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NEWSCIENCENEWSCIENCENEWSCIENCE Watching a child go through our education system is like watching reverse metamorphosis: in flies a beautiful butterfly; out crawls a caterpillar. (from Jf You Want To Be Rich And Happy, Don't Go To School, by Robert Kiyosaki, 1992) THE MAGIC OF VEDIC MATHEMATICS by Jain © 2003 ago, and which is currently employed in our global silicon chip technology, was none other than the invention of zero and the use of the decimal point. We call our common numbers "Arabic numerals" but, really, they extend back to the Hindu con- cept of creation and void known as Bindu or "the Zero Point". All Vedic mathematics is based upon the understanding of Unity con- sciousness, which means the utilisation of number bases that corre- spond to: 0, 10, 100, 1,000, 10,000, ete., all of which add to 1. T= gift that the Hindus gave to world, thousands of years When the number being squared is above the base—of 100, here—we add the excess and square the excess: 104x104 = 104+4/4x4 = 108/ 16 = 10,816 104x105 = 104+5/4x5S = 109/20 = 10,920 What if we enlarged our numbers to 998 squared? It is close to 1,000, so we say Base 1,000 and know to have three spaces (for zeroes or digits) on the right hand side of the (/ ). 998 squared = 998-2 / 2x2 = 99% /__4 = 996 / 004 = 996,004 100, 1,000, There are 16 sutras, or simple Sanskrit word formulas, which solve all known mathematical problems in the branches of arith- metic, algebra, geometry and calculus. They are easy to under- stand, easy to apply and easy to remember. This Vedic one-line mental arithmetic is very helpful in stimu- lating modern mathematicians to adopt it for its simplicity and speed. Once initiated into these Vedic rules, students of all ages tend to appreciate and enjoy the enhancement of mathematics. Vedic mathematics is a previously long-hidden treasure trove of intelligent mathematical knowledge, and it should be within easy reach of everyone who wishes to obtain it and benefit by it. Vedic mathematics is a total system. The Vedic mathematician was also an astronomer, an engineer, a musician, a healer and a poet. The temple builder had no pen and paper; he simply calcu- lated in his head. So, you are out in the field and you need to tile a floor that is, say 98 units square. How do you do it with such mental ease? Let's look at some practical examples. Understanding this, you can be calculating digits in the millions: 9998 squared = 9998-2 /2x2 = 9996 /___4 Since we are in Base 10,000, the four zeroes determine the need for four spaces (zeroes or digits) after the (/ ). = 9996 / 0004 = 99,960,004 There is a worldwide debate currently raging about the efficacy of Vedic mathematics versus the crumbling foundations of Western mathematics. Generally speaking, the theorems we all learned at school are not wrong, but clumsy. Some of the Western geometrical formulas are certainly inadequate. For example, the formulas for sphere packing in the higher dimensions increase up to the sixth dimension, then suddenly decrease for higher dimen- sions, which is simply absurd. Unfortunately, some diehard senior mathematicians, in an attempt to protect the crumbling foundations that they now stand on, feel threatened by the lightning-quick mental calculations of Vedic mathematicians and go to great lengths to deride Vedic maths as a "bag of tricks". The Squaring of Numbers Near a Base To solve 98 squared (98 x 98, or 98°), we must first determine what base we are in. It is close to 100, therefore we say Base 100. We must now choose one of the 16 major sutras to solve the prob- lem. The one to use here is called 'By the Deficiency—by what- ever the deficiency, lessen it further by that much and set up the square thereof". Sounds cryptic and meaningless, yet it quickly solves the problem. We get our answer by merely knowing how much is 100 less 98. Knowing that the deficiency is 2, we merely lessen 98 by 2 and then we tag on the squaring of that 2. As a one-line answer, the setting out would appear as thus: 98 squared = 98-2 /2x2 Simplifying it: = 9 / _4 We almost have our answer. What we need to know is that since our base is 100, it has two zeroes; therefore, this fact governs the need for two spaces for two zeroes or digits after the "forward slash" symbol (/ ). By inserting or inventing the zero as a "place marker", the answer is achieved: 98 squared = 96 / 04 = 9604 The Squaring of Numbers Ending in Five Here is another example illustrating the Vedic mathematical sys- tem's utter simplicity in demonstrating "the path of least resis- tance". If we wanted to square the number 25, i.e., 25 x 25, we would conventionally take three lines of working out. Vedic math- ematics merely looks at the question, applies one of the 16 sutras, and solves it mentally in one line. In this case, the sutra at work is "By One More than the One Before", that is, the previous digit. We observe that 25 is a two-digit number and 5 is the last digit, but we are mainly interested in "the previous digit", which is 2. We say, mentally, "What is one more than two? It is three." The word "By" in the sutra really means "to multiply". The setting out for the first half of the answer is thus: 25 squared = 2"by"3 /.... = 2x3 /... NEXUS = 39 10,000, etc., all of which add to 1. OCTOBER — NOVEMBER 2003 www.nexusmagazine.com