Mathematics Before and After Pythagoras

This book provides the reader with a comprehensive account of the contributions of Pythagoras to mathematics and philosophy, using them as a starting point to compare pre-Pythagorean accomplishments with the myriad mathematical developments that followed. It begins with a thorough study of Pythagoreanism and the early Pythagoreans, including the major events in Pythagoras' life and the origins of the mystical significance attributed by Pythagoreans to natural numbers. From Chapter 3 onward, the book describes how mathematical thinking works and prepares the reader for the subsequent chapters, which cover mathematical logic and proofs, their application to the study of natural and prime numbers, the investigation of Pythagorean triples, figurative numbers, and irrational numbers, all interwoven with rich historical context.

Aimed at students and teachers at all levels, this work is accessible to non-mathematicians as well, with the main prerequisite being an avid curiosity about some of the ideas and thinkers that helped to forge the mathematical world as we know it.

Early praises for Mathematics Before and After Pythagoras:

Your book is charming and fun to read. It would be fine to be able to teach from it. (Steve Krantz, USA)

...your new book, an obvious labor of love... I can see that it will be an inspiration for young students. (Bruce Berndt, USA)

It is an excellent book, and I am deeply grateful for sending it to me. It is an extraordinary gift, and I am so grateful for this. (Carlo Cattani, Italy)

I am really impressed by the wealth of interesting material you have collected and presented. (Rainer Kress, Germany)

Offers a thorough study of Pythagoreanism and the early Pythagoreans, providing insights into Pythagoras' legacy Employs the most relevant Pythagorean concepts to discuss mathematical thinking and the tools that support it Useful for students and teachers at all levels, and accessible to non-mathematicians with a genuine curiosity for math

Autorentext

Ravi P. Agarwal is an Emeritus Professor at the Florida Institute of Technology, USA. Previously, he served as a Professor at Texas A&M University in Kingsville, USA, for many years. He completed his Ph.D. (1973) at the Indian Institute of Technology, India. Dr. Agarwal has authored or co-authored 50 books (mostly with Springer) and 2,000 research articles. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities.

Inhalt

Preface.- Foreword.- Life and Teaching of Pythagoras.- Numbers and Number Mysticism.- Mathematics, Mathematicians, and Proofs.- Prime Numbers.- Pythagorean Theorem.- Pythagorean Triples.- Pythagorean Figurative Numbers.- Pythagorean Irrationality of Numbers.- Name Index.- Subject Index.