Talk:Indian mathematics/Archive 2

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Changes made by India rising

User India rising has made a number of recent changes which need to be clarifies. First, s/he has removed the criticism of "Vedic Mathematics," moved the "Vedic Mathematics" section itself to the end of the article, and replaced the criticism by Amartya Sen and Michael Witzel by a link to an article by S. G. Dani.

The problem is that user India rising has the two "Vedic Mathematics" confused. The "Vedic Mathematics" that Sen and Witzel are criticizing is the broad program revisionist history involving Vedic Science and Vedic Mathematics (i.e. all kinds of claims for mathematics—for example, diophantine equations and the decimal place value system—originating in the Vedas) that was given a lot of publicity in the late 1990s, especially after the BJP government was formed in India, and even introduced in textbooks for children. The "Vedic Mathematics" that S. G. Dani is writing about is specifically about a book of that title, by Swamiji etc. etc. That book has been around since the mid-60s and Dani's criticism is not the first. Other critics have noted that the methods in that book are similar to the so called Tractenberg system.

I am surprised that user India rising got the two confused, especially since the section on Vedic Mathematics made a note of this fact. As for user India risings contention that Sen and Witzel are not qualified, I am not sure what is entailed in being "qualified?" Witzel is one of the world's foremost scholars on Rig Vedic sanskrit (and is Wales Professor of Sanskrit at Harvard); Sen, while primarily an economist and philosopher, is also a cultural critic, and his last book, The Argumentative Indian: Essays on Indian Culture and History is specifically about such topics. The quote from Witzel and Farmer was not included in order to be polemical, but rather to point out a number of authors (for example, S. Kak) who are involved in creating this revisionist literature.

As for the section "Vedic Mathematics" (and the Dani link) created by user India rising, it is really irrelevant, since it addresses one particular book, not the broad program of finding mathematics—created much later—in the Vedas.

I am therefore removing the new section on Vedic Mathematics created by user India rising and reinstating some of the text from the previous version of the article. Fowler&fowler«Talk» 10:02, 10 February 2007 (UTC)

India Rising has been indef-blocked for being a sock account of the banned user Hkelkar. - Aksi_great (talk) 11:15, 10 February 2007 (UTC)


Does Amartya Sen or even Witzel qualify WP:RS? Amey Aryan DaBrood© 18:04, 10 February 2007 (UTC)

Yes, they do. We are not talking about "Harmonic Analysis of Semi-Simple Lie Groups" or some other 20th century topic in mathematics. This is basic, like whether the decimal place value system was stated in the Vedas, or whether Diophantine equations were solved in the Vedas. As for India rising's edit, as I explained above, he has confused "Vedic Mathematics" (i.e. the broad revisionist and political program of claiming all kinds of mathematical credit for the Vedas) with a hackneyed book Vedic Mathematics that has been around since the mid-60s, whose author use to travel around India giving demonstrations. S. G. Dani's well-written criticism applies to that book, but that is not what is being discussed here. Basically, there are two options: either do away with the section on "Vedic Mathematics" (which doesn't have any citations anyway) or admit the critical appraisal. Fowler&fowler«Talk» 18:20, 10 February 2007 (UTC)
The last 2 ip edits were made by Hkelkar. Both IPs have been blocked. Please feel free to revert their edits. - Aksi_great (talk) 09:42, 11 February 2007 (UTC)

Reverts by user:Freedom skies

First it was banned user Hkelkar, now it is user:Freedom skies, who has reverted (or rather simply blanked content in) the article. The issue on hand is the section on criticism of "Vedic mathematics," which has been described in the above section. Freedom skies refuses to join the discussion here, being content instead with enigmatic edit summaries:

“ Edit summary 1:ancient mathematics not as sophesticated as modern mathematics needs editorialization now ? rm the very odd note, see also within the article itself and Wikiquote material" ”

and

“ Edit summary 2:To fowler&fowler, kindly refrain from adding wikiquote material and odd notes in an encyclopedic article. Refer to WP:Soap and other mathematics related articles for addition of such sections ”

