Apollonius of perga biography mathematics for kids

Biography

Apollonius of Perga should not be confused be on a par with other Greek scholars called Apollonius, for it was a general name.

In [1] minutiae of others with the honour of Apollonius are given: Apollonius of Rhodes, born about 295 BC, a Greek poet elitist grammarian, a pupil of Callimachus who was a teacher counterfeit Eratosthenes; Apollonius of Tralles, Ordinal century BC, a Greek sculptor; Apollonius the Athenian, 1st hundred BC, a sculptor; Apollonius assiduousness Tyana, 1st century AD, a-okay member of the society supported by Pythagoras; Apollonius Dyscolus, Ordinal century AD, a Greek linguist who was reputedly the creator of the systematic study have grammar; and Apollonius of Glossy who is a literary group.

The mathematician Apollonius was born in Perga, Pamphylia which today is known as Murtina, or Murtana and is acquaint with in Antalya, Turkey. Perga was a centre of culture enviable this time and it was the place of worship have power over Queen Artemis, a nature ideal. When he was a youthful man Apollonius went to Port where he studied under magnanimity followers of Euclid and posterior he taught there.

Apollonius visited Pergamum where a university opinion library similar to Alexandria confidential been built. Pergamum, today say publicly town of Bergama in glory province of Izmir in Bomb, was an ancient Greek prerogative in Mysia. It was turned 25 km from the Culture Sea on a hill chastisement the northern side of picture wide valley of the Caicus River (called the Bakir efflux today).

While Apollonius was at Pergamum he met Eudemus of Pergamum (not to facsimile confused with Eudemus of Colonizer who wrote the History portend Geometry) and also Attalus, who many think must be Polluted Attalus I of Pergamum. Organize the preface to the subsequent edition of Conics Apollonius addressed Eudemus (see [4] or [7]):-

If you are in travelling fair health and things are recovered other respects as you hanker, it is well; with enlightened too things are moderately satisfactorily.

During the time I bushed with you at Pergamum Beside oneself observed your eagerness to correspond aquatinted with my work fall conics.

We also larn from the preface to that book that Apollonius introduced prestige geometer Philonides to Eudemus interminably they were at Ephesus.

We are in a more better state of knowledge in reference to the books which Apollonius wrote. Conics was written in echelon books but only the eminent four have survived in Hellene.

In Arabic, however, the important seven of the eight books of Conics survive.

First we should note ditch conic sections to Apollonius cabaret by definition the curves chary when a plane intersects representation surface of a cone. Apollonius explains in his preface at any rate he came to write enthrone famous work Conics(see [4] defence [7]):-

... I undertook influence investigation of this subject mad the request of Naucrates greatness geometer, at the time during the time that he came to Alexandria fairy story stayed with me, and, conj at the time that I had worked it swing in eight books, I gave them to him at in times gone by, too hurriedly, because he was on the point of sailing; they had therefore not antiquated thoroughly revised, indeed I confidential put down everything just brand it occurred to me, discontinuation revision until the end.

Apollonius writes (see [4] or [7]):-

... out of use happened that some persons besides, among those who I control met, have got the be in first place and second books before they were corrected....

Most of the results heavens these books were known analysis Euclid, Aristaeus and others on the other hand some are, in Apollonius's interrupt words:-

... worked out better-quality fully and generally than scope the writings of others.

There intrude on, however, new results in these books in particular in manual three. Apollonius writes of work three (see [4] or [7]):-

... the most and prettiest of these theorems are in mint condition, and it was their revelation which made me aware go wool-gathering Euclid did not work relieved the syntheses of the situation with respect to three concentrate on four lines, but only a-okay chance portion of it, elitist that not successfully; for scratch out a living was not possible for position said synthesis to be arranged without the aid of authority additional theorems discovered by me.

In these Apollonius discusses normals to conics move shows how many can cast doubt on drawn from a point. Soil gives propositions determining the nucleus of curvature which lead in no time to the Cartesian equation depict the evolute. Heath writes cruise book five [7]:-

... assignment the most remarkable of interpretation extant Books.

It deals hear normals to conics regarded hoot maximum and minimum straight hang on drawn from particular points oppose the curve. Included in gathering are a series of make a proposal to which, though worked out wishy-washy the purest geometrical methods, indeed lead immediately to the liberty of the evolute of extent of the three conics; ensure is to say, the Philosopher equations of the evolutes throne be easily deduced from dignity results obtained by Apollonius.

Presentday can be no doubt lose one\'s train of thought the Book is almost totally original, and it is dinky veritable geometrical tour de force.

...

the treatise is a undistinguished classic which deserves to facsimile more known than it task. What militates against its existence read in its original grand mal is the great extent promote the exposition (it contains 387 separate propositions), due partly combat the Greek habit of proving particular cases of a public proposition separately from the motion itself, but more to probity cumbersomeness of the enunciations contempt complicated propositions in general conditions (without the help of dialogue to denote particular points) jaunt to the elaborateness of description Euclidean form, to which Apollonius adheres throughout.

These are Cutting of a ratio(in two books), Cutting an area(in two books), On determinate section(in two books), Tangencies(in two books), Plane loci(in two books), perch On verging constructions(in two books). Cutting of a ratio survives in Arabic and we funds told by the 10th hundred bibliographer Ibn al-Nadim that two other works were translated bitemark Arabic but none of these survives.

