**Vedic Mathematics: rapid mental calculation**

What is Vedic Mathematics? It is a Mental, One-Line system of Arithmetic developed in India over 2,000 years ago, that gets children off the calculator and enabling them to do large multiplications in their head within seconds. There are 16 Universal Sutras or Formulae to learn, and in this Lecture, you will be familiarized with about 6 of them.

It improves Memory Skills and Confidence. Teenage children welcome, as they will benefit from this demonstration. People all over the world are currently getting excited about this ancient lost Knowledge, and over 20 schools in the world have now adopted this technique.

**VEDIC MATHEMATICS REDISCOVERED**

ARTICLE by JAIN

for NEXUS MAGAZINE Aug 2003

ARTICLE by JAIN

for NEXUS MAGAZINE Aug 2003

Some questions to ponder upon:

• How could the Aryan civilization, near the Hunza Valley, 3,000 years

ago, mentally compute mathematical operations that today only a

calculator could achieve?

• And if the mathematics could not be done mentally, how could they do everything we know today, IN ONE-LINE? eg: converting the fraction 1/19 into a decimal is an 18 digit answer that requires 35

lines of exhausting long division, how could they do it in a one simple

line solution?

• Why is NASA secretly using this MENTAL, ONE-LINE SYSTEM OF ARITHMETIC in the field of Advanced Artificial Intelligence? and not incorporating it into our current mathematics curriculum?

• Why are many of Bill Gate's Mathematicians Indians?

• Is the decimal form of Pi (3.141592) a sonic code for dedications to Krishna?

• What does the Bhagavad Gita have to say about this lost science of Clairvoyant Calculation that the ancient Temple Builders employed?

• How can you become a Human Bio-Calculator?

• Is the current Western Mathematics Curriculum keeping our Children in a state of limited intelligence?

The answers to all these questions are found by understanding the ancient system of Vedic Mathematics as rediscovered by Bharati Krsna Tirthaji (1884-1960), of Puri Govardhan Math, dux of India in Mathematics and a Sanskrit Philosopher who wrote and spoke perfect

English, he reached the position of a Shankacharya (the spiritual head of India 100 years ago, like a Dalai Lama or Vatican Pope), renunciated several high official positions in society to retreat into a forest for 7 years as a yogi, between 1911 and 1918 in which time he collected all the lost mathematical knowledge (Ganita

Sutras), improved and reconstructed them to 16 basic Sutras or word formulae that solve every known mathematical problem. These 16 Volumes relating to the 16 Sutras was our legacy from the ancient past.

This highly intelligent and sophisticated system of Mental, One-Line Arithmetic was taught by The Master to his main student, who today is the leading exponent in the world: Maharishi Mahesh Yogi, the long white-haired and bearded yogi that many of the 60s generation know of as the Beatle’s guru. He is considered as the greatest human bio-calculator on the planet today, holding the vision of raising the collective consciousness of all nations by re-introducing the lost Vedic Mathematics Sutras early in a child’s spiritual and educational development. Imagine a maths class in India today, like in the times of old when knowledge was passed on as an oratradition, and the teacher quickly calls or drills out certain numbers to multiply or divide and the children instantly reply with the correct intuitive answers! Today, in schools where Maharishi’s Transcendental Meditation technique are used students perform remarkably well academically, viewing Mathematics as a Universal Language and therefore often winning the highest competitive prizes in mathematics.

Maharishi organized the scattered Vedic Literature into a complete science of consciousness for both its theoretical and practical value, describing the 16 Sutras as fundamental impulses of intelligence that structure all the Laws of Nature and those that govern the Universe.

Maharishi, the Founder of TM, once said:

"Vedic Mathematics is that one field of knowledge which fulfils the purpose of education by developing the total creative genius of the individual, giving him/her the ability to be always spontaneously right and automatically precise so that his/her action, supported by Natural Law, is always effortlessly fulfilling."

"Vedic Mathematics is that one field of knowledge which fulfils the purpose of education by developing the total creative genius of the individual, giving him/her the ability to be always spontaneously right and automatically precise so that his/her action, supported by Natural Law, is always effortlessly fulfilling."

