"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.
Reviews / Votes
"This book provides an essential presentation of concepts and ideas as well as problems with their solutions in Euclidean Geometry, a traditional and still challenging part of Geometry. -Dorian Andrica, Zentralblatt
Product info
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Edition
Language
Place of publication
Target group
Professional and scholarly
Lower undergraduate
Illustrations
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 17 mm
Weight
ISBN-13
978-1-4614-7272-8 (9781461472728)
DOI
10.1007/978-1-4614-7273-5
Schweitzer Classification
Michael Th. Rassias is a brilliant young mathematician and son of a highly regarded author and acclaimed mathematician, Themistocles Rassias. He has received several awards in competitive mathematical problem solving. He received first prize in the Jozef Wildt International Mathematics Competition for three consecutive years in 2004, 2005 and 2006. He was also the silver medalist at the 44th International Mathematics Olympiad of 2003 held in Tokyo, Japan.
Rassias's last book with Springer is entitled "Problem-Solving and Selected Topics in Number Theory" and was published Nov. 23, 2010.
S.E. Louridas does not hold a present affiliation but has written 6 olympiad related books and has trained young people in math olympiads for several years in Greece.
Foreword.- Preface.- Basic Concepts and Theorems of Euclidean Geometry.- Methods of Analysis, Synthesis, Construction and Proof.-Geometrical Constructions.- Geometrical Loci.- Problems of Olympiad Caliber.- Solutions of the Problems.- Bibliography.- Index.
