The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients.
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.
Approximation of π :
Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"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.
There, under the Gupta emperors, 1,000 years before Galileo and Kepler and Newton, Indian thinkers developed a revolutionary idea without which modern science could not exist: the concept of mathematical zero, along with the related system of numerals that is called Arabic but was, in fact, invented here. By the fifth century, an Indian had discovered the earth's axial rotation. Well before the Renaissance re-illuminated Europe, Indian mathematicians had explored the upland realms of quadratic equations and cube roots, had become the first to assign 3.1416 as the value of pi, and had mastered the concept of infinity. Throughout most of history, in fact, Indian science and Indian culture generally matched and at times exceeded anything anywhere else in the world.
The above material is collected from various sources.However the conceptualization comes possibly from various slokas of Ganapati atharva sheersha which will be discussed later in my blog.
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