Actually the approximate value of pi was known in the Shulba Sutras in ancient India (not in the Vedas per se). Obviously knowing it to 32 places of decimal is impossible without the usage of modern numerical methods applied to analytical expressions unknown at the time.
The motivations for estimating pi in the Shulba Sutras was the construction of circular fire altars (which will obviously require at least a rough estimate of the ratio of the circumference to the diameter). They certainly determined that the ratio was universal, though estimating it to any degree of accuracy beyond 3.1416 was highly unlikely.
Contrary to the claims made by some of the posters, there was little transmigration to India from the Middle East between the Vedic period and the common era, so knowledge transmission from "older" (not really) Semitic societies is highly unlikely. Claims of middle eastern transmigrations were made by British scholars in the 19th century and have largely been discredited outside Britain.
I should qualify this remark by saying that I'm excluding those periods and/or parts of the middle east that were under Hittite, Indo-Greek, Selucid, Graeco-Bactrian or Achemeneid-Persian control during the period in question, and I'm excluding Afghanistan and Iran from my definition of the "middle east", since those societies were predominantly Indo-European like Northern and Central India.