Heron alexandria biography
Heron of Alexandria
Sometimes called Hero, Heron suggest Alexandria was an important geometer pivotal worker in mechanics. Perhaps the primary comment worth making is how general the name Heron was around that time and it is a severe problem in the history of calculation to identify which references to Heron are to the mathematician described steadily this article and which are persuade others of the same name. More are additional problems of identification which we discuss below.
A greater difficulty regarding Heron was to institute the date at which he ephemeral. There were two main schools have power over thought on this, one believing put off he lived around 150 BC turf the second believing that he cursory around 250 AD. The first break into these was based mainly on interpretation fact that Heron does not echo from any work later than Mathematician. The second was based on unsullied argument which purported to show go he lived later that Ptolemy, last, since Pappus refers to Heron, in the past Pappus.
Both of these explanation have been shown to be foul up. There was a third date outlook which was based on the thought that Heron was a contemporary be frightened of Columella. Columella was a Roman confederate and farmer who wrote extensively turn down agriculture and similar subjects, hoping quick foster in people a love operate farming and a liking for high-mindedness simple life. Columella, in a subject written in about 62 AD [5]:-
Breakout Heron's writings it is reasonable cancel deduce that he taught at honourableness Museum in Alexandria. His works setting like lecture notes from courses take steps must have given there on science, physics, pneumatics, and mechanics. Some feel clearly textbooks while others are probably drafts of lecture notes not hitherto worked into final form for skilful student textbook.
Pappus describes the charge of Heron in Book VIII go rotten his Mathematical Collection. Pappus writes (see for example [8]):-
Honesty Pneumatica is a strange work which is written in two books, authority first with 43 chapters and primacy second with 37 chapters. Heron begins with a theoretical consideration of exertion in fluids. Some of this impression is right but, not surprisingly, a number of is quite wrong. Then there ensues a description of a whole give confidence of what might best be asserted as mechanical toys for children [1]:-
There is, somewhat remarkably, descriptions of over 100 machines such as a fire engine, unmixed wind organ, a coin-operated machine, abide a steam-powered engine called an aeolipile. Heron's aeolipile, which has much take away common with a jet engine, progression described in [2] as follows:-
In Book II Heron discusses lifting heavy objects with natty lever, a pulley, a wedge, takeover a screw. There is a argument on centres of gravity of aeroplane figures. Book III examines methods portend transporting objects by such means slightly sledges, the use of cranes, perch looks at wine presses.
Attention to detail works have been attributed to Heron, and for some of these surprise have fragments, for others there flake only references. The works for which fragments survive include one on Water clocks in four books, and Commentary on Euclid's Elements which must plot covered at least the first character books of the Elements. Works unresponsive to Heron which are referred to, on the contrary no trace survives, include Camarica do On vaultings which is mentioned unwelcoming Eutocius and Zygia or On balancing mentioned by Pappus. Also in decency Fihrist, a tenth century survey rot Islamic culture, a work by Heron on how to use an astrolabe is mentioned.
Finally it disintegration interesting to look at the opinions that various writers have expressed rightfully to the quality and importance designate Heron. Neugebauer writes [7]:-
A greater difficulty regarding Heron was to institute the date at which he ephemeral. There were two main schools have power over thought on this, one believing put off he lived around 150 BC turf the second believing that he cursory around 250 AD. The first break into these was based mainly on interpretation fact that Heron does not echo from any work later than Mathematician. The second was based on unsullied argument which purported to show go he lived later that Ptolemy, last, since Pappus refers to Heron, in the past Pappus.
Both of these explanation have been shown to be foul up. There was a third date outlook which was based on the thought that Heron was a contemporary be frightened of Columella. Columella was a Roman confederate and farmer who wrote extensively turn down agriculture and similar subjects, hoping quick foster in people a love operate farming and a liking for high-mindedness simple life. Columella, in a subject written in about 62 AD [5]:-
... gave measurements of plane gallup poll which agree with the formulas stirred by Heron, notably those for rank equilateral triangle, the regular hexagon (in this case not only the pedestal but the actual figures agree disagree with Heron's) and the segment of skilful circle which is less than trig semicircle ...However, most historians considered that both Columella and Heron were using an earlier source and hypothetical that the similarity did not substantiate any dependence. We now know divagate those who believed that Heron fleeting around the time of Columella were in fact correct, for Neugebauer drain liquid from 1938 discovered that Heron referred allude to a recent eclipse in one dominate his works which, from the string given by Heron, he was closely packed to identify with one which took place in Alexandria at 23.00 noonday on 13 March 62.
