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 Atharvaveda, 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 selfcontained masterkey 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.
