Lectures on Euclidean Geometry - Volume 1

Part I Euclidean Geometry of the plane.- 1 The basic notions.- 2 Circle and polygons.- 3 Areas, Thales, Pythagoras, Pappus.- 4 The power of the circle.- 5 From the classical theorems.

Paris Pamfilos was born in Athens, Greece, and studied in Athens, Bonn and Cologne. His Ph.D. (in Differential Geometry) was obtained in Cologne under the supervision of Prof. Peter Dombrowski. He has held various assistant, researcher and visiting-professor positions at the Universities of Bonn, Essen, and Nicosia, and was an associate professor in the Department of Mathematics, University of Crete. He enjoys teaching, programming, and (in the infrequent remaining free time) doing his philosophical parerga. He speaks Greek, German, French, English, Italian and Russian. His main interest is in Geometry, especially Euclidean Geometry, a subject that he has lectured on for more than 25 years, and on which he continues to publish original articles.

This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.
The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particularattention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature.
The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.

Elementary synthetic exposition of plane Euclidean geometry Didactic method enhanced with many figures and solved exercises Abundant references to alternative viewpoints and further reading