Unfortunately, all of Bharati Krsna's 16 Volumes for the 16 Sutras were confirmed lost in 1958 after Bharati Krsna Tirthaji returned from the USA tour, sponsored by the Self-Realization Foundation: the successors of Paramahansa Yogananda (who died in 1952, and who

introduced Yoga to the West). Disciples observed that people in the streets of India were imitating Tirthaji's lectures and dazzling audiences with mathematically mis-used psychic powers, and begged the Master to write a book just before his death in 1960. This single volume, called VEDIC MATHEMATICS, has become the bible on this subject and spawned a thousand web-sites worldwide. Maharishi schools disseminated the teachings to England where certain schools have adopted the Vedic curriculum but the irony is that today

India is struggling to release the British curriculum and NASA have adopted it fully in the realms of advanced robotics. Calculations that can be solved as quick as lightning are a great tool to adopt, but you wouldn’t want to teach it worldwide in the fear that you may churn out a generation of child geniuses that may threaten the intellectual status quo.

The gift that the Hindus gave to world, thousands of years ago, and that which is currently responsible for 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 concept of creation and void known as "Bindu" or The Zero Point. In Maths, it makes the magic work eg: if you wish to multiply 98 x 98 we need to understand Zero and Unity. All Vedic Maths is based on the understanding of Unity Consciousness which means they utilize processes or Number Bases that correspond to:

0, 10, 100, 1000, 10000 etc all of which add to 1.

Let us look at some practical examples, in light of the fact that the Vedas, literally "the illimitable storehouse of All Knowledge" came under 4 headings or categories like Ayurveda (Healing), and Vedas for Music and Astronomy etc and one relevant sub-Veda that related to Temple Building and Engineering and therefore Mathematics called SthapathyaVeda. Thus a Vedic Mathematician was also an astronomer, healer and poet. It was a total system. As a temple builder, there was no pen and paper, you simply calculated in your head. You are out in the field and you need to tile a square floor that is, say 108 units square. How do you do it with mental ease?

I think only of the excess "8", saying how much is 108 more than my Base of 100. It is "8". So I will merely add this "8" to the number in question "108" and tag on the squaring of this excess:

108 Squared = 108 + 8 / 8x8

= 116 / 64

= 11,664

Its very simple.

Here is another Mental, One-Line Calculation:

**Sutra: By The Excess**

The Multiplication of Numbers Over a Base

108 x 109 can be computed in one second by understanding this Pattern Recogition:

I add the excess of "8" to the other number "109" and then tag on the multiplicatin of those two excesses: "8" and "9".

108 x 109 = 109 + 8 / 8 x 9

= 117 / 72

= 11,772

**Sutra: By The Deficiency**

The Squaring of Numbers Under a Base

To solve 98 Squared (98 x 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 Sutras to effectively solve the problem. It is called: "By The Deficiency":

"By whatever the deficiency, lessen it further by that much and set up the square thereof"

says one of the 16 Sutras. 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:

= 96 / _ 4

We almost have our answer. What we need to know is that since our Base is 100, it has 2 zeroes, therefore this fact governs the need for 2 spaces or 2 digits after the "forward slash" symbol ( / ). By inserting or inventing The Zero as a "Place Marker", the answer is achieved:

98 Squared = 96 / 04

= 9,604.

(Perhaps the greatest invention of all time, the Hindu creation of the Zero was to change the world unimaginably as time passed on leading to the ability to send Vimana U.F.O craft and rockets into space, to supercomputers and thus the ancient and continuing battle between Michael and Lucifer:

Archangel Michael's Internal Light Vehicle Merkabah Time/Space Travel and Natural Spiritual Powers Versus Lucifer's daring invention of the External Merkabah or Artificial Technological Metal Spacecraft).

Observe similar examples:

97 squared = 97 - 3 / 3x3

= 94 / 09

96 squared = 96 - 4 / 4x4

= 92 / 16.

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 3 zeroes on the right hand side of the ( / ).

998 squared = 998 - 2 / 2x2

= 996 / _ _ 4

= 996 / 004.

= 996,004

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 4 Zeroes determine the need for 4 digits after the ( / ).

= 9996 / 0004

= 99,960,004.

There is a world-wide 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 formulae are certainly wrong or inadequate: for example, the formulae for sphere packing in the higher dimensions increase up to the 6th Dimension then suddenly decrease for higher dimensions, which is simply absurd.

Unfortunately, some die-hard senior mathematicians in an attempt to protect the crumbling foundations that they now stand on feel threatened by the lightning quick mental calculations of the Vedic seers, and go to great lengths to deride Vedic maths as a "bag of tricks". And of course, many insecure teachers worldwide are afraid to rewrite all their course material.