What exactly is an "odd note?" The reason why that section is included, as I have explained above, is that "Vedic mathematics" is part of a broad revisionist political program—there being very little mathematics, other than some ritual geometry, in the Vedas. The section explains the politics behind the notion of "Vedic mathematics." As for "wikiquote" material, the quotes are specific to the section on hand, not meant for inclusion at a general site for quotations. Please explain why you are doing what you are doing. Fowler&fowler«Talk» 16:11, 11 February 2007 (UTC)

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as I have explained above, is that "Vedic mathematics" is part of a broad revisionist political program

Wikipedia is not a place for furthering agendas based on personal opinion. Inserting odd sections and needlessly adding flamebait material based on fears of "a broad revisionist political program" does not amount to fair rationale. "there being very little mathematics, other than some ritual geometry" is open to interpretation, your edits being based on very personal ones. I will, vigilantly remove content which is inappropriate for this article. The other related articles do not feature content of similar nature and inappropriate additions will similarily not be allowed in this one.

Regards.

Freedom skies| talk  22:38, 11 February 2007 (UTC)

The agenda that is being furthered (to use your words) is the myth of "Vedic mathematics." There was no mathematics in the Vedas other than some ritual geometry. I am happy to remove the criticism if all text on anything other than ritual geometry are removed. Fowler&fowler«Talk» 02:18, 12 February 2007 (UTC)
Quoting amartya sen is out of context. What does a random guy writing a book (I got more respect for Mohammed Yunus) know about math or Hindu scriptures? Unless there is actual criticism from other eminent Hindu figures or mathematics experts it doesnt belong in this article.Bakaman 21:48, 12 February 2007 (UTC)
"A random guy writing a book!" Well, as I mentioned in the section above, we are not talking about some contemporary topic in mathematics like "Ricci flows in three-dimensional manifolds." We are talking about whether the decimal place value system was stated in the Vedas, or whether Diophantine equations were solved in the Vedas. You may know Amartya Sen as the author of works on poverty and famine or as a philosopher, but Sen has had a long and prolific career and he was a mathematical economist for the first half of his career. See for example: Wiebke Kuklys's, Amartya Sen's Capability Approach: Theoretical Insights and Empirical Applications and search on page 41, or indeed look at Sen's own Collective choice and social welfare (Mathematical economics texts). He certainly knows enough mathematics to hold forth on this topic. Mohammad Yunis got the Nobel Prize for Peace and not Economics and is not a mathematical economist (by a long shot). Fowler&fowler«Talk» 22:41, 12 February 2007 (UTC)

There was no mathematics in the Vedas other than some ritual geometry.

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GEOMETRY, is that branch of Mathematics which treats of the magnitude and relation of figures, in the most general acceptation of the word - Elements of the Geometry of Planes and Solids: With Four Plates - by Ferdinand Rudolph Hassler

There is no branch of Mathematics which occupies so large a place in the school curriculum as Geometry - The Teaching of Mathematics in the United Kingdom - by Great Britain Board of Education, Edward Doyle

Mathematics became so vast a subject that mathematicians were forced to confine their efforts to one major branch: algebra, geometry, ... - Encyclopedia of Library and Information Science - edited by Miriam A. Drake

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Geometry is a field of Mathematics, Fowler&fowler.

I am happy to remove the criticism if all text on anything other than ritual geometry are removed.

Good to know. I'll do the honors.

Freedom skies| talk  11:45, 13 February 2007 (UTC)

Freedom skies: Please stop pasting a puerile sequence of quotes. No one is saying that Geometry is not a branch of mathematics; what I and the people quoted are saying is that it is incorrect to claim that topics like the decimal place value system, Diophantine equations or even Quadratic equations, which are not a part of geometry, were treated in the Vedas. The geometry Vedas was of a numerical nature involving ropes and altar constructions. Fowler&fowler«Talk» 14:16, 13 February 2007 (UTC)

No one is saying that Geometry is not a branch of mathematics

Yes you are, fowler. For everyone's benefit:-

There was no mathematics in the Vedas other than some ritual geometry.