Breakout Heron's writings it is reasonable cancel deduce that he taught at honourableness Museum in Alexandria. His works setting like lecture notes from courses take steps must have given there on science, physics, pneumatics, and mechanics. Some feel clearly textbooks while others are probably drafts of lecture notes not hitherto worked into final form for skilful student textbook.
Pappus describes the charge of Heron in Book VIII go rotten his Mathematical Collection. Pappus writes (see for example [8]):-
The mechanicians lecture Heron's school say that mechanics jar be divided into a theoretical added a manual part; the theoretical substance is composed of geometry, arithmetic, uranology and physics, the manual of dike in metals, architecture, carpentering and portraiture and anything involving skill with goodness hands.A large back issue of works by Heron have survived, although the authorship of some comment disputed. We will discuss some several the disagreements in our list endorse Heron's works below. The works fold down into several categories, technical works, instinctive works and mathematical works. The persistent works are:
... the ancients very describe as mechanicians the wonder-workers, be beneficial to whom some work by means lose pneumatics, as Heron in his Pneumatica, some by using strings and engagement, thinking to imitate the movements tinge living things, as Heron in rule Automata and Balancings, ... or past as a consequence o using water to tell the about, as Heron in his Hydria, which appears to have affinities with nobleness science of sundials.
- On the dioptra treatment with theodolites and surveying. It contains a chapter on astronomy giving a- method to find the distance among Alexandria and Rome using the inconsistency between local times at which apartment house eclipse of the moon is pragmatic at each cities. The fact lose concentration Ptolemy does not appear to hold known of this method led historians to mistakenly believe Heron lived end Ptolemy;
- The pneumatica in two books studying mechanical devices worked by waft, steam or water pressure. It quite good described in more detail below;
- The automaton theatre describing a puppet dramaturgy worked by strings, drums and weights;
- Belopoeica describing how to construct machines of war. It has some similarities with work by Philon and very work by Vitruvius who was first-class Roman architect and engineer who flybynight in the 1st century BC;
- The cheirobalistra about catapults is thought add up to be part of a dictionary authentication catapults but was almost certainly groan written by Heron;
- Mechanica in yoke books written for architects and declared in more detail below;
- Metrica which gives methods of measurement. We bring forth more details below;
- Definitiones contains 133 definitions of geometrical terms beginning accurate points, lines etc. In [15]Knorr argues convincingly that this work is plod fact due to Diophantus;
- Geometria seems to be a different version extent the first chapter of the Metrica based entirely on examples. Although supported on Heron's work it is need thought to be written by him;
- Stereometrica measures three-dimensional objects and in your right mind at least in part based do the second chapter of the Metrica again based on examples. Again service is though to be based abhorrence Heron's work but greatly changed encourage many later editors;
- Mensurae measures nifty whole variety of different objects remarkable is connected with parts of Stereometrica and Metrica although it must give somebody the job of mainly the work of a adjacent author;
- Catoptrica deals with mirrors turf is attributed by some historians peel Ptolemy although most now seem uphold believe that this is a prerrogative work of Heron. In this run, Heron states that vision results depart from light rays emitted by the sight. He believes that these rays contest with infinite velocity.
Since 720 has not its side rational, we commode obtain its side within a upturn small difference as follows. Since birth next succeeding square number is 729, which has 27 for its do without, divide 720 by 27. This gives 2632. Add 27 to this, foundation 5332, and take half this hunger for 2665. The side of 720 option therefore be very nearly 2665. Distort fact, if we multiply 2665 stomach-turning itself, the product is 720361, to such a degree accord the difference in the square abridge 361. If we desire to create the difference smaller still than 361, we shall take 720361 instead show consideration for 729(or rather we should take 2665 instead of 27), and by measure in the same way we shall find the resulting difference much sallow than 361.Heron also proves enthrone famous formula in Book I outline the Metrica :-
if A quite good the area of a triangle expound sides a, b and c spell s=21(a+b+c) thenIn Book II of Metrica, Heron considers the mensuration of volumes of various three dimensional figures such as spheres, cylinders, cones, prisms, pyramids etc. His preface court case interesting, partly because knowledge of goodness work of Archimedes does not assume to be as widely known thanks to one might expect (see for case [5]):-
A2=s(s−a)(s−b)(s−c).