Here is another example illustrating its utter simplicity:

"The Path of Least Resistance", or "The Law of Economy".

**Sutra: By One More:**

The Squaring of Numbers Ending in 5

If we wanted to square the number 25, i.e. 25 x 25, we would conventionally take 3 lines of working out. Vedic Mathematics 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 Previous Digit". Observing that 25 is a 2 digit number, 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 3. The word "By" in the Sutra really means "to multiply". The setting out for the first half of the answer is thus:

252 = 2 "By" 3 / ........

= 2 x 3 / ........

To this we tag on the last digit "5" squared:

= 2 x 3 / 5 x 5

= 6 / 25

Thus the answer is 625.

Similarly, all other numbers that end in 5, when squared, can be done instantly:

152 = 1 x 2 / 5 x 5 = 2 / 25 = 225

352 = 3 x 4 / 5 x 5 = 12 / 25 = 1,225

452 = 4 x 5 / 5 x 5 = 20 / 25 = 2,025

952 = 9 x 10 / 5 x 5 = 90 / 25 = 9, 025

**Sutra: Vertically and Crosswise:**

Fig 137d

*Sutra: Vertically and Crosswise*

Here is another simple Sutra, the one that Bharati Krsna Tirthaji refers to as most widely used, called "Vertically and Crosswise" and solves all multiplication by application of a pattern (which is registered by the Right Brain as Feminine-Natured Mathematics in contrast to the logical Male Left Brain style of moths you learnt at school).

eg: To find 26 Multiplied by 31 in One-Line, we need to look at a Pattern,

viz: This Sutra, known as: "Vertically and Crosswise" shows we will have

a 3-Digit Answer represented by the 3 short horizontal lines.

Here is how we traditionally write the setting out for "26 x 31":

2 6

x

3 1

------

_ _ _

Notice there are 4 digits involved ( 2, 6, and 3, 1) and let them be represented by a small circle or dot and that explains the format seen in Fig 137e. This will help you to understand "CROSS ADDITION" which is shown as the middle part:

[ (2 x 1) + (6 x 3) ] and uses both multiplication and addition in the form of the letter "X" and corresponds to the "cross-over of the optical nerve in the brain" shown in Fig 137e below. (Here, the symbol "x" = Multiplication):

= 2 x 3 (2 x 1) + (6 x 3) 6 x 1

= 6 2 0 6 (nb: the "2" of the �20” is carried over to the left hand side).

= 8 0 6

= 806 (This shows only the mental workings. The Multiplication of 26 by 31 can be solved mentally!)

There are 16 Jaw-Dropping Sutras or simple Sanskrit Word Formulae which solve all known mathematical problems in the branches of Arithmetic, Algebra, Geometry and Calculus are easy to understand, easy to apply and easy to remember.

This Vedic One-Line Mental Arithmetic is very helpful in stimulating Modern Mathematicians to adopt its simplicity and quickness. Once initiated to these Vedic rules, students of all ages will appreciate and enjoy the enhanced subject.

The aim of Vedic Mathematics is to bring this long-hidden treasure trove of intelligent mathematical knowledge within easy reach of everyone who wishes to obtain it and benefit by it.

Sutra: Digital Sums: For Multiplication By Eleven

Sutra: Digital Sums: For Multiplication By Eleven

When scientists have a problem, say with electronic data, and they need to send it efficiently, the solution is invariably Compression. Digital Compression is a powerful Sutra that solves multiplication by 11 very quickly.

If we wanted to multiply 25 x 11 we merely add the two digits of the 25 and say "2 + 5" which is 7 and insert it between the two digits. Thus the answer is 275. Another way of showing this is to separate the two digits and insert their digital sum:

25 x 11 = 2 (2+5) 5

= 2 7 5

39 x 11 = 3 (3+9) 9

= 3 12 9 (nb, the "1" of the "12" gets carried over to the left)

= 429

RAPID MENTAL CALCULATION

Eg: What is 108 x 109 in 5 seconds?

Solution. In Base 100, both numbers exceed the Base by 8 and 9 respectively.

Add the 8 to the 109, giving 117 / _ _

which gives us half the answer.

Then tag on the multiplication of those two excesses,

which is 8 x 9 = 72.

Thus the mental answer is 117 / 72 or 11,772

Its brilliant and simple.

Visit Jain Mathematics website : http://www.jainmathemagics.com/page/5/default.asp