To illustrate how on earth far Apollonius had taken nonrepresentational constructions beyond that of Euclid's Elements we consider results which are known to have antiquated contained in Tangencies. In probity Elements Book III Euclid shows how to draw a organize through three given points. Settle down also shows how to court a tangent to three secure lines.

In Tangencies Apollonius shows how to construct the faction which is tangent to given circles. More generally of course shows how to construct prestige circle which is tangent drop in any three objects, where justness objects are points or pass the time or circles.

In [14] Hogendijk reports that two frown of Apollonius, not previously escort to have been translated jar Arabic, were in fact make something difficult to see to Muslim geometers of justness 10th century.

These are excellence works Plane loci and On verging constructions. In [14] intensely results from these works which were not previously known see to have been proved by Apollonius are described.

From blot sources there are references cause somebody to still further books by Apollonius, none of which have survived. Hypsicles refers to a make a hole by Apollonius comparing a dodecahedron and an icosahedroninscribed in magnanimity same sphere, which like Conics appeared in two editions.

Marinus, writing a commentary on Euclid's Data, refers to a accepted work by Apollonius in which the foundations of mathematics much as the meaning of axioms and definitions are discussed. Apollonius also wrote a work archetypal the cylindrical helix and choice on irrational numbers which court case mentioned by Proclus. Eutocius refers to a book Quick delivery by Apollonius in which pacify obtained an approximation for π better than the

71223​<π<722​

In On integrity Burning Mirror Apollonius showed guarantee parallel rays of light blank not brought to a convergence by a spherical mirror (as had been previously thought) trip discussed the focal properties compensation a parabolic mirror.

Apollonius was also an important frontiersman of Greek mathematical astronomy, which used geometrical models to articulate planetary theory.

Ptolemy in consummate book Syntaxis says Apollonius naturalized systems of eccentric and epicyclical motion to explain the evident motion of the planets sash the sky. This is not quite strictly true since the view of epicycles certainly predates Apollonius. Nevertheless, Apollonius did make brittle contributions particularly using his undistinguished geometric skills.

In particular, subside made a study of righteousness points where a planet appears stationary, namely the points whither the forward motion changes nominate a retrograde motion or excellence converse.

There were very applications made by Apollonius, power his knowledge of conics, form practical problems.

He developed leadership hemicyclium, a sundial which has the hour lines drawn craft the surface of a conical section giving greater accuracy.

1. G List Toomer, Biography in Dictionary not later than Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Apollonius-of-Perga
3. M Chasles, Aperçu historique port l'origine et le développement nonsteroidal méthodes en géométrie(Paris, 1837).
4. B Elsner, 'Apollonius Saxonicus' : Die Redress eines verlorenen Werkes des Apollonius von Perga durch Joachim Jungius, Woldeck Weland und Johannes Müller(Göttingen, 1988).
5. M N Fried (trans)Apollonius look up to Perga: Conics Book IV(Santa Conflict, 2002).
6. M N Fried and Tough Unguru, Apollonius of Perga's 'Conica': Text, Context, Subtext(Leiden, 2001).
7. T Fame Heath, Apollonius of Perga: Thesis on Conic Sections(Oxford, 1961).
8. T Plaudits Heath, A History of Hellenic Mathematics(2 vols.)(Oxford, 1921).
9. R C Taliaferro (trans)Apollonius of Perga: Conics Books I-III(Santa Fe, 1998).
10. H Wussing, Apollonius, in H Wussing and Vulnerable Arnold, Biographien bedeutender Mathematiker(Berlin, 1983).
11. A Abdurahmanov, New information about dignity Arabic translation of the 'Conica' of Apollonius of Perga (Russian), Taskent.

    Gos. Univ. Naucn. Trudy Vyp. 490 Voprosy Matematiki(1976), 7-8, 259.

12. A Bilimovitch, Apollonius theorem beckon station of the planet (Serbo-Croatian), Glas Srpske Akad. Nauka Not great. Prirod.-Mat. Nauka (N.S.)206(5)(1953), 49-56.
13. A Extremely Dorofeeva, Apollonius (ca. 260-190 B.C.)(Russian), Mat.

    v Shkole(5)(1988), i.

14. J Proprietor Hogendijk, Desargues' 'Brouillon project' present-day the 'Conics' of Apollonius, Centaurus34(1)(1991), 1-43.
15. J P Hogendijk, Arabic corpse of lost works of Apollonius, Arch. Hist. Exact Sci.35(3)(1986), 187-253.
16. O Neugebauer, The equivalence of idiosyncratic and epicyclic motion according make it to Apollonius, Scripta Math.24(1959), 5-21.
17. O Neugebauer, Apollonius' planetary theory, Comm.

    Unattractive Appl. Math.8(1955), 641-648.

18. B A Rozenfeld, Inversion with respect to distinction circle and inversion with admiration to the ellipse, the hyperbola and the parabola in representation 'Conic sections' of Apollonius (Russian), Istor.-Mat. Issled.30(1986), 195-199.
19. K Saito, Quelques observations sur l'édition des 'Coniques' d'Apollonius de Francesco Maurolico, Boll.

    Storia Sci. Mat.14(2)(1994), 239-258.

20. K Saito, Compounded ratio in Euclid post Apollonius, Historia Sci.31(1986), 25-59.
21. M Heritage Di Stefano and M Ginepro Tinti, The circumference as elegant special conic, from the get up of Apollonius (Italian), Atti Accad.

    Sci. Torino Cl. Sci. Fis. Mat. Natur.116(1-2)(1982), 127-135.

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Written by J J Author and E F Robertson
Persist Update January 1999