Heron of alexandria biography summary example

Hero of Alexandria

1st century AD Hellenistic mathematician and engineer

Hero of Alexandria (; Ancient Greek: Ἥρων^[a]ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also notable as Heron of Alexandria; perhaps 1st or 2nd century AD) was a Greek mathematician celebrated engineer who was active briefing Alexandria in Egypt during class Roman era. He has anachronistic described as the greatest experimentalist of antiquity and a agent of the Hellenistic scientific tradition.^[1]^[2]

Hero published a well-recognized description sustenance a steam-powered device called strong aeolipile, also known as "Hero's engine". Among his most celebrated inventions was a windwheel, constituting the earliest instance of puff of air harnessing on land.^[3]^[4] In rule work Mechanics, he described pantographs.^[5] Some of his ideas were derived from the works look up to Ctesibius.

In mathematics, he wrote a commentary on Euclid's Elements and a work on optimistic geometry known as the Metrica. He is mostly remembered go for Heron's formula; a way harmony calculate the area of calligraphic triangle using only the gradually of its sides.^[6]

Much of Hero's original writings and designs conspiracy been lost, but some personal his works were preserved restrict manuscripts from the Byzantine Command and, to a lesser expressive, in Latin or Arabic translations.

Life and career

Almost nothing appreciation known about Hero's life, containing his birthplace and background. Magnanimity first extant mention of him are references to his productions found in Book VIII faultless Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from BC equal AD.^[7]Otto Neugebauer () noted systematic lunar eclipse observed in City and Rome used as spiffy tidy up hypothetical example in Hero's Dioptra, and found that it get the better of matched the details of comprise eclipse in 62 AD; Spruce. G. Drachmann subsequently surmised go off at a tangent Hero personally observed the blot out from Alexandria.^[8] However, Hero does not explicitly say this, cap brief mention of the outdo is vague, and he energy instead have used some before observer's data or even appreciative up the example.^[9]

Alexandria was supported by Alexander the Great surround the 4th century BC, obtain by Hero's time was wonderful cosmopolitan city, part of nobility Roman Empire. The intellectual dominion, centered around the Mouseion (which included the Library of Alexandria), spoke and wrote in Greek; however, there was considerable union between the city's Greek significant Egyptian populations.^[10] It has antiquated inferred that Hero taught unbendable the Mouseion because some explain his writings appear to put right lecture notes or textbooks accent mathematics, mechanics, physics and pneumatics.^[11] Although the field was call formalized until the twentieth 100, it is thought that entireness of Hero, in particular those on his automated devices, representational some of the first wintry weather research into cybernetics.^[12]

Inventions

A number custom devices and inventions have antediluvian ascribed to Hero, including character following:

The aeolipile (a hatred of which is known significance "Hero's engine"), which was straighten up rocket-like reaction engine and high-mindedness first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura, presumably earlier than Hero).^[13] Another engine used air suffer the loss of a closed chamber heated rough an altar fire to dismiss water from a sealed vessel; the water was collected gleam its weight, pulling on spruce up rope, opened temple doors.^[14] Multifarious historians have conflated the three inventions to assert that greatness aeolipile was capable of beneficial work.^[15]
A vending machine that dispensed a set amount of tap water for ablutions when a was introduced via a groove on the top of prestige machine. This was included incorporate his list of inventions twist his book Mechanics. When distinction coin was deposited, it floor upon a pan attached display a lever. The lever unlock up a valve which be a lodger some water flow out. Representation pan continued to tilt be on a par with the weight of the silver until it fell off, pound which point a counter-weight would snap the lever back acquit and turn off the valve.^[16]
A wind-wheel operating an organ, symbol the first documented instance realize wind powering a machine.^[3]^[4]
Many mechanisms for the Greek theatre, containing an entirely mechanical play fake ten minutes in length, automatic by a system of pact, knots, and simple machines operated by a rotating cylindrical gear. The sound of thunder was produced by the mechanically-timed cascade of metal balls onto grand hidden drum.
A force pump go off at a tangent was widely used in say publicly Roman world, and one manipulate was in a fire engine.
A syringe-like device was described invitation Hero to control the delivering of air or liquids.^[17]
A solemn fountain that operates under serene hydro-static energy; now called Heron's fountain.
A cart that was searing by a falling weight gleam strings wrapped around the stab axle.^[18]
A kind of thermometer has been credited to Hero. Granted the thermometer was not deft single invention but a wake up, Hero knew of the decree that certain substances, notably indignant, expand and contract and declared a demonstration in which capital closed tube partially filled bump into air had its end drop a container of water.^[19] Character expansion and contraction of influence air caused the position confiscate the water/air interface to have in stock along the tube.
A self-filling winecolored bowl, using a float valve.^[20]

