BASIC LESSONS ISOMETRIES, SIMILAR & INVERSIONS EUCLIDEAN ..

The aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.Contents:

• Biography
• Acknowledgements
• Prologue
• Some Preliminaries
• Isometries
• Exercises on Isometries
• Similarities
• Exercises on Similarities
• The Transformation of Inversion
• Exercises on Circles
• Exercises on Radical Axis
• Exercises on Inversion
• Bibliography
• Index

Readership: College and high school students in mathematics, computational geometry, computational sciences.

Isometries;Parallel Translations;Rotations;Reflections;Glides;Similarities;Direct Similarities;Opposite Similarities;Inversions;Compositions;Applications;Examples;Notable Theorems;Steiner Chains;Radical Axis;Radical Center;Exercises0Key Features:

• Provides a complete synthetic exposition of plane isometries, similarities and inversions in the Euclidean plane
• Contains all proofs of the results combined with 335 figures carefully constructed using the computer
• Contains 50 excellent examples and useful applications
• Contains 450 exercises (many of which have several parts) or projects classified in groups of general content, geometrical constructions and geometrical loci
• Is different from all books in circulation dealing with these topics and so is a new addition to the mathematical literature