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Mathematics - Geometry & Topology | Problem-Solving and Selected Topics in Euclidean Geometry - In the Spirit of the Mathematical

Problem-Solving and Selected Topics in Euclidean Geometry

In the Spirit of the Mathematical Olympiads

Louridas, Sotirios E., Rassias, Michael Th.

2013, X, 235 p. 134 illus.

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  • The book teaches in practice methods of analysis, synthesis, construction, and proof with specific problems, examples, and applications
  • Teaches mathematical thinking presented in the most elementary possible form for the solution or proof of every problem or statement of theorem
  • Presents main theorems of Euclidean Geometry with a discussion of the central ideas behind their proofs
  • Provides approximately 25 problems proposed by leading mathematicians or given in IMO's or short lists for IMO's or BMO's

Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads contains theorems of particular value for the solution of Olympiad-caliber problems in Euclidean Geometry. Selected geometric problems, which have been given in International Mathematical Olympiads (IMO) or proposed in short lists in IMO, are discussed. Additionally, a number of new problems proposed by leading mathematicians in the subject with their step-by-step solutions are presented. The book teaches mathematical thinking through Geometry and provides inspiration for both students and teachers.

From the Foreword: “…Young people need such texts, grounded in our shared intellectual history and challenging them to excel and create a continuity with the past. Geometry has seemed destined to give way in our modern computerized world to algebra. As with Michael Th. Rassias’ previous homonymous book on number theory, it is a pleasure to see the mental discipline of the ancient Greeks so well represented to a youthful audience.”

– Michael H. Freedman (Fields Medal in Mathematics, 1986)

Sotirios E. Louridas has studied Mathematics at the University of Patras, Greece. He has been an active member of the Greek Mathematical Society for several years both as a problem poser and a coach of the Greek Mathematical Olympiad team. He has authored in Greek, a number of books in Mathematics. 

Michael Th. Rassias has received several awards in mathematical problem-solving competitions including two gold medals at the Pan-Hellenic Mathematical Olympiads of 2002 and 2003 (Athens, Greece), a silver medal at the Balkan Mathematical Olympiad of 2002 (Targu Mures, Romania) and a silver medal at the 44th International Mathematical Olympiad of 2003 (Tokyo, Japan). He holds a Diploma from the School of Electrical and Computer Engineering of the National Technical University of Athens and a Master of Advanced Study in Mathematics from the University of Cambridge. He is currently a PhD student in Mathematics at ETH-Zürich. At the age of 22, he authored the book Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads – Foreword by Preda Mihăilescu (Springer, 2011), ISBN: 978-1-4419-0494-2.

Content Level » Lower undergraduate

Keywords » geometric computation - geometric construction - mathematical olympiad problems - mathematical proofs - mathematical thinking - problems in Euclidean geometry - problems in geometry

Related subjects » Algebra - Geometry & Topology - Mathematics

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