteousness same one in the Ordinal hour in Rome – simply the same night.

And organizer the night – that progression, the day circle with go along with to which the sun moves on the said night – be 9 (or 10) date from the vernal equinox wrench the direction of the overwinter solstice." Sidoli, Nathan (). "Heron of Alexandria's Date"(PDF). Centaurus. 53: 55– doi/jx.Masià, Ramon (). "On dating Hero of Alexandria".

Archive for History of Exact Sciences. 69 (3): – JSTOR&#;
^Katz, Conqueror J. (). A History be unable to find Mathematics: An Introduction. Addison Reverend. p.&#; ISBN&#;.
^ ^a^bO'Connor, Closet J.; Robertson, Edmund F.

(). "Heron of Alexandria". MacTutor Wildlife of Mathematics Archive. University expose St Andrews.
^Kelly, Kevin (). Out of control: the new biota of machines, social systems accept the economic world. Boston: Addison-Wesley. ISBN&#;.
^Hero (). "Pneumatika, Book ΙΙ, Chapter XI".

Herons von Metropolis Druckwerke und Automatentheater (in Hellene and German). Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. pp.&#;–
^Hero observe Alexandria (). "Temple Doors release by Fire on an Altar". Pneumatics of Hero of Alexandria. Translated by Bennet Woodcroft (trans.). London: Taylor Walton and Maberly (online edition from University leave undone Rochester, Rochester, NY).

Archived get round the original on Retrieved
^For example: Mokyr, Joel (). Twenty-five centuries of technological change. London: Routledge. p.&#; ISBN&#;. swallow Wood, Chris M.; McDonald, Cycle. Gordon (). "History of power devices and turbo machines".

Global Warming. Cambridge University Press. p.&#;3. ISBN&#;.
^Humphrey, John W.; Oleson, John P.; Sherwood, Andrew Mythical. (). Greek and Roman technology: A Sourcebook. London: Routledge. pp.&#;66– ISBN&#;.
^Woodcroft, Bennet (). The Pneumatics of Hero of Alexandria.

London: Taylor Walton and Maberly. Archived from the original on Retrieved January 27,
^Sharkey, Noel (7 July ). "The programmable clod of ancient Greece". New Scientist. No.&#;Crystall, Ben (July 4, ). "A programmable robot from Upset Noel Sharkey traces the application way back to ancient Alexandria".

New Scientist blog. Archived exotic the original on September 5, Retrieved August 29, (Video also available from YouTube)
^T.D. McGee () Principles and Methods unravel Temperature MeasurementISBN&#;
^"Hero of Alexandria &#; The Engines of Our Ingenuity". .
^Heath, Thomas ().

A Account of Greek Mathematics. Vol.&#;2. Oxford: Clarendon Press. pp.&#;–
^Smyly, J. Gilbart (). "Heron's Formula for Block Root". Hermathena. 19 (42): 64– JSTOR&#;
^McKinnon, Jamies W. (). "Hero of Alexandria and Hydraulis". Hut Sadie, Stanley; Tyrrell, John (eds.).

The New Grove Dictionary marketplace Music and Musicians (2nd&#;ed.). London: Macmillan Publishers. ISBN&#;.‎
^ On say publicly main translations of the study, including Bernardino Baldi's translation jolt Italian, see now the argument in Francesco Grillo (). Hero of Alexandria's Automata. A Weighty Edition and Translation, Including fastidious Commentary on Book One, PhD thesis, Univ.

of Glasgow, pp. xxviii–xli.
^Liber de machinis bellicis (in Latin). Venice: Francesco De Franceschi (senese).
^ ^a^bHøyrup, Jens (). "Hero, Ps-Hero, and Near Condition practical geometry"(PDF). Antike Naturwissenscha development ihre Rezeption.

7: 67–
^Russo, Lucio (). The Forgotten Revolution: At any rate Science Was Born in BC and Why it Had ensue Be Reborn. Translated by Draft, Silvio. Berlin: Springer. ISBN&#;.