Apollonius of Perga

by Alicia Schamburg

 


Apollonius of Perga, also known as “The Great Geometer” was born around

262 BC in Perga, Pamphylia. We know Perga today as Murtina, in Antalya, Turkey. In Apollonius's earlier years, he went to Alexandria where he studied under the followers of Euclid. Little information is known on the details of Apollonius of Perga's life, but what is certain is the great influence he had on the development of early mathematics.

 

Apollonius is so greatly remembered because during his lifetime he was able to write more than 20 books. His works included Cutting of a ratio , Cutting an area , On determinate section , Tangencies , Plane loci and On verging constructions .

 

The most famous of Apollonius's works however were the Conics . Conics was written in eight books. Unfortunately only the first seven survive today. To get an understanding of what Conics is, in definition it means of or relating to a cone. Also, Conic sections are the curves formed when a plane intersects the surface of a cone.   

 

In the eight books of which Conics consisted, books one to four form an introduction to the basics of conics. In book one the relations satisfied by the diameters and tangents of conics are studied while in book two Apollonius investigates how hyperbolas are related to their asymptotes, and he also studies how to draw tangents to given conics. In his third book, Apollonius told how it would not have been possible for the synthesis to be completed without the additional theorems that he discovered. Books five to seven discuss normals to conics and shows how many can be drawn from a point. Apollonius credited Conon of Samos (c 280-c 220 BC) and Euclid of Alexandria

(c 325-c 265 BC) with the original work on conical sections that inspired his work.

 

Apollonius's contributions to the development of mathematics are countless. Apollonius showed how to construct the circle, which is tangent, to three given circles.   He extended Euclid's theory of irrationals and improved Archimedes's approximation of ‘pi.' Apollonius showed that parallel rays of light are not brought to a focus by a spherical mirror and discussed the focal properties of a parabolic mirror. In his mathematical astronomy studies he found the point where a planet appears stationary, namely the points where the forward motion change to a retrograde motion or the converse. To top everything off, Apollonius developed the hemicyclium, a sundial which has the hour lines drawn on the surface of a conic section.

 

In conclusion, it is clear that Apollonius of Perga was able to contribute very much to the early development of mathematical geometry. One of the most significant factors to us today was the introduction of the Parabola, Ellipse and Hyperbola.

 

This is an Illustration of the Conic Sections.

conic section 1: 1 straight lines, 2 circle, 3 ellipse, 4 parabola, 5 hyperbola

 

 

Intersections of parallel planes and a double cone, forming ellipses, parabolas, and hyperbolas respectively.

 

The Hemicyclium Sundial created by Apollonius

    

 

RESOURCES:

 

Http://www.scienceworld.wolfram.com/biography/Apollonius.html

 

Http://www.nahste.ac.uk/isaar/GB_0237_NAHSTE_P1095.html

 

http://www.m-w.com/mw/art/conicsec.htm

 

http://www.xahlee.org/SpecialPlaneCurves_dir/ConicSections_dir/conicsFocusDirectrix.gsp

 

http://www.sundials.co.uk/%7Eleicester.htm