The Story of Numbers

This book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.

Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of "Chaos". Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.

The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.

The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.

Contents:

• Introduction

• Integers

• Real Numbers

• Imaginary and Complex Numbers

• Special Numbers

• Appendix A:

  • Solution of Equation (1.2)
  • Brahmagupta's Equation and Its Solution
  • Solution to Equation (2.26)

• Appendix B:

  • Sum of Integral Powers of Natural Numbers

• Appendix C:

  • Origin of Curious Patterns (Section 3.7.6)

Readership: Elementary and secondary education students as well as high school students and non-mathematicians.
Key Features:

• For the first time the readers are exposed to the joy of creating mathematics going beyond the problem-solving skills
• The story of inventing and using different numbers is told lucidly to generate interest in mathematics
• It combines serious and recreational mathematics; it also includes anecdotes for the students and general adult readers to enjoy mathematics as an entertaining human activity
• Lucid story form of presentation rather than a series of formula and techniques
• It avoids rigorous presentation and emphasizes an intuitive approach which is within the grasp of both elementary and secondary education students as well as high-school students and non-mathematician adults