Talk:Bhāskara II

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Contents 1 Dubious 2 Contributions 3 Very dubious 4 References ?

[edit] Dubious

"Proved that anything divided by zero is infinity in addition to establishing that infinity divided by anything remains infinity."

The above sentence is incorrect. Only non-negative real numbers divided by zero result in infinity. However, I don't know what Bhaskara proved. I'm tagging the article as dubious. --hdante 06:01, 18 June 2006 (UTC)

If you are suggesting that negative real numbers divided by zero result in a distinct negative infinity, it is certainly possible that Bhaskara identified positive and negative infinities, a la the real projective line. However, I'd agree that the article needs clarification on what exactly it was that Bhaskara "proved" about division and infinity. -Chinju 21:58, 4 July 2006 (UTC)

(Let me also note right off the bat that it's difficult to see a good motivation for concluding that 0/0 is infinity or that infinity/infinity = infinity; even if Bhaskara was thinking of something like the real projective line, on these particulars it would not support him [if the statement above of his conclusions is accurate].) -Chinju 22:03, 4 July 2006 (UTC)

I've removed the sentence. If someone knows what he actually said then they might put that in, but as it stands, it was nonsense. Gene Ward Smith 07:34, 19 August 2006 (UTC)

As an answer to Chinju. In the Lïlävatï, we find this text: a number divided by zero will be: "what has zero for divisor"; multiplied by zero, it is only zero but, in case of another prescription (ie. a new operation), it must remain in mind that it is "what has zero as a multiplier"; if zero is a multiplier and, again, zero is a divisor then the number has to be considered as unaltered

This means that ax0/0=a. And this is used by commentators in order to prove that a number divided by zero is infinite (I'll give Bhäskara's stanza later on about this word): suppose you have to calculate a/0 + b; you reduce to the same denominator: [a + (bx0)]/0 = a/0. So a/0 remains inchanged if you add (or remove) any number to this quantity.

In the Bïjagaṇita, Bhäskara says that a number divided by zero has also the name "illimited" (an-anta) and he explains the meaning of illimited with a stanza (based on a religious image): There must not be any change for it, which has been divided by zero, when quantities are added to, or removed from, it, as there is no change to the "Illimited" (ananta, another name of god Viṣṇu) when, at the time of the destruction of the world, as at the time of its creation, a multitude of beings enter in, or go out of, Viṣṇu.

François Patte 13:51, 30 August 2006 (ITC)

[edit] Contributions

I have no doubt about Bhaskara's significant contributions to Mathematics (including subfields), but the article seems a bit lengthy. Is it really necessary to list every single thing he ever did? Why not shorten the list(s) to the more important items (as opposed to what he "conceived" or conceptualized)?--ndyguy 16:46, 15 July 2006 (UTC)

[edit] Very dubious

This article about Bhäskara seems very dubious to me.

I cannot, right now, give a point to point criticism, it would be too long; I will just pick out some points in this article.

• Bhaskara (1114-1185) was born near Bijjada Bida (in present day Bijapur district, Karnataka state, South India) in Deshastha Brahmin family...

As Bhäskara says himself: There was in Vijjaḍaviḍa, town located in the Sahya mountains... The Sahyadri are located in northern Maharashtra state, almost 300km from Bijapur; it seems to be impossible that Bijapur was the place where Bhäskara was born.

• • Sahyadri is a long mountain range, covering the entire western coast of the Indian Peninsula, and not just 'located in northern maharashtra'.Shree (talk) 13:29, 10 December 2007 (UTC)

Moreover, in these Sahyadri, there exists a 12th century temple near Chalisgaon in the basement of which there is an inscription, written by Bhäskara's grand son, celebrating the foundation at this very place where Bhäskara lived, of a school dedicated to the studies of Bhäskara's works (See the translation by F. Kielhorn in Epigraphia Indica, Vol 1, Calcutta, 1892). The same stanza by Bhäskara says: ... a twice-born (dvija) from the Śäṇḍilya family... The Śäṇḍilya family is very famous and the inscription quoted above gives the genealogy of the Bhäskara's branch of this family established under the ruling Yädava dynasty in northern Maharashtra also.

The date for the death of Bhãskara (1185) is hypothetical; the last known work of Bhäskara (the Karaṇakutühala) is dated, in the text itself, 1183. The place where he died is also unknown and there is absolutely no proof, in texts or inscriptions, that Bhäskara went to Ujjain.

• In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations.

No, definitely not! The only equations mentioned in the Lïlävatï are Diophantine linear equations in chapter The kuṭṭaka, duplicated with some additions in the Bïjagaṇita. The same error occurs in the table of contents of the Lïlävatï (given later in the article): Indeterminate equations (Kuttaka), integer solutions (first and second order); only first order!

• A cyclic, Chakravala method for solving indeterminate equations of the form a² + bx + c = y.

The cakraväla is a chapter of the Bïjagaṇita used to solve Diophantine equations of second order of the form: ax² + c = y², and the solution of the complete quadratic equations appears in a later chapter the madhyamäharaṇa (the removal of the middle term).

I cannot understand the distinction between Diophantine equations of second order and Pell's equation which a particular case. All this is discussed by Bhäskara in the two chapters of the Bïjagaṇita entitled vargaprakṛti and cakraväla.

• Further extensive numerical work, including use of negative numbers and surds. In the table of contents of the Lïlävatï.

There are no negative numbers in the Lïlävatï; this is the first chapter of Bïjagaṇita. And there are only the rule of calculation for the square root ot an integer. The surds, according to the english denomination of calculation with square roots, is a chapter of the Bïjagaṇita entitled karaṇï and it is much more than what is call surds in ancient books of mathematics.

• Still in arithmetic section: Estimation of π.

Nothing like that in the Lïlävatï, this comes in the astronomical parts of the Siddhāntaśiromaṇi.

There are so many astonishing assertions in this article, when you master both mathematics and Sanskrit and can have a direct access to the texts in their original language, that I cannot quote everything... One more thing: the paragaph on differential calculus: differential calculus implies the notion of proximity, what mathematicians call topology, we cannot find any notion of this kind in Sanskrit texts, even in the sixteen and seventeen centuries.

François Patte 13:05, 30 August 2006 (ITC)

[edit] References ?

When I look at the math history article MacTutor History of mathematics page I find no reference to calculus under Bhaskara's article. The only references given to this seem to be slides on a physists webpage. Are their any scholarly articles on the subject? Shouldn't those be listed. Thenub314 14:58, 27 September 2006 (UTC)