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
Notes and Explanations
added addition answer base bers binary calculation carry Chapter close compute continue corrected partial dividend decimal places described determine deviations divided dividend digit divisible by 11 divisor digit Dwandwa earlier Example final Find the square following numbers gives go-back greater higher digits inches India INDIAN MATHEMATICS involves known less Let us illustrate Let us take mathematics mentally method Mishrank multi multiplied Navasesh needs negative Ekadhika Nikhilam normalisation Note number is divisible obtained Once operation original overlapping pairs Perform positive preferable previous quotient digit procedure proceed reduce remainder represented result right-most second digit shifted shown Similarly simple single digit sqft sqin square root step straight-division sub-base subtract technique term third three digits tion tradition understanding upto Urdhva Tiryaka verified vertical whereas wish write written yields zeros