topics: |  science | history | india

Short overview of Sanskritic contributions to
  a. astronomy,
  b. geometry [shulva],
  c. arithmetic algebra and trigonometry,
  d. ayurveda,
  e. chemistry,
  f. botany,
  g. physics,
  h. other sciences.

Greeks could count till 10,000, Romans till 1000, but in vedic times, numbers
upto the parArdha (1014) had been used in computation, and all numbers below
these could be easily and clearly expressed.  The orders of ten - dash,
shata, sahasra, niJut, (ten-thousand) etc.  How to divide one thousand
evenly was a special problem, and in the taittariya saMhita, Indra and VishNu
were praised for arriving at a satisfactory solution to this problem.

mathematical series:
	taittariya saMhitA: 1,3,5; 19, 29, 39... 99 etc.
	vAjseniya saMhitA:  4, 8, 12, ... 48
	paNchaviMsha brAhmaNa: 24, 48, 96, ... 49152, 98304, 393216 and other
		series
	shatapatha brAhmaNa: 24+28+32...48 = 756
	vrihaddevatA: 2+3+4+...1000 = 500499

based on results in the baudhAyana sutra, it is presumed that this formula
   may have been known:  1+3+5+... 2n+1 = (n+1)² [sic]
shulva sutra: fractions, e.g. 7 ½ ÷ 1/25 = 187 ½

Decimal system: Although Arab scholars openly admitted learning the place
	value system from India, until recently many European scholars would
	not accept Hindus as the inventors of this system.

"fortunately there is no evidence [of the place-value notation] in ancient
Greece or Rome, otherwise Europeans would definitely have claimed that
Indians had learned these from those lands."

For instance, the "sine" notation used in trigonometry: in the 3d-4th
c. surya siddhAnta has a table of sines, Arabs admit they learned its use
from India, and from the Arabs this reached Europe in the 12th century.

Despite this, noted historian of mathematics Paul Tannery claims that it was
known in Greece, although Hipparchus had used a table of chord lengths.  One
European scholar has commented that Tannery and his tribe could not believe
that Indian mathematics may have discovered anything.  [chapter
2C. Arithmetic, Algebra and Trigonometry. p.25-28]

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