23 July 2016

# Geometry

Summary:

The first part is an overview of the achievements of ancient Greek geometers based on the original sources. In particular, it will contain a list of the known geometers, the texts they have written and a discussion about the surviving manuscripts and were they can be found today. The second part will have some diamonds from Greek geometry by giving a selection of some theorems and the brilliant proofs given by the ancients.

The course:

Chapter I

The beginning of Greek Mathematics and its impact. Our sources of Greek Mathematics and in particular of Geometry. Who are the ancient Greek geometers (we have a list of more than 300 names) and which are the texts they have written. Which of those texts survive today and where they can be found today.

Chapter II

Thales, Pythagoras and the Pythagoreans, early geometers and their achievements. The discovery of irrationality, Platonic solids and the three famous problems (squaring the circle, trisecting the angle and duplicating the cube). Conic sections.

Chapter III

The school of Plato. Eudoxus and Euclid. Discussion about the Elements of Euclid which is the earliest surviving Greek Mathematical text and undoubtedly the most read mathematical book of all times. The impact of the Elements to Renaissance and modern Mathematics.

Chapter IV

Later geometers, Archimedes, Apollonius, Pappus, Ptolemy, their work and their lasting contribution to Mathematics.

Chapter V

Examples of some theorems and their brilliant proofs taken from the ancient texts. For example we shall discuss Archimedes’s method of finding the volume and surface area of a sphere and Ptolemy’s method of constructing trigonometrical tables.

### Course leader

Michael Lambrou

### Target group

High School students, 1st and 2nd year University students

### Course aim

The course aims at the achievements of ancient Greek geometers based on the original sources.

There will be given a selection of some theorems and their brilliant proofs.

### Fee info

EUR 0: The course is a part of the complete program "1st Science Summer School", with total cost 770 EUR (accommodation and transport are included).