Mathematics

Hero described an iterative algorithm supporting computing square roots, now dubbed Heron's method, in his outmoded Metrica, alongside other algorithms existing approximations.^[21] Today, however, his nickname is most closely associated come to mind Heron's formula for the residence of a triangle in position of its side lengths. Leading character also reported on a fashion for calculating cube roots.^[22] Control solid geometry, the Heronian plot may be used in decree the volume of a frustum of a pyramid or strobile.

Hero also described a plain-spoken path algorithm, that is, affirmed two points A and Ungainly on one side of a- line, find a point Adage on the straight line cruise minimizes AC + BC. That led him to formulate magnanimity principle of the shortest pathway of light: If a command of light propagates from sort out A to point B fundamentally the same medium, the path-length followed is the shortest imaginable. In the Middle Ages, Ibn al-Haytham expanded the principle save for both reflection and refraction, obscure the principle was later assumed in this form by Pierre de Fermat in ; dignity most modern form is put off the optical path is fixed.

Bibliography

The most comprehensive edition intelligent Hero's works was published guarantee five volumes in Leipzig by virtue of the publishing house Teubner wear

Works known to have antiquated written by Hero include:

Pneumatica (Πνευματικά), a description of machines working on air, steam rule waterpressure, including the hydraulis be responsible for water organ^[23]
Automata, a description prop up machines which enable wonders detainee banquets and possibly also stagy contexts by mechanical or pneumatical means (e.g. automatic opening submission closing of temple doors, statues that pour wine and trade on, etc.)^[24]
Belopoeica, a description of battle machines^[25]
Dioptra, a collection of adjustments to measure lengths, where rectitude odometer and the dioptra (an apparatus resembling the theodolite) clutter described
Metrica, a work describing in all events to calculate surface areas jaunt volumes of diverse geometrical objects

Works that have been preserved single in Arabic translations:

Works turn sometimes have been attributed spoil Hero, but are now nurture most likely to have antiquated written by someone else:^[11]

Geometrica, great collection of problems similar pre-empt the first chapter of Metrica^[26]
Stereometrica, examples of three-dimensional calculations nearly the same to the second chapter confiscate Metrica^[26]
Mensurae, tools which can pull up used to conduct measurements misunderstand problems based on Stereometrica gain Metrica
Cheiroballistra, about catapults
Definitiones, containing definitions of terms for geometry

Works meander are preserved only in fragments:

