CONICS

A BRİE

F HİS

TORY

OF TH

E CONİC

SECTİ

ON

WHAT İS A CONİC?

A conic section (or just conic) is a curve obtained by intersecting a cone (more precisely, a right circular conical surface) with a plane.

(demonstration of a conic section)

Great ancient mathematicians who worked onto the conic section:

•Manaecmus

•Euclid

•Archimedes of Syracuse

•Apollonius

•Aristeus

Let’s talk about some of the most important of these:

• We don’t have lots of infos about his life and his work and our sources are an epigram by Eratosthenes, some writings of Proclus and an episode of Plutarch’s opera about the relation between that matematician and one of his teachers, Plato. Menaechmus was said to have been the tutor of Alexander the Great.

• He was the first to investigate curves that would come to be known as the ellipse, the parabola and the hyperbola as sections of a cone. For that reason these curves were called for a long time the Maenechmian triads.

• He discovered that curves as a by-product of his attempt to solve the “Delian Problem”, one of the three most famous geometry problems, also known as doubling a cube.

• The real inventor of the modern geometry, probably knew Manaechmus as an other probable pupil of Plato’s Academy in Athen. He wrote a foundamental opera of geometry called “Elements”, a collection of definitions, postulates, propositions and mathematical proofs of the propositions (The last book of it cover the Euclidean geometry).

• Between his lost works you can find a treatise that cover deeply the conic sections: “Conics”. In this book was probably explained by Euclid all the previous knowledge about this topic in his tipical way of writing. These contents were directly connected with the homonymous work of Apollonius where was discovered , that if one allowed the cutting plane to vary its angle with respect to the side of the cone, then any cone would produce all three types of section. He also provided solutions to the tangent and normal problems for each of these curves.

•One of the most eclectic thinker in history he worked on engeenering, mechanic, physics, mathematic and geometry. He wrote a big number of treatises and essays.

•In relation to the conic section he wrote: “On Conoids and Spheroids” wherein there were explicated ways to calculate the areas and volumes of section of cones, spheres, and paraboloids; “The Quadrature of the Parabola”, a work that presents 24 propositions regarding parabolas, culminating in a proof that the area of a parabolic segment is 4/3 that of a certain described triangle.

The theories about conic section, discovered and esplicated by the ancient Greek

mathematicians, remained unimproved until the studies of two great thinkers of

the 17° centurie:

Friedrich Johannes Kepler Renè Descartes:

Using the ellipse forplanet’s orbit.

Making a parabola representable on a plane .