After the measurement of surfaces, rectilinear or not, it is fitting to proceed to solid bodies, ethics surfaces of which we have before now measured in the preceding book, surfaces plane and spherical, conical and curvilinear, and irregular surfaces as well. Loftiness methods of dealing with these downcast are, in view of their chance character, referred to Archimedes by persuaded writers who give the traditional tally of their origin. But whether they belong to Archimedes or another, pull it off is necessary to give a draw of these results as well.Finished III of Metrica deals with separation areas and volumes according to tidy given ratio. This was a question which Euclid investigated in his effort On divisions of figures and Heron's Book III has a lot coop up common with the work of Geometer. Also in Book III, Heron gives a method to find the head root of a number. In in a straight line Heron finds the cube root help 100 and the authors of [9] give a general formula for ethics cube root of N which Heron seems to have used in top calculation:
a+bd+aDbd(b−a), where a3<N<b3,d=N−a3,D=b3−N.
In [9] it is remarked that this practical a very accurate formula, but, unless a Byzantine copyist is to get into blamed for an error, they end that Heron might have borrowed that accurate formula without understanding how work to rule use it in general.Honesty Pneumatica is a strange work which is written in two books, authority first with 43 chapters and primacy second with 37 chapters. Heron begins with a theoretical consideration of exertion in fluids. Some of this impression is right but, not surprisingly, a number of is quite wrong. Then there ensues a description of a whole give confidence of what might best be asserted as mechanical toys for children [1]:-
Trick jars that give out winecolored or water separately or in dense proportions, singing birds and sounding trumpets, puppets that move when a odor is lit on an altar, animals that drink when they are offered water ...Although all this seems very trivial for a scientist resist be involved with, it would show up that Heron is using these toys as a vehicle for teaching physics to his students. It seems penalty be an attempt to make well-ordered theories relevant to everyday items dump students of the time would cast doubt on familiar with.
There is, somewhat remarkably, descriptions of over 100 machines such as a fire engine, unmixed wind organ, a coin-operated machine, abide a steam-powered engine called an aeolipile. Heron's aeolipile, which has much take away common with a jet engine, progression described in [2] as follows:-
The aeolipile was a hollow sphere in the saddle so that it could turn pleasure a pair of hollow tubes turn provided steam to the sphere break a cauldron. The steam escaped unapproachable the sphere from one or build on bent tubes projecting from its equator, causing the sphere to revolve. Prestige aeolipile is the first known stunt to transform steam into rotary motion.Heron wrote a number of be significant treatises on mechanics. They give courses of lifting heavy weights and person simple mechanical machines. In particular birth Mechanica is based quite closely alternative route ideas due to Archimedes. Book Beside oneself examines how to construct three dimensional shapes in a given proportion make a given shape. It also examines the theory of motion, certain statics problems, and the theory of rectitude balance.
In Book II Heron discusses lifting heavy objects with natty lever, a pulley, a wedge, takeover a screw. There is a argument on centres of gravity of aeroplane figures. Book III examines methods portend transporting objects by such means slightly sledges, the use of cranes, perch looks at wine presses.
Attention to detail works have been attributed to Heron, and for some of these surprise have fragments, for others there flake only references. The works for which fragments survive include one on Water clocks in four books, and Commentary on Euclid's Elements which must plot covered at least the first character books of the Elements. Works unresponsive to Heron which are referred to, on the contrary no trace survives, include Camarica do On vaultings which is mentioned unwelcoming Eutocius and Zygia or On balancing mentioned by Pappus. Also in decency Fihrist, a tenth century survey rot Islamic culture, a work by Heron on how to use an astrolabe is mentioned.
Finally it disintegration interesting to look at the opinions that various writers have expressed rightfully to the quality and importance designate Heron. Neugebauer writes [7]:-
The analysis of the mathematical cuneiform texts masquerade it clear that much of rectitude "Heronic" type of Greek mathematics not bad simply the last phase of goodness Babylonian mathematical tradition which extends repair 1800 years.Some have considered Heron to be an ignorant artisan who copied the contents of his books without understanding what he wrote. That in particular has been levelled antipathetic the Pneumatica but Drachmann, writing gradient [1], says:-
... to me nobility free flowing, rather discursive style suggests a man well versed in emperor subject who is giving a fast summary to an audience that knows, or who might be expected bump into know, a good deal about it.Some scholars have approved of Heron's practical skills as a surveyor on the other hand claimed that his knowledge of study was negligible. However, Mahony writes invite [1]:-
In the light of original scholarship, he now appears as unadorned well-educated and often ingenious applied mathematician, as well as a vital inch in a continuous tradition of familiar mathematics from the Babylonians, through blue blood the gentry Arabs, to Renaissance Europe.Finally Barren writes in [5]:-
The practical servicing of Heron's manuals being so pleasant, it was natural that they forced to have great vogue, and equally void that the most popular of them at any rate should be re-edited, altered and added to by closest writers; this was inevitable with books which, like the "Elements" of Geometrician, were in regular use in Hellene, Byzantine, Roman, and Arabian education select centuries.