Vedic Mathematics is a form of mathematics, which was in practice in the prehistoric India. Vedic Mathematics is basically a set of Algorithms to solve frequently encountered Mathematical problems. Many ancient Hindu saints and others (including Shankaracharyas) contributed to this amazing mathematical idea.

Recently, Vedic mathematics has increasingly gained popularity all over the world as a simple technique to carry out algebraic and geometric operations by hand.

The concepts of Vedic Mathematics were studied in detail and revised by Jagadguru Swami Bharathikrishna Tirthaji of Puri Jaganath. He did extensive researches on the topic for a whole lifetime and many of the results were published by his desciples in the book, Vedic Mathematics, in the 1960s.

Vedic Mathematicians used Sanskrit alphabets to represent big numbers. It has been found that many of the Sanskrit Mantras represent numbers. (The famous Gayatri Mantra is said to have a number representation 108, while added after decoding).

A Few Simple Examples

Note: (x)(y) represents a number obtained by concatenating the digits of x with those of y.

• To multiply a positive integer with 9, 99, 999, ...
• Result= (Original number -1) (Digits obtained by subtracting 9 from each of these new digits).

Example: 999x343=342657

i.e, 342 and (9-3)(9-4)(9-2)

• To calculate the square of any number ending with five:
• ((x)(5))^2 = (x)(x+1)(25)

Examples: 15^2 = ((1)(1+1))25 = 225.
95^2 = (9(9+1))25 = 9025.

(Pronounced "Vay-dick") A system based on 16 sutras contained in the Vedas, Vedic Mathematics makes it possible to solve long mathematical problems very quickly in one's head. Some of the sutras and corollaries do require paper and pen, however.

Vedic maths were lost for centuries before Sri Bharati Krisna Tirthaji rediscovered them from 1911 to 1918. The original 16 volumes of his work were synthesized into his final work, Vedic Mathematics, published in 1965, five years after his death.

These 16 mathematical shortcuts and their corollaries (also called the upsutras or subsutras) are explained in the nodes below:

1. Ekadhikina Purvena; corollary: Anurupyena

2. Nikhilam Navatashcaramam Dashatah; corollary: Sisyate Sesasamjnah

3. Urdhva-Tiryagbyham; corollary: Adyamadyenantyamantyena

4. Paraavartya Yojayet; corollary: Kevalaih Saptakam Gunyat

5. Shunyam Saamyasamuccaye; corollary: Vestanam

6. Anurupye - Shunyamanyat; corollary: Yavadunam Tavadunam

7. Sankalana - Vyavakalanabhyam; corollary: Yavadunam Tavadunikritya Varga Yojayet

8. Puranapuranabyham; corollary: Antyayor Dasakepi

9. Chalana - Kalanabyham; corollary: Antyayoreva

10. Yaavadunam; corollary: Samuccayagunitah

11. Vyashtisamanstih; corollary: Lopanasthapanabhyam

12. Shesanyankena Charamena; corollary: Vilokanam

13. Sopaantyadvayamantyam; corollaries: Gunitasamuchyah and Samuccayagunitah

14. Ekanyunena Purvena; corollary: Dhvajanka

15. Gunitasamuchyah; corollary: Dwandwa Yoga

16. Samuccayagunitah; corollary: Adyam Antyam Madhyam

So far, I have only noded the 18 sutras and corollaries that I was absolutely certain I understood. The sutras and corollaries that are italicized are not currently noded.

Important Note: There is much controversy over whether these sutras were actually found in the Vedas, or if Tirthaji invented some or all of them. Tirthaji said these sutras were found in an appendix of Atharvaveda, which is now lost. There is also controversy (and some conspiracy theory) over whether these sutras can be called a mathematical system. To read about the controversy, see the last three links listed in the resources below.

RESOURCES:
Vedic Mathematics by Sri Bharati Krisna Tirthaji
http://www.vedamu.org/Mathematics/course.asp
http://www.sanalnair.org/articles/vedmath/intro.htm
http://www.vedicganita.org/ganitsutras.htm
http://hinduism.about.com/library/weekly/aa062901a.htm
http://www.vedicmaths.org/
http://www.hinduism.co.za/vedic.htm
http://www.wired.com/news/culture/0,1284,64575,00.html
Mathemagics by Arthur Benjamin and Michael B. Shermer
http://en.wikipedia.org/wiki/Vedic_math
http://www.tifr.res.in/~vahia/dani-vmsm.pdf
http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html

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