Talk:Aryabhata

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[edit] Birth

See the book on Aryabhatiya by Shukla and Sarma (Indian National Science Academy, 1976) that is clear that the Kerala birth has no evidence to support it. MarcAurel 17:57, 11 February 2006 (UTC)

First, a disclaimer: I know nothing about Āryabhaṭa that I haven't read on this page (or found very recently on the web). So, take anything I say (or edit) with a grain of salt. The only edits I've made have been attempts to clarify meaning or make something easier to read. Now, my comment about his birth: in trying to find out more about this Konwar Chandra Hari and the Institute of Reservoir Studies of Oil and Natural Gas Commission that he works for, it seems he is not notable at all. (Also, on the Institute site, his name is referenced as Hari Chandra Konwar, but perhaps this is an Indian custom that I am unfamiliar with.) Now on the talk page, I read that (at least according to MarcAurel, that he was born in Kerala is possibly speculative. The source for this claim is not sourced, making MarcAurel's comment (from over a year ago) extremely interesting in that no one has responded to it. Ben Hocking ^{(talk|contribs)} 17:46, 21 July 2007 (UTC)

Good catch. I have replaced that fringe and speculative claim, by a published journal citation. I guess, we can add Hari Chandra's claims once he publishes it in a peer-reviewed article.

Aside: The ordering of the (so called) first-name- middle name and family-name in India is traditionally very region dependent and the people often need to adapt the sequence to fit the rigid requirements of official forms and databases. So finding the variants of Konwar Chandra Hari's names is not really surprising. Cheers. Abecedare 18:28, 21 July 2007 (UTC)

Thanks for the information. Do you know enough about the material in the section "Pi as Irrational" to clean it up? I don't know what they're trying to say, or I'd clean it up myself. Ben Hocking ^{(talk|contribs)} 18:41, 21 July 2007 (UTC)

I have clarified the second part of the section based on the refernce I previously added and fact tagged the first (unsourced) claim. Aryabhata I, His Life and His Contributions seems to be a useful and citable source for expanding and reorganizing this article; the other source which may be worth looking up is the book by K. S. Shukla - he seems to be an expert on the topic. Happy editing. Abecedare 19:27, 21 July 2007 (UTC)

Thanks again! 19:29, 21 July 2007 (UTC)

[edit] Arabic translation section

The section said:

"The 8th century Arabic translation of Aryabhata's Magnum Opus, the Āryabhatīya was translated into Latin in the 13th century, before the time of Copernicus. Through this translation, European mathematicians got to know methods for calculating the areas of triangles, volumes of spheres as well as square and cube root, while it's also likely that Aryabhata's work had an influence on European astronomy."

Clearly, methods for calculating areas of triangles are at least as old as Euclid's Elements (~300 BC), probably much older. Similiarly, you can find methods for calculations of volumes of spheres and many other shapes in Archimedes work. Also, one of your sources (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata_I.html) even states that it is widely believed that Aryabhata's expressions for the volume of spheres and pyramids was actually incorrect!

Also, while this isn't currently mentioned in this article, something I noticed in the source (http://www.dialogweb.org/Contribute/Bineesha%20project.htm), was the statement:

"According to him the period of one rotation of the earth is 23 hours 56 mn 4.1s while the modern value is 23 hours 56 mn 4.091s. His accuracy regarding this is amazing."

While I would agree that his accuracy is amazing, keep in mind that the value today is not exactly the same as what it was 1500 years ago. So, while his accuracy is very good, it is not actually correct to 1/10th of a second, as is implied by the article. Just a heads up if someone wants to add a statement about his length of the day to the article. Grokmoo 16:52, 8 March 2006 (UTC)

[edit] Trig Identity

The trig identity mentioned under Mathematics is not true. Can someone fix this?

I removed the offending line: "One of the trigonometric formulas Aryabhata developed was sin(n + 1)x - sin nx = sin nx - sin(n - 1)x - (1/225)sin nx." While I don't claim to know every trig identity in existance, this particular statement is patently untrue, and I am unable to find an obvious variation this is true. I also looked through quite a few tables of identites and was unable to find any statement similar to the above one. Worse still, in light of the double angle and similar formulas, I can't imagine that anything similar to this could possibly hold gjktjthjhjhjfhjfhjfor arbitrary (I assume integer, although this is not stated) n.Grokmoo 04:02, 15 March 2006 (UTC)fjfjfhjhjhjhj

[edit] (see Etymology above)

This statement isnt very clear it appears to refer to an etymology heading that doesnt exist, I didnt want to change it tho just incase I had misundersood the meaning. --AjP 11:32, 14 April 2006 (UTC)

