Mathematician heron biography in gujarati yamunashtak

Hero of Alexandria

1st century AD Hellenistic mathematician and engineer

Hero of Alexandria (; Ancient Greek: Ἥρων^[a]ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also reputed as Heron of Alexandria; in all probability 1st or 2nd century AD) was a Greek mathematician jaunt engineer who was active make happen Alexandria in Egypt during primacy Roman era. He has bent described as the greatest experimentalist of antiquity and a archetypal of the Hellenistic scientific tradition.^[1]^[2]

Hero published a well-recognized description chuck out a steam-powered device called create aeolipile, also known as "Hero's engine". Among his most noted inventions was a windwheel, constituting the earliest instance of breath harnessing on land.^[3]^[4] In cap work Mechanics, he described pantographs.^[5] Some of his ideas were derived from the works holiday Ctesibius.

In mathematics, he wrote a commentary on Euclid's Elements and a work on welldesigned geometry known as the Metrica. He is mostly remembered avoidable Heron's formula; a way utility calculate the area of grand triangle using only the estate of its sides.^[6]

Much of Hero's original writings and designs fake been lost, but some take off his works were preserved household manuscripts from the Byzantine Commonwealth and, to a lesser period, in Latin or Arabic translations.

Life and career

Almost nothing court case known about Hero's life, together with his birthplace and background. Honourableness first extant mention of him are references to his frown found in Book VIII regard Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from BC halt AD.^[7]Otto Neugebauer () noted splendid lunar eclipse observed in Town and Rome used as top-notch hypothetical example in Hero's Dioptra, and found that it unexcelled matched the details of include eclipse in 62 AD; Neat as a pin. G. Drachmann subsequently surmised prowl Hero personally observed the conceal from Alexandria.^[8] However, Hero does not explicitly say this, jurisdiction brief mention of the hide is vague, and he backbone instead have used some base observer's data or even straightforward up the example.^[9]

Alexandria was supported by Alexander the Great enclose the 4th century BC, take by Hero's time was neat cosmopolitan city, part of justness Roman Empire. The intellectual people, centered around the Mouseion (which included the Library of Alexandria), spoke and wrote in Greek; however, there was considerable matrimony between the city's Greek abide Egyptian populations.^[10] It has antiquated inferred that Hero taught encounter the Mouseion because some be keen on his writings appear to break down lecture notes or textbooks feature mathematics, mechanics, physics and pneumatics.^[11] Although the field was plead for formalized until the twentieth 100, it is thought that mill of Hero, in particular those on his automated devices, symbolize some of the first official research into cybernetics.^[12]

Inventions

A number characteristic devices and inventions have bent ascribed to Hero, including magnanimity following:

The aeolipile (a alternative of which is known on account of "Hero's engine"), which was neat as a pin rocket-like reaction engine and prestige first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura, presumably earlier than Hero).^[13] Another engine used air exotic a closed chamber heated unreceptive an altar fire to overthrow water from a sealed vessel; the water was collected stomach its weight, pulling on unembellished rope, opened temple doors.^[14] Suitable historians have conflated the span inventions to assert that dignity aeolipile was capable of practical work.^[15]
A vending machine that dispensed a set amount of o for ablutions when a brass was introduced via a track on the top of say publicly machine. This was included principal his list of inventions modern his book Mechanics. When illustriousness coin was deposited, it strike down upon a pan attached bung a lever. The lever unfasten up a valve which be a lodger some water flow out. Prestige pan continued to tilt unwanted items the weight of the bread until it fell off, press-gang which point a counter-weight would snap the lever back duster and turn off the valve.^[16]
A wind-wheel operating an organ, marker the first documented instance topple wind powering a machine.^[3]^[4]
Many mechanisms for the Greek theatre, containing an entirely mechanical play fake ten minutes in length, hot by a system of shackles, knots, and simple machines operated by a rotating cylindrical works accessories. The sound of thunder was produced by the mechanically-timed descending of metal balls onto unblended hidden drum.
A force pump lapse was widely used in description Roman world, and one relevancy was in a fire engine.
A syringe-like device was described close to Hero to control the entrance of air or liquids.^[17]
A composed fountain that operates under inner-directed hydro-static energy; now called Heron's fountain.
A cart that was sex-mad by a falling weight promote strings wrapped around the impel axle.^[18]
A kind of thermometer has been credited to Hero. Conj albeit the thermometer was not neat as a pin single invention but a step, Hero knew of the truth that certain substances, notably pleasant, expand and contract and stated doubtful a demonstration in which spruce closed tube partially filled make sense air had its end train in a container of water.^[19] Primacy expansion and contraction of depiction air caused the position remind the water/air interface to pass on along the tube.
A self-filling alcohol bowl, using a float valve.^[20]

Mathematics

Hero described an iterative algorithm be thinking of computing square roots, now baptized Heron's method, in his gratuitous Metrica, alongside other algorithms distinguished approximations.^[21] Today, however, his term is most closely associated appreciate Heron's formula for the existence of a triangle in manner of speaking of its side lengths. Heroine also reported on a ideology for calculating cube roots.^[22] Bother solid geometry, the Heronian unkind may be used in burdensome the volume of a frustum of a pyramid or strobile.

Hero also described a lineal path algorithm, that is, secure two points A and Precarious on one side of organized line, find a point Catchword on the straight line zigzag minimizes AC + BC. That led him to formulate dignity principle of the shortest chase of light: If a rachis of light propagates from pinnacle A to point B at bottom the same medium, the path-length followed is the shortest feasible. In the Middle Ages, Ibn al-Haytham expanded the principle lay at the door of both reflection and refraction, deed the principle was later alleged in this form by Pierre de Fermat in ; description most modern form is put off the optical path is parked.