Such inconsistencies are best demonstrated for everyone's benefit by "a puerile sequence of quotes" as you like to call them, fowler. You'll understand that I'll disregard your request of not quoting you.

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The geometry Vedas was of a numerical nature involving ropes and altar constructions.

Let's hold that little line to a challenge then; If Vedic mathematics is held to be more than altars and ropes then will you refrain from incessant, irritable reverts?

Did'nt think so.

Freedom skies| talk  15:59, 13 February 2007 (UTC)

Well, here is S. G. Dani, Professor of Mathematics at Tata Institute, Bombay:[1]
“ The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras. ”
Here Dani describes a procedure using ropes, which he calls "cords." (Note that a "cord" is different from "chord" which is a straight line joining two points on the circumference of a circle.):
“ The endpoints P and Q of the cord are to be tied at the points A and B respectively. The cord is now stretched away from the segment AB, to one side of the plane, holding it at the Nyancana mark. ”
Here is Dani again on Pythagorean triples, which were known in Babylon many centuries earlier than in India:
“ It is well-known13 that the Babylonian cuneiform tablet Plimpton 322 contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating in particular that there was sophisticated understanding on the topic (see however Note 6 in the Appendix). Since these tablets predate the Sulvasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India. ”
I will provide more references in the coming days. Fowler&fowler«Talk» 19:05, 13 February 2007 (UTC)

The sources Fowler&fowler brings explicitely state that:-

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

The elaborate practical use of the Shabla Sutras then? Excellent for adding to the Shabla Sutra section.

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It is well-known that the Babylonian cuneiform tablet Plimpton 322 contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating in particular that there was sophisticated understanding on the topic (see however Note 6 in the Appendix). Since these tablets predate the Sulvasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India.

Speculation?

You seem to have missed the following, Fowler. Must have slipped your mind:-

If we follow the suggestion of some historians that the writers of the Sulbasutras were merely copying an approximation already known to the Babylonians then we might come to the conclusion that Indian mathematics of this period was far less advanced than if we follow Datta's suggestion.

Quoting selectively/misrepresnting, fowler?

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I will provide more references in the coming days.

Of what, fowler? The fact that Vedic mathematics contained geometry? or that it was applied for practical use as your sources imply?

Sections based on flawed rationale like "There was no mathematics in the Vedas other than some ritual geometry" and "The section explains the politics behind the notion of Vedic mathematics" will be removed and editors will have to work vigilanty to remove sections like these. I, for one, will.

Freedom skies| talk  21:42, 13 February 2007 (UTC)

Your callow sarcasm will not help your ignorance of what is being discussed. For the third time: No one is saying that there is no geometry in the Sulvasutras, or that geometry is not mathematics, but simply that (a) the geometry is "experimental" geometry focused around the task of rituals (b) the geometry is all without any proofs or theory (unlike Greek geometry) (c) the ritual geometry uses the language of "ropes" and "alters" (d) topics like Diophantine equations or the decimal place value system are not geometry and were certainly not solved in the Vedas. Fowler&fowler«Talk» 22:20, 13 February 2007 (UTC)

Your callow sarcasm will not help your ignorance of what is being discussed.

I have asked you to refrain from edits based on flawed rationale. Now I'll ask you to refrain from insults. Observe WP:Civility rules, Fowler.

No one is saying that there is no geometry in the Sulvasutras

No one said that anyone was saying that "there is no geometry in the Sulvasutras."

or that geometry is not mathematics

So you're claiming that you did not say "There was no mathematics in the Vedas other than some ritual geometry" now?

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the geometry is "experimental" geometry focused around the task of rituals

Your sources contradict your personal claims. Here:-

The performance of the fire rituals (yajna) practised by the Vedic people involved construction of altars (vedi) and fireplaces (agni) in specific geometrical shapes. The constructions and the geometric principles involved in them have been elaborately described in the Sulvasutras.

