Tuesday, March 31, 2015

MARCH 14,2015

Ancient India vis-à-vis Modern Science.'s photo.
Indian mathematician Aryabhata, among his many accomplishments, he discovered long before the west did, the approximate value of this Irrational and also famous Transcendental Number.
Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya... (499 CE, when he was 23 years old) and the Arya-siddhanta.

Ancient India vis-à-vis Modern Science.'s photo. Aryabhata worked on the approximation for pi (\pi), and may have come to the conclusion that \pi is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
Ancient India vis-à-vis Modern Science.'s photo. "Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."
This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.
It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert.
After Aryabhatiya was translated into Arabic (c. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.



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