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#3182. A forgotten Science

Mathematics, level: all
Posted Sun Jul 11 05:15:20 PDT 2004 by Ajhar Mahmood (milepearl12@hotmail.com).
Magical Methods
Education Consultant, India
Materials Required: Vedic Mathematics Books
Concepts Taught: Vedic Mathematics

It is being taught in some of the most prestigious institutions in England and Europe. NASA scientists applied its principles in the area of artificial intelligence. And yet, in the country of its birth it languishes as a forgotten science.
Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over. Experts suggest that it could be a handy tool for those who need to solve mathematical problems faster by the day.


1.What is Vedic Mathematics?
It is an ancient technique, which simplifies multiplication, divisibility, complex numbers, squaring, cubing, square and cube roots. Even recurring decimals and auxiliary fractions can be handled by Vedic mathematics


2.Who Brought Vedic Maths to limelight?
The subject was revived largely due to the efforts of Jagadguru Swami Bharathikrishna Tirthaji of Govardhan Peeth, Puri Jaganath(INDIA) (1884-1960). Having researched the subject for years, even his efforts would have gone in vain but for the enterprise of some disciples who took down notes during his last days. That resulted in the book, Vedic Mathematics, in the 1960s. These are now available in a book called
"VEDIC MATHEMATICS"
by H.H. Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaj or online in comprehensive format on www.magicalmethods.org

3.What is the basis of Vedic Mathematics?
The basis of Vedic mathematics, are the 16 sutras, which attribute a set of qualities to a number or a group of numbers. The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras (Phrases) and 120 words laid down simple steps for solving all mathematical problems in easy to follow 2 or 3 steps.
Vedic Mental or one or two line methods can be used effectively for solving divisions, reciprocals, factorisation, HCF, squares and square roots, cubes and cube roots, algebraic equations, multiple simultaneous equations, quadratic equations, cubic equations, bi-quadratic equations, higher degree equations, differential calculus, Partial fractions, Integrations, Pythogorus theoram, Apollonius Theoram, Analytical Conics and so on.


4.What is the Speciality of Vedic Mathematics?
Vedic scholars did not use figures for big numbers in their numerical notation. Instead, they preferred to use the Sanskrit alphabets, with each alphabet constituting a number. Several mantras, in fact, denote numbers; that includes the famed Gayatri mantra, which adds to 108 when decoded.


5.Is it useful today?
Given the initial training in modern maths in today's schools, students will be able to comprehend the logic of Vedic mathematics after they have reached the 8th standard. It will be of interest to every one but more so to younger students keen to make their mark in competitive entrance exams.
India's past could well help them make it in today's world.
It is amazing how with the help of 16 Sutras and 16 sub-sutras, the Vedic seers were able to mentally calculate complex mathematical problems.


6. Why did the Vedic Seers need Vedic Mathematics or Mental Mathematics?
The Vedic Seers were highly ritualistic in practice. All the four Vedas namely Rig Veda, Yajur Veda, Sama Veda and Atharva Veda, consist of Samhitas, Brahmanas, Aranyakas and Upanishads. Of these four, the first three namely Samhitas, Brahmanas and Aranyakas contain several thousand Mantras or Hymns, Ritual practices and their interpretations. The Vedic Seers were very particular about the time of doing the rituals. Hence they needed a very scientific and accurate calendar and time measurements. Hence we have the adage IST which once meant Indian Standard Time. But in recent times due to our laziness and carelessness, it has come to mean Indian Stretchable Time.
The Vedic culture was that of Yajna and the Vedic Purohits or priests were also very particular about the shape and size of the Yajna Kund. For this they needed a very highly developed Geometry and Trigonometry.


7. Where is Vedic Mathematics found?
Vedic Mathematics forms part of Jyotish Shastra which is one of the six parts of Vedangas. The Jyotish Shastra or Astronomy is made up of three parts called Skandas. A Skanda means the big branch of a tree shooting out of the trunk.

Some of the Sutras (Phrases) used in Vedic Mathematics :

1.Ekadhikena Purvena (One More than the Previous) is useful in solving Special Multiplications like 25X25, 95X95, 105X105 etc. Special Divisons like 1 divided by 19, 29, 39, . . .. 199 etc.

2. Eka Nunena Purvena (One less than the Previous) is useful in solving Special Multiplications like 777 X 999, 123456789X 999 999 999.

3. Urdhva Tiryak bhyam (Vertically and Cross-wise) is useful in General Multiplication of any number by any number.

4. Paravartya Yojayet (Transpose and Apply) is useful in solving Algebraic factors and divisions of some numbers etc.

5. Anurupyena (Proportionately)

6. Adhyam-Adhyena, Antyam-antyena (first by the first and the last by the last)
are useful in solving Quadratics

7. Lopana-stapana-bhyam (by (alternate) Elimination and Retention) is useful in factorizing long and harder quadratics..

8. Gunita-Samuchhayah Samuchhaya-gunitah which means "The product of the sum of the coefficients in the factors is equal to the sum of the coefficients in the product" is a Sub-sutra of immense utility for the purpose of verifying the correctness of our answers in multiplications, divisions and factorisations:

9. Sunyam Samya samuccaye(when Samuccaya is the same, that Samuccaya is zero) Samuccaya is a technical term which has several meanings. This is useful in solving many complex factors and equations.