Greatest Greek mathematician?

[Kyriakos]

One of my favorite mathematicians:



I find Apollonios of Perga's (Perga was a village near Pergamon, where he later moved to) work on Conic sections to be extremely interesting. Even his definitions of the four conic sections (circle, ellipse, parabola, hyperbola) are highly innovative (he defined them by corresponding courses taken by squares and parallelograms to form the four parts of the conic section).



http://en.wikipedia.org/wiki/Apollonius_of_Perga

Afaik his full work on Conics survives.

Let alone that even the titles of his works are beautiful

Κωνικά (Conics)


Λόγου ἀποτομή, De Rationis Sectione ("Cutting of a Ratio")
Χωρίου ἀποτομή, De Spatii Sectione ("Cutting of an Area")
Διωρισμένη τομή, De Sectione Determinata ("Determinate Section")
Ἐπαφαί, De Tactionibus ("Tangencies")
Νεύσεις, De Inclinationibus ("Inclinations")
Τόποι ἐπίπεδοι, De Locis Planis ("Plane Loci").


Περὶ τοῦ πυρίου, On the Burning-Glass, a treatise probably exploring the focal properties of the parabola
Περὶ τοῦ κοχλίου, On the Cylindrical Helix (mentioned by Proclus)
A comparison of the dodecahedron and the icosahedron inscribed in the same sphere
Ἡ καθόλου πραγματεία, a work on the general principles of mathematics that perhaps included Apollonius's criticisms and suggestions for the improvement of Euclid's Elements
Ὠκυτόκιον ("Quick Bringing-to-birth"), in which, according to Eutocius, Apollonius demonstrated how to find closer limits for the value of π (pi) than those of Archimedes, who calculated 3+1/7 as the upper limit (3.1428571, with the digits after the decimal point repeating) and 3+10/71 as the lower limit (3.1408456338028160, with the digits after the decimal point repeating)
an arithmetical work (see Pappus) on a system both for expressing large numbers in language more everyday than that of Archimedes' The Sand Reckoner and for multiplying these large numbers
a great extension of the theory of irrationals expounded in Euclid, Book x., from binomial to multinomial and from ordered to unordered irrationals (see extracts from Pappus' comm. on Eucl. x., preserved in Arabic and published by Woepcke, 1856).

 

[Leoreth]

I know nothing about Apollonios, could you summarize which of his contributions left their mark well into modern mathematics?

 

[Kyriakos]

I know nothing about Apollonios, could you summarize which of his contributions left their mark well into modern mathematics?

I don't think i can answer that, but for starters Fermat did try to reconstruct his work on Flat fields (de locis planis). I did read a number of examinations by Apollonios and was quite interested in the definitions of the shapes cut from a conic space, in direct juxtaposition to the modern Cartesian 2d space that parabolas, ellipses, hyperbolas and so on are afaik mostly examined now.

The conic systems allow for more complexity, due to the full 3d

As i noted before, i am currently on a very extented break from any real math reading, so maybe in the future i will have more specific things to post..

 

[Leoreth]

Alright, thanks anyway

 

[Kyriakos]

Btw: (lit related..)

Spoiler :

The phrase merely means “Flat fields” and it is obvious that it alludes to one of the lost works of Apollonios of Perga, the important mathematician of the Hellenistic era. I also managed to verify that an unusually prolonged reference to that book's contents had the effect that a few mathematicians of the distant aeons attempted a full restoration of the text, as for example the Swiss Fermat.
Apart from that I only know what you yourself are aware of, although on my part I definitely have the urge for constructing far darker assumptions, and not entirely the same starting point in the examination of this affair...

Just an opening bit i wrote (translated here) a few seconds ago, in the case i decide to form something general with that as a vague backdrop

 

[Takhisis]

Archimedes with the giant ancient laser beam for the win.

Frickin' laser beams!