Author: A A Hattangadi
Publisher: Universities Press
Year: 2001
Language: English
Pages: 222
ISBN/UPC (if available): 81 7371 387 1
Description
This book is definitely for those who love mathematics; but even more so for those who hate mathematics. It strives to kindle the curiosity and wonder about mathematics amongst those who are misled into believing that it is a boring and difficult subject.
Mathematics - often considered as operations in the realm of the abstract - is in fact an edifice that is well connected within itself and the world around us. This book delves a little deeper into topics based on elementary number theory covered in the school curriculum, to reveal the beauty, symmetry, diversity and rationality of the subject, Several mathematical puzzles, curious facts and insights to historical developments are included along with BASIC programmes for solving some of the problems. Often, an explorer is thwarted in his or her attempts at new explorations in mathematics because of the voluminous calculations and complex analyses involved. Programming in BASIC is shown as a powerful tool for overcoming this hurdle, thereby opening up new avenues of research in the fascinating world of numbers.
This book is definitely for those who love mathematics; but even more so for those who hate mathematics. It strives to kindle the curiosity and wonder about mathematics amongst those who are misled into believing that it is boring and difficult subject.
Contents
Preface
CHAPTER 1
CALCULATING THE VALUE OF PI
Introduction
Calculations of the Value of Pie in ancient India
The Value of Pie in other countries around the world
How accurate is the value 22/7 for Pie?
Calculation of the Value of Pie from first principal
Calculation of the value of Pie by summation of convergent infinite series
Calculation of Pie by infinite products
Suggestions for further investigation
Appendics
The Katapayadi system of Sanskrit alphabetic code for numerals
BASIC program PIVALUE1
Program PIVALUE2
Program PIVALUE3
Program PIVALUE4
Infinite series
BASIC Program PIPRODUC
CHAPTER 2
THE FIBONACCI SEQUENCE AND ITS VARIATIONS
The making of millionaire
The Fibonacci sequence
The Fibonacci ration 1.618. . .
Properties of Fibonacci sequences
Mathematical basic of Fibonacci sequence properties
Computer programs for Fibonacci sequence calculations
Damped oscillation of Fibonacci ratio
The Golden Section and the Golden Rectangle
A Variation of the Fibonacci sequence
Another variation of the Fibonacci sequence
Reciprocals of the Fibonacci numbers
Suggestions for further exploration
Biographical not on Fibonacci
Appendices
BASIC program FIBONAC3
BASIC program FIBONAC1
BASIC program FIBOVARI
BASIC program FIBONAC2
Solution to the puzzle ‘Making of a Millionaire’
BASIC program FIBOREC1
CHAPTER 3
PYTHAGOREAN TRIPLETS
Introduction
Generation of Pythagorean triplets by trial and error
Lists of Pythagorean triplets
Generation of Pythagorean triplets by formulae
Algebraic identities for generating Pythagorean triplets
Variations on Pythagoras’ equation
Right angled triangle in Tamil poetry
Variations on this theme
Appendices
BASIC program PYTHAGOR
BASIC program TAMIPOET
CHAPTER 4
MULTIPLICATION OF VERY LARGE NUMBERS
Introduction
Multiplication of very large numbers
Checking the correctness of the BASIC program
Product of two 100-digit numbers on a PC
Verifying the program in Appendix 4.1
Long division of very large numbers
Appendices
BASIC program for multiplying very large numbers
BASIC program for testing above program
CHAPTER 5
PRIME NUMBERS
Introduction
Determination of Prime numbers
Computer program to discover prime numbers
Prime numbers are infinite in number
The number RSA 129
Extremely large prime numbers
Some explorations
Twin primes
Further work on prime numbers
Appendices
BASIC program PRIMENUN
BASIC program PRINUMEX
BASIC program PRINUMRE
BASIC program RECITWIN
CHAPTER 6
PERPETUAL CALENDAR AND BIORHYTHMS
Introduction
Natural divisions of time
Reasons for differences in day of months
BASIC program for perpetual calendar
Biorhythms
BASIC program BIORHYTHM
Appendices
BASIC program PERCAL
BASIC program BIORHYTHM
CHAPTER 7
CONSTRUCTION OF TABLES OF LOGARITHMS
Introduction
Tables of logarithms and anti-logarithms
Napierian and common logarithms
Infinite series for calculating e.
Use of logarithms today
Infinite series for logarithms to base e
Calculating logarithms of large numbers
Other infinite series for calculating logarithms
Applications of logarithms
Conclusion
Appendices
BASIC program LOGBASE
BASIC program LOGARITHM
BASIC program LOGTABLE
BASIC program LOGLARGE
CHAPTER 8
PLAYING TIC-TAC-TOE WITH THE COMPUTER
Introduction
Rules of Tic-Tac-Toe
Playing Tic-Tac-Toe with a computer
How the BASIC program TICTACTO works
SEGMENTS OF THE BASIC program TICTACTO
Gomuku
Appendix
BASIC program TICTACTO
CHAPTER 9
NUMBER SYSTEM
Introduction
Other number systems
The octal system
The binary and the hexadecimal systems
Systems to bases higher than 16
Conversion of numbers from any system to the decimal system
BASIC program ANYTDECI and ANYTDEC2
BASIC program DECTANY 1 and DECTANY 2
General conversion program
Appendices
BASIC program ANYTDEC1
BASIC program ANYTDEC2
BASIC program DECTANY1
BASIC program DECTANY2
CHAPTER 10
CHEQUE WRITER
Introduction
Software packages which include cheque writers
BASIC program CHEKRITE
Appendix
BASIC program CHEKRITE
CHAPTER 11
THE 3X = 1 SEQUENCE
Introduction
The awesome power of “3X + 1”
The mystery of “3X + 1”
The 3X + 3 sequence
Avenues for further exploration
Appendix
BASIC program THREEXPLUS
CHAPTER 12
DIOPHANTINE EQUATIONS
What is a Diophantine equation ?
Solution of Diophantine equations
Diophantine equations with large coefficients
Solving Diophantine equations on the computer
Second order indeterminate equations
Appendices
Diophantine equation with large coefficients
Program for solving Diophantine equations
CHAPTER 13
THE NAME OF THE GAME IS . . . LIFE!
Can a cluster of dots have life?
Rules of the game LIFE
Exercise care when playing this game
Some simple life forms
The R-pentonimo and other curiosities
Scope for creative play
Variations of the game Life
Use of a computer for playing Life
Appendix
BASIC program for Conway’s simulation game life
CHAPTER 14
MAGIC SQUARES
Introduction
Magic square type I
Magic square type II
Fourth order magic squares
Higher order magic squares
How to generate an odd-order magic square
Alternative method for generation 3 x 3 magic squares
4 x 4 magic squares of type III
Appendices
BASIC program for magic squares
Magic square of order 15 generated by the program in Appendix 14.1
CHAPTER 15
A Select Bibliography
Index