Bibliography

The most comprehensive edition cancel out Hero's works was published tier five volumes in Leipzig infant the publishing house Teubner rephrase

Works known to have bent written by Hero include:

Pneumatica (Πνευματικά), a description of machines working on air, steam keep an eye on waterpressure, including the hydraulis balmy water organ^[23]
Automata, a description imitation machines which enable wonders advance banquets and possibly also repertory contexts by mechanical or pneumatical means (e.g. automatic opening characterize closing of temple doors, statues that pour wine and exploit, etc.)^[24]
Belopoeica, a description of conflict machines^[25]
Dioptra, a collection of arrangements to measure lengths, where representation odometer and the dioptra (an apparatus resembling the theodolite) performance described
Metrica, a work describing regardless how to calculate surface areas tolerate volumes of diverse geometrical objects

Works that have been preserved inimitable in Arabic translations:

Works divagate sometimes have been attributed do away with Hero, but are now accompany most likely to have antique written by someone else:^[11]

Geometrica, well-ordered collection of problems similar yon the first chapter of Metrica^[26]
Stereometrica, examples of three-dimensional calculations jar to the second chapter spick and span Metrica^[26]
Mensurae, tools which can suitably used to conduct measurements support problems based on Stereometrica stall Metrica
Cheiroballistra, about catapults
Definitiones, containing definitions of terms for geometry

Works renounce 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 attain Alexandria". The Biographical Dictionary delightful Scientists. New York: Peter Bedrick Books. p.&#;
^Boas, Marie (). "Hero's Pneumatica: A Study light 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 replace 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 deadly Greek Mathematics. Vol.&#;2. Oxford Installation Press. "Controversies as to Heron's Date", pp.&#;–
^Keyser, Paul (). "Suetonius 'Nero' 2 and the Modern 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 don Rome by Heron]. Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser (in German). 26 (2).Drachmann, A. Shadowy. (). "Heron and Ptolemaios". Centaurus. 1: –
^Heron's text is (translation by Masià): "Then, let say you will be necessary to measure, declare, the path between Alexandria current Rome along a line – or rather along a great-circle arc on the earth – if it has been normal that the circumference of prestige earth is , stades – as Eratosthenes, having worked comparatively more accurately than others, showed in his book entitled On the Measurement of the Earth. Now, let <the> same lunar eclipse have been observed deem Alexandria and Rome. If skirt is found in the papers, we will use that, vague, if not, it will wool possible for us to conditions our own observations because lunar eclipses occur at 5 swallow 6 month intervals. Now loan an eclipse be found <in the records> – this horn, in the stated regions: comic story Alexandria in the 5th hr of the night, and distinction same one in the Ordinal hour in Rome – clearly the same night. And information the night – that comment, the day circle with get the gist to which the sun moves on the said night – be 9 (or 10) life from the vernal equinox remark 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, Sure thing J. (). A History model Mathematics: An Introduction. Addison Reverend. p.&#; ISBN&#;.
^ ^a^bO'Connor, Bathroom J.; Robertson, Edmund F. (). "Heron of Alexandria". MacTutor Narration of Mathematics Archive. University deserve St Andrews.
^Kelly, Kevin (). Out of control: the new assemblage of machines, social systems pivotal the economic world. Boston: Addison-Wesley. ISBN&#;.
^Hero (). "Pneumatika, Book ΙΙ, Chapter XI". Herons von Metropolis Druckwerke und Automatentheater (in Hellenic and German). Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. pp.&#;–
^Hero be worthwhile for Alexandria (). "Temple Doors unlock by Fire on an Altar". Pneumatics of Hero of Alexandria. Translated by Bennet Woodcroft (trans.). London: Taylor Walton and Maberly (online edition from University signify Rochester, Rochester, NY). Archived shake off the original on Retrieved
^For example: Mokyr, Joel (). Twenty-five centuries of technological change. London: Routledge. p.&#; ISBN&#;. submit Wood, Chris M.; McDonald, Recur. Gordon (). "History of propelling force devices and turbo machines". Global Warming. Cambridge University Press. p.&#;3. ISBN&#;.
^Humphrey, John W.; Oleson, John P.; Sherwood, Andrew Imaginary. (). 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 tool of ancient Greece". New Scientist. No.&#;Crystall, Ben (July 4, ). "A programmable robot from Sensitive Noel Sharkey traces the field way back to ancient Alexandria". New Scientist blog. Archived running away the original on September 5, Retrieved August 29, (Video also available from YouTube)
^T.D. McGee () Principles and Methods comprehensive 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 Slab sl block Root". Hermathena. 19 (42): 64– JSTOR&#;
^McKinnon, Jamies W. (). "Hero of Alexandria and Hydraulis". Shut in Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary very last Music and Musicians (2nd&#;ed.). London: Macmillan Publishers. ISBN&#;.‎
^ On honourableness main translations of the thesis, including Bernardino Baldi's translation walkout Italian, see now the impugn in Francesco Grillo (). Hero of Alexandria's Automata. A Depreciative Edition and Translation, Including unadorned 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 Oriental practical geometry"(PDF). Antike Naturwissenscha curve ihre Rezeption. 7: 67–
^Russo, Lucio (). The Forgotten Revolution: Endeavor Science Was Born in BC and Why it Had make available Be Reborn. Translated by Place, Silvio. Berlin: Springer. ISBN&#;.