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Identifier

uch.math.msc//2005bounakis

Title

Ιστορία και μελέτη με Eυκλείδεια μέσα των κωνικών τομών

Alternative Title

History and study of conic sections with the help of Euclidean means

Author

Μπουνάκης, Δημήτρης

Abstract

In the first part (Chapter 1) of this work the history of Conic Sections is recorded, starting from the time of their invention in Ancient Greece to their definitive study in the 16th and 17th centuries, in the Latin West. Furthermore, we mention the books on Conic Sections that were published in the Greek territory from the time of the Ottoman Occupation until recent times. In the second part (Chapter 2), starting with the three-dimensional definition of Conic Sections, we prove their characteristic properties, which concern the plane (focal and constant ratio property). The next chapters (3 to 6) deal with the study of these curves using Euclidean means, i.e. with the so called synthetic method, used extensively by the ancient Greek geometers. Namely, the starting point is the (new and equivalent) definition of Conic Sections, i.e. the constancy of the ratio of the distance from a given point and a given straight line. Thus, we prove most of the important (classic) properties of parabola, ellipse and hyperbola in the form of propositions and corollaries. Some further properties of Conic Sections are stated without proof at the end of the respective chapters.

Language

Greek

Issue date

2005-03-17

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Permanent Link

https://elocus.lib.uoc.gr//dlib/f/6/6/metadata-dlib-2005bounakis.tkl

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