This was a source bought in by you, Fowler.

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the geometry is all without any proofs or theory (unlike Greek geometry)

Again, the articles in this encyclopedia are not based on personal opinion. Since you claim that "the geometry is all without any proofs or theory" are you willing to refrain if any theory or proof is provided. I can ask Subhash Kak to produce specific verses since I have had e mail contact with him.

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the ritual geometry uses the language of "ropes" and "alters"

topics like Diophantine equations or the decimal place value system are not geometry

The rationale of these statements and the context is beyond my comprehension. I'll refrain from commenting in response to them.

the decimal place value system were certainly not solved in the Vedas

Does the article say that the Rigveda solved the Diophantine equations or the decimal place value system?

I find your edits and responses extraordinary, Fowler. Not only are they based on flawed rationale but I sense the furthering of an agenda. You will understand that pollution of this encyclopedia with such material is an act that vigilant editors will not allow.

Regards,

Freedom skies| talk  02:00, 14 February 2007 (UTC)

Email contact with S. Kak (or any other engineer masquerading as a historian of science) is not going to help. Here is Michael Witzel on immigrant Hindutva activists:
“ The current "revisionist" models ... imagine massive lost literatures filled with "scientific" knowledge unimaginable anywhere in the ancient world ... Ironically, many of those expressing views ... are emigrants themselves, engineers or technocrats like N.S. Rajaram, S. Kak, and S. Kalyanaraman, who ship their ideas to India from U.S. shores. They find allies in a broader assortment of home-grown nationalists including university professors, bank employees, and politicians (S. S. Misra, S. Talageri, K.D. Sethna, S.P. Gupta, Bh. Singh, M. Shendge, Bh. Gidwani, P. Chaudhuri, A. Shourie, S.R. Goel). They have even gained a small but vo cal following in the West among "New Age" writers or researchers outside mainstream scholarship, including D. Frawley, G. Feuerstein, K. Klostermaier, and K. Elst. Whole publishing firms, such as the Voice of India and Aditya Prakashan, are devoted to propagating their ideas. ”
When was the last time that any internationally recognized journal of history of mathematics published anything by Kak? Fowler&fowler«Talk» 03:00, 14 February 2007 (UTC)
BTW, the statement, "There is no mathematics in the Vedas other than ritual geometry," means that (a) There is ritual geometry in the Vedas and (b) there is no other kind of mathematics in the Vedas (i.e. algebra, arithmetic, or geometry with proofs). As for your asking where are there references to algebra or arithmetic, well, here is the list:
In the subsection Vedas it says:
In the subsection Sulbasutra geometry, it says:
For example, the last claim that they computed the sin(π / 4) seems a little ludicrous, since they had no developed theory of trigonometry. They may have computed the ratio of the side of a square to its diagonal by measurement, but that is not the same thing as knowing about trigonometric functions. That's like saying that if they computed half the area of a square of side 1, they also computed the integral: \int_0^1xdx and therefore they knew about integration. A bit far fetched, don't you think? India had a lot of great mathematics, but all that happened in the first millennium CE and not in the Vedas. I think it is an insult to the Indian mathematicians of the first millennium CE, like Aryabhatta or Brahmagupta, to claim that their hard-won results were all anticipated in the Vedas. Fowler&fowler«Talk» 03:33, 14 February 2007 (UTC)
PS Notice also, that I didn't say anything about Panini since the work attributed to him is both genuinely his and also profound. Fowler&fowler«Talk» 03:33, 14 February 2007 (UTC)

Email contact with S. Kak (or any other engineer masquerading as a historian of science) is not going to help.

What did I tell you about civility, Fowler?

When was the last time that any internationally recognized journal of history of mathematics published anything by Kak?

Subhash Kak contributed to the Stanley Wolpert - edited Encyc. of India (Scribner's, 2006); Edited by Stanley Wolpert himself.

