history of kerala mathematics

With three-fourths Puruṣa went up: one-fourth of him again was here.The formula is accurate up to five decimal places, the true value being 1.41421356...According to mathematician S. G. Dani, the Babylonian cuneiform tablet An important landmark of the Vedic period was the work of Among the scholars of the post-Vedic period who contributed to mathematics, the most notable is Draw a square. ... as is shown by the elements of Mesopotamian omen literature and astronomy that entered India at that time and (were) definitely not ... preserved orally.The earliest mathematical prose commentary was that on the work, Typically, for any mathematical topic, students in ancient India first memorised the It is well known that the decimal place-value system The earliest surviving evidence of decimal place value numerals in India and southeast Asia is from the middle of the first millennium CE.There are older textual sources, although the extant manuscript copies of these texts are from much later dates.A third decimal representation was employed in a verse composition technique, later labelled

"The oldest extant mathematical manuscript in India is the The surviving manuscript has seventy leaves, some of which are in fragments. The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results.

These include the following (infinite) geometric series: Their work includes commentaries on the proofs of the arctan series in Parameshvara (c. 1370–1460) wrote commentaries on the works of For each case, Citrabhanu gave an explanation and justification of his rule as well as an example. The origins of mathematical thought lie in the concepts of number, magnitude, and form. 3,. pp. Such concepts would have been part of everyday life in hunter-gatherer societies. "Ideas of Calculus in Islam and India." The idea of the \"number\" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between \"one\", \"two\", and \"many\", but not of numbers larger than two. 61-62.

"Was Calculus Invented in India?"
In In this segment of indiavideo's conversation series, we feature Dr. K. Ramasubramanian. Beginning at half the square, draw two other similar squares below it; below these two, three other squares, and so on. This period saw mathematicians such as This ancient text uses the following as trigonometric functions for the first time:Later Indian mathematicians such as Aryabhata made references to this text, while later This Chhedi calendar (594) contains an early use of the modern Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalisation of Chapter 18 contained 103 Sanskrit verses which began with rules for arithmetical operations involving zero and negative numbersTo the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value.Also in chapter 18, Brahmagupta was able to make progress in finding (integral) solutions of He then used this lemma to both generate infinitely many (integral) solutions of Pell's equation, given one solution, and state the following theorem:

In particular, their fascination with the enumeration of very large numbers and Mathematicians of ancient and early medieval India were almost all Prodigious energy was expended by ancient Indian culture in ensuring that these texts were transmitted from generation to generation with inordinate fidelity.That these methods have been effective, is testified to by the preservation of the most ancient Indian religious text, the Mathematical activity in ancient India began as a part of a "methodological reflexion" on the sacred Extreme brevity was achieved through multiple means, which included using II.64. Archive for History of Exact Sciences, vol 18.The value of this approximation, 577/408, is the seventh in a sequence of increasingly accurate approximations 3/2, 7/5, 17/12, ... to Mathematics Department, University of British Columbia, harv error: multiple targets (2×): CITEREFSingh1936 ( harv error: no target: CITEREFNeugebauerPingree_(eds.
The contributions from other civilisations – most notably China and India, are perceived either as borrowers from Greek sources or having made only minor contributions to mainstream mathematical development.

Link A. Seidenberg, 1978.

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