[edit] Heliocentrism

I admire the dedication of many Wikipedians to expanding coverage of science in different cultures. Most encyclopedias do a terrible job of this subject area. I'm just not sure all of it is grounded in reality--in particular, the many-times-repeated statement that Aryabhata's astronomy was "heliocentric." To most people, "heliocentric" means that the Earth revolves around the Sun, but it seems like something else is meant here. Can someone who has actually read his work explain what role the Sun had in his astronomy? Is it different from what Ptolemy did with the Sun in the Almagest? Also, I wonder about the statement that he thought the planets moved on ellipses. Not that it's false, but it could mean different things. Is there someone who can explain? Maestlin 22:58, 23 April 2006 (UTC)

I've been troubled by the same problem as Maestlin, and have recently traced down a source for this theory to a 1970 publication by B. L. van der Waerden. This book was given a lengthy critical review in Isis by the historian of astronomy, Noel Swerdlow and briefly dismissed by the late David Pingree in his "The Greek Influence on Early Islamic Mathematical Astronomy," Journal of the American Oriental Society, 93 (1973: 32-43 (at p. 32, n. 1).

Given the rejection of this view by two leading western experts on the history of Indian astronomy in two leading journals, the concept of Indian heliocentrism should be treated as a minority fringe opinion and does not deserve an important place (if any) in this and other articles on Indian astronomy. SteveMcCluskey 14:43, 29 May 2007 (UTC)

[edit] What kind of a sick language is that?

The article says that "Aryabhata [...] writes: chaturadhikaM shatamaShTaguNaM dvAShaShTistathA sahasrANAm AyutadvayaviShkambhasyAsanno vr^ttapariNahaH.", which is then translated into English. I'm wondering if I'm having some kind of problem with Image:My computer, or is that citation supposed to look like that? Shouldn't it be written on some other alphabet than the Roman one, for example the one that looks like this:

~~हिन्दुस्तान? == Now it looks like klingon to me, not like a natural language at all. --[[~~

User:Riojajar|Riojajar]] 19:41, 30 May 2006 (UTC)

[edit] Perplexities...

I was looking for heliocentrism in wikipedia and I have found a lot of references to Indian astronomy: see heliocentrism, history of astronomy and Aryabhata. I have a deep respect for all civilizations, and I think that we have still to learn a lot on Indian astronomy, but I believe these texts are biased and with a number of errors. I limit myself to what concerns the relations with Greek astronomy, because admittedly I am not an expert in Indian astronomy. The first to propose the rotation of the Earth was Heraclides of Pontus (IV century BC); Aristarchus of Samos was the first to propose the heliocentric system (III century BC). I have not found in academic sites that Aryabhata had the idea of an heliocentric system; if I understand well he simply calculated the relative distances of the planets from the Sun. It has to be taken into account that after Alexander the Great hellenistic science had a direct influence on Indian science, a fact which is well documented. As concerning Vedic quotations, they appear quite obscure to me... I suspect they have the same value as the claim that the Genesis anticipates the Big Bang theory, but maybe I am wrong... I think that in a page on the history of science such references should not be present. --Alcap 09:48, 26 June 2006 (UTC)

Hello, while I appreciate your deep respect for all civilisations of known history, and I am not going to argue about Aryabhata, I have to mention that, that the earth rotates on its own axis, and that it revolves around the Sun, and EVEN the Heliocentric concept were FIRST mentioned in known history in some of the surviving Hindu texts known as the Shatapatha Brahmana and the Aitareya Brahmana, which according to even the most conventional scholars and Western historians date back to at least 1000 BC. I am sure the relevant page Heliocentrism would be of great help in enlightening you on that such texts mentioned above, and scientists like Yajnavalkya said these things amongst many others several centuries before the Greeks you named. Also, the Greeks who stayed back in the then India intermarried with the local population in a part of present-day Afghanistan region giving rise to the Bactrian Kingdom. While they were a great culture they did not really influence the whole of the then India but only a part of it.

Regarding Alexander the greek, Some of the less documented facts says that India is the only place where his soldiers rebelled ... of course due to "homesickness" :)Bharatveer 10:50, 26 June 2006 (UTC)

That's true! However the point here is not Alexander, but the hellenistic period which followed his death when Occidental and Oriental civilizations (Egyptian, Babylonian, and Indian) met and gave rise to an original culture. The civilizations which successively received this heritage (Indian, Arabic, and Renaissance Europe) had an extraordinary and rapid scientific progress. I stress that this is a great merit of these civilizations: think to the celebrated Romans, who never had an interest in science and had no scientist at all! But of course mathematics and astronomy existed before the Greeks, and I am sure that a lot remains to be discovered. My point is that one should try to report facts as accurate as possible and separate the history of science from a more general history of ideas which can be discussed elsewhere. For example, I am skeptical that Aryabhata could discover the ellipticity of planetary orbits, I do not think this was possible observationally (planetary orbits are nearly circular), and I agree with a previous comment suggesting that this "ellipticity" could mean something else. Anyway, I find Aryabhata a very fascinating scