Indian Mathematics, an Introduction
This Book Taps The Mathematical Traditions Of India For Some Simple And Elegant Methods Of Performing Arithmetic Calculations. There Are Techniques For Multiplication, Division, Squaring, Square-Rooting And Factorisation That, Once Mastered, Are Faster Than The Conventional Approaches Currently In Wide Use. Errors Arising Out Of Carelessness In Calculation Were Apparently A Problem Faced By Our Ancestors Too! They Devised An Amazingly Simple Technique To Catch Such Errors. These Techniques Are Presented In This Book In A Lucid Manner, With A Large Number Of Examples To Illustrate The Basic Ideas And Elaborate On Their Variations. The Use Of Sanskrit Terms Has Been Minimised. Most Of The Methods Described Are General And Work For All Numbers, Not Just For Special Cases. The Mixed-Number, Or Mishrank, Which Contains Both Positive And Negative Digits, Is Extremely Useful In Simplifying Calculations And Is Widely Used In This Book. The Reader Will Find That Ideas Such As These Can Be Effectively Grafted To The Conventional Methods.The Book Will Interest A Wide Audience. Students Will Benefit The Most, Since They Can Easily Make The Methods Of This Book Their Own. They Will Soon Find That Much Of Their Arithmetic Can Be Performed Orally. Adults Will Find It A Pleasure To Discover New And Elegant Ways Of Doing Things They Already Know. The Computer Enthusiast May Find Hidden In The Simple Methods Ideas To Speed-Up Machine Computation. Finally, The Mathematically-Inclined May Find Their Curiosity Sufficiently Aroused To Go Beyond This Book And Delve Deeper Into The Indian Mathematical Legacy.
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Nikhilam Special Multiplication
Multiplication Using Urdhva Tiryaka
Evaluation of Powers
Redundant Number System 42
Notes and Explanations
3-digit algorithm ASHOK JHUNJHUNWALA back one step bers binary number system calculation using Navasesh Chapter Check the calculation check your results compute corrected partial dividend cross-multiplication cross-subtraction decimal base decimal places determine deviations digit number digits are obtained divided dividend digit divisible by 11 Dwandwa Find the square higher digits hundreds place India INDIAN MATHEMATICS last digit left-most Let us illustrate Let us take long multiplication mathematics Mishrank multi multiplication technique negative Ekadhika negative number negative partial dividends normalisation Note number is divisible number of digits number system numbers close obtain the quotients original number overlapping digits Perform the following positive Ekadhika previous quotient digit prime numbers reduce the previous remainder digit results using Navasesh right-most digit second digit second divisor digit shifted left single digit sqft sqin sub-base subtracted to obtain third digit three digits three numbers units digits Urdhva Tiryaka multiplication Vedic Mathematics verified using Navasesh