Vedic Mathematics

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Om Namah Sivaya all

 

A very interesting article:

 

|| Vedic Mathematics ||

 

One of the foremost exponents of Vedic mathematics, the late Bharati

Krishna Tirtha Maharaja, author of Vedic Mathematics, has offered a

glimpse into the sophistication of Vedic mathematics. Drawing from the

Atharva-veda, Tirtha Maharaja points to many sutras (codes) or

aphorisms which appear to apply to every branch of mathematics:

arithmetic, algebra, geometry (plane and solid), trigonometry (plane

and spherical), conics (geometrical and analytical), astronomy,

calculus (differential and integral), etc.

Utilising the techniques derived from these sutras, calculations can

be done with incredible ease and simplicity in one's head in a

fraction of the time required by modern means. Calculations normally

requiring as many as a hundred steps can be done by the Vedic method

in one single simple step. For instance the conversion of the fraction

1/29 to its equivalent recurring decimal notation normally involves 28

steps. Utilising the Vedic method, it can be calculated in one simple

step.

Secular and spiritual life were so intertwined in Vedic India that

mathematical formulas and laws were often taught within the context of

spiritual statements (mantras). Thus while learning spiritual lessons,

one could also learn mathematical rules. The Vedic mathematicians

prefer to use the devanagari letters of Sanskrit to represent the

various numbers in their numerical notations rather than the numbers

themselves, especially where large numbers are concerned. This made it

much easier for the students of this mathematics to record the

arguments and the appropriate conclusions. In order to help the pupil

to memorise the material studied and assimilated, they made it a

general rule of practice to write even the most technical and abstruse

textbooks in sutras or in verse (which is so much easier - even for

children - to memorise). And this is why we find not only theological,

philosophical, medical, astronomical and other such treatises but even

huge dictionaries, in Sanskrit verse! So from this standpoint, they

used verse, sutras and codes for lightening the burden and

facilitating the work (by versifying scientific and even mathematical

material in a readily assimilable form)!

The code used is as follows:

The Sanskrit consonants

ka, ta, pa, and ya all denote 1;

kha, tha, pha, and ra all represent 2;

ga, da, ba, and la all stand for 3;

Gha, dha, bha, and va all represent 4;

gna, na, ma, and sa all represent 5;

ca, ta, and sa all stand for 6;

cha, tha, and sa all denote 7;

ja, da, and ha all represent 8;

jha and dha stand for 9; and

ka means zero.

Vowels make no difference and it is left to the author to select a

particular consonant or vowel at each step. This great latitude allows

one to bring about additional meanings of his own choice. For example

kapa, tapa, papa, and yapa all mean 11. By a particular choice of

consonants and vowels one can compose a poetic hymn with double or

triple meanings. Here is an actual sutra of spiritual content, as well

as secular mathematical significance:

gopi bhagya madhuvrata

srngiso dadhi sandhiga

khala jivita khatava

gala hala rasandara

While this verse is a petition to Lord Krishna, when learning it one

can also learn the value of pi/10 (i.e. the ratio of the circumference

of a circle to its diameter divided by 10) to 32 decimal places. It

has a self-contained master-key for extending the review to any number

of decimal places. The translation is as follows: "O Lord anointed

with the yoghurt of the milkmaids' worship (Krishna), O saviour of the

fallen, O master of Shiva, please protect me."

At the same time, by application of the consonant code given above,

this verse directly yields the decimal equivalent of pi divided by 10:

pi/10 = 0.31415926535897932384626433832792. Thus, while offering

mantric praise to Godhead in devotion, by this method one can also add

to memory significant secular truths.

 

Source: http://archives.amritapuri.org/bharat/

 

Yours in the Service of the Divine

sridhar