Now your reasoning and agenda have become too clear too bear reasoning with you fowler. The zeal that you display is commendable, but I rarely have seen worse arguments or rationale. The amount of effort you're willing to devote to the sabotage of this article amazes me.

there is no other kind of mathematics in the Vedas

So if I display mathematics other than "ritual" geometry then would you stop? I'm willing to wonder if your extraordinary edits are based on any reasoning at all. I see a strong anti Hindu bias motivating the exertions.

India had a lot of great mathematics, but all that happened in the first millennium CE and not in the Vedas

Would that depend on personal interpretation of "great mathematics", or are you implying that we actually need to editorialize on the fact that Modern mathematics outweighs ancient ones.

With all due respect, such zealous monstrosities are not found in other similar articles and you'll understand that I'll not going to allow them here as well.

Freedom skies| talk  10:33, 14 February 2007 (UTC)

An Encyclopedia of India is not the same thing as an "internationally recognized journal on the history of mathematics." An encyclopedia (as we all know) is a tertiary source and can only produce what is already out there. It is not clear what Kak wrote in that encyclopedia (in other words, if he claimed that the Hindu-Arabic numerals were developed in the Vedas etc.).
If I had an "anti-Hindu" bias, I would go after Aryabhatta or Brahmagupta or Panini, but I don't. If you think I have anti-Hindu bias, please read the first half of the History section (Ancient Indian astronomy) that I wrote in Indian Standard Time (an FA that was featured on the WP main page on Jan 21/22) or for that matter the lead I rewrote in Arabic Numerals, where I added that they arose in India etc.
My problem is with vague writing: compare for example my ancient Indian astronomy section in Indian Standard Time (which is very precise and careful in what it says) with the Vedic mathematics section on this page. I am happy to clean up the Vedic mathematics section, but then most of its vague unsubstantiated claims will have to go. Fowler&fowler«Talk» 12:26, 14 February 2007 (UTC)
The Encyclopedia is similar to Amartya Sen's book and books published by fringe theorists like Farmer in that regard then. None are recognized as authorities on mathematics.Bakaman 02:12, 15 February 2007 (UTC)
The references to both Sen and Farmer are no longer there in the text. The only people included in the criticism are J. F. Staal, J. J. O'Connor and E. F. Robertson, and S. G. Dani, all recognized experts in History of Mathematics. Also the title of the sub-section has been changed from "Criticism of Vedic Mathematics" to "Assessment of Mathematics of the Vedic Period." Fowler&fowler«Talk» 21:49, 15 February 2007 (UTC)

An Encyclopedia of India is not the same thing as an "internationally recognized journal on the history of mathematics."

You're right, it contans topics in addition to mathematics. I requested a few journals as well and procured them; they seem to disagree with your personal claims.

An encyclopedia (as we all know) is a tertiary source and can only produce what is already out there.

So that would mean that you are aware of the WP:OR? you still continue to violate that when you discover that mathematics and geometry are independent, Fowler.

The only people included in the criticism are J. F. Staal, J. J. O'Connor and E. F. Robertson, and S. G. Dani, all recognized experts in History of Mathematics.

I do agree that these men have been elaborately misrepresented by you, fowler.

"Of course the method used by these mathematicians is very important to understanding the depth of mathematics being produced in India in the middle of the first millennium BC. If we follow the suggestion of some historians that the writers of the Sulbasutras were merely copying an approximation already known to the Babylonians then we might come to the conclusion that Indian mathematics of this period was far less advanced than if we follow Datta's suggestion."[1] [2]

It is well-known that the Babylonian cuneiform tablet Plimpton 322 contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541) which is a primitive triple, indicating in particular that there was sophisticated understanding on the topic (see however Note 6 in the Appendix). Since These tablets predate the Sulbasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India.- Dani

Severe OR issues here. Severe misinterpretation issues. These are in addition to the original issues which can be found earlier in the section. Freedom skies| talk  01:54, 18 February 2007 (UTC)