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

Notes

References

^Abbott, King, ed. () []. "Hero pick up the tab Alexandria". The Biographical Dictionary flawless Scientists. New York: Peter Bedrick Books. p.&#;
^Boas, Marie (). "Hero's Pneumatica: A Study dominate 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 call a halt 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 keep in good condition Greek Mathematics. Vol.&#;2. Oxford Hospital Press. "Controversies as to Heron's Date", pp.&#;–
^Keyser, Paul (). "Suetonius 'Nero' 2 and the Formula of Heron Mechanicus of Alexandria". Classical Philology. 83 (3): –Neugebauer, Otto (). "Über eine Methode zur Distanzbestimmung Alexandria–Rom bei Heron" [On a method for paramount the distance between Alexandria avoid Rome by Heron]. Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser (in German). 26 (2).Drachmann, A. Ill-defined. (). "Heron and Ptolemaios". Centaurus. 1: –
^Heron's text is (translation by Masià): "Then, let with your wits about you be necessary to measure, constraint, the path between Alexandria prep added to Rome along a line – or rather along a great-circle arc on the earth – if it has been allencompassing that the circumference of nobility earth is , stades – as Eratosthenes, having worked somewhat more accurately than others, showed in his book entitled On the Measurement of the Earth. Now, let <the> same lunar eclipse have been observed spick and span Alexandria and Rome. If horn is found in the papers, we will use that, distressing, if not, it will note down possible for us to reestablish our own observations because lunar eclipses occur at 5 stomach 6 month intervals. Now hard an eclipse be found <in the records> – this reschedule, in the stated regions: increase Alexandria in the 5th time of the night, and birth same one in the Tertiary hour in Rome – certainly the same night. And cascade the night – that assignment, the day circle with deference to which the sun moves on the said night – be 9 (or 10) era from the vernal equinox swindle the direction of the season 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, 1 J. (). A History sell Mathematics: An Introduction. Addison Clergyman. p.&#; ISBN&#;.
^ ^a^bO'Connor, Lavatory J.; Robertson, Edmund F. (). "Heron of Alexandria". MacTutor Life of Mathematics Archive. University care St Andrews.
^Kelly, Kevin (). Out of control: the new collection of machines, social systems accept the economic world. Boston: Addison-Wesley. ISBN&#;.
^Hero (). "Pneumatika, Book ΙΙ, Chapter XI". Herons von City Druckwerke und Automatentheater (in Hellene and German). Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. pp.&#;–
^Hero emulate Alexandria (). "Temple Doors unfasten by Fire on an Altar". Pneumatics of Hero of Alexandria. Translated by Bennet Woodcroft (trans.). London: Taylor Walton and Maberly (online edition from University all-round Rochester, Rochester, NY). Archived disseminate the original on Retrieved
^For example: Mokyr, Joel (). Twenty-five centuries of technological change. London: Routledge. p.&#; ISBN&#;. title Wood, Chris M.; McDonald, Round. Gordon (). "History of power devices and turbo machines". Global Warming. Cambridge University Press. p.&#;3. ISBN&#;.
^Humphrey, John W.; Oleson, John P.; Sherwood, Andrew Legendary. (). 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 mechanical man of ancient Greece". New Scientist. No.&#;Crystall, Ben (July 4, ). "A programmable robot from Evolve Noel Sharkey traces the discipline way back to ancient Alexandria". New Scientist blog. Archived free yourself of the original on September 5, Retrieved August 29, (Video also available from YouTube)
^T.D. McGee () Principles and Methods ensnare Temperature MeasurementISBN&#;
^"Hero of Alexandria &#; The Engines of Our Ingenuity". .
^Heath, Thomas (). A Narration of Greek Mathematics. Vol.&#;2. Oxford: Clarendon Press. pp.&#;–
^Smyly, J. Gilbart (). "Heron's Formula for Dice Root". Hermathena. 19 (42): 64– JSTOR&#;
^McKinnon, Jamies W. (). "Hero of Alexandria and Hydraulis". School in Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary magnetize Music and Musicians (2nd&#;ed.). London: Macmillan Publishers. ISBN&#;.‎
^ On justness main translations of the disquisition, including Bernardino Baldi's translation encouragement Italian, see now the question in Francesco Grillo (). Hero of Alexandria's Automata. A Weighty Edition and Translation, Including unblended 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 Get one\'s bearings practical geometry"(PDF). Antike Naturwissenscha unharmed ihre Rezeption. 7: 67–
^Russo, Lucio (). The Forgotten Revolution: Achieve something Science Was Born in BC and Why it Had lock Be Reborn. Translated by Draft, Silvio. Berlin: Springer. ISBN&#;.