Freedom skies, you are obviously trolling a topic with which you are not familiar. I suggest you sit back and watch F&f's work on the article, and maybe learn something. Any reasonable discussion of ancient Indian mathematics will rely centrally on the work of Staal. We are not here to fool around, hence I hope you will leave Kak and his ilk out of this from now on. This "revisionist" movement is just that, revisionism, not scholarship. It is completely unsurprising and indeed boring that all the bad faith editing, sockpuppetry, insane hype and broken grammar is only ever used unilaterally, on the part of the revisionists. Per WP:ENC we should not even honour this sort of thing with discussion, but just clean it out as a matter of course. dab (𒁳) 10:10, 19 February 2007 (UTC)

I suggest you sit back and watch F&f's work on the article, and maybe learn something.

Learn? Like, "There was no mathematics in the Vedas other than some ritual geometry." You'll understand that I'll pass such learning.

This "revisionist" movement is just that, revisionism, not scholarship.

Unless you convince Stanley Wolpert to have Kak's works removed from the his works you'll understand that I will disregard your personal opinions.

Per WP:ENC we should not even honour this sort of thing with discussion, but just clean it out as a matter of course.

I'll see to it that it's done. Edits based on distortion of sources and personal opinions belong, after all, in an underground discussion forum, not in an encyclopedia.

Freedom skies| talk  10:28, 19 February 2007 (UTC)

"some ritual geometry", precisely. As it happens, comparatively advanced, or indeed very advanced for its age, but not the magical wisdom of the ancient astronauts from the north pole people would like you to believe. If you keep bringing up Kak, all you'll do is convince us that you don't know the first thing about the topic. Now cut the edit-warring, and cut the belligerent trolling. dab (𒁳) 10:46, 19 February 2007 (UTC)

Anyone who cites Michael Witzel or other adherents of Max Mueller's hypothesis immediately loses credibility. Witzel studied India in Germany and Nepal, and like Max Mueller, never spent time in India. The knowledge of these pseudo-Indologists is based on information they acquired in the West, without any direct person to person contact with Indians in India. Their views were nurtured in an environment where Indians, like other non-White folks, were not considered equal. Their attitudes and views reflect the racist bias of the previous century. It is high time institutions like Harvard stop providing credibility to pseudo-Indologists who have never been to India. —The preceding unsigned comment was added by 207.237.66.201 (talk • contribs). at 03:10, 20 March 2007

The Sulba Sutras

I am removing two unsourced claims about the Sulba Sutras containing trigonometric functions. There is no evdidence of this. Since these claims were made in the WP page on trigonometric functions as well, I decided to probe it more and realized that the source provided was G. G. Joseph's book The Crest of the Peacock: The Non-European Roots of Mathematics (p. 232). However what is provided in Joseph's book is a modern-day proof of some results stated in the Sulba sutras, and that proof uses sinθ, (and that too a little redundantly since the angle is 45 degrees and he is really talking about the diagonal of a square). However, there is no indication in Joseph's book anywhere that sine, cosine, or anything resembling trigonometric functions is mentioned in the Sulbasutras. What is mentioned in the Sulbasutras is: "Divide the diameter of a circle into 15 equal part and take 13 of them to be the side of the square," (for "squaring the circle"). The Sulbasutras say that and nothing else (and no indication is given of how the result was discovered.) That is not evidence for knowledge of trigonometric functions. Fowler&fowler«Talk» 14:04, 22 February 2007 (UTC)

However what is provided in Joseph's book is a modern-day proof of some results stated in the Sulba sutras, and that proof uses sinθ, (and that too a little redundantly since the angle is 45 degrees and he is really talking about the diagonal of a square).

I was about to suggest OR violation as are apparent by constant vandalism you have caused in Indian mathematics related articles but then "The whole of Indian geometry and trignometry is dominated by the theorum of the suqare and the diagonal." (Geometry in Ancient and Mediaeval India By T.A. Sarasvati Amma page 58). Freedom skies| talk  03:17, 23 February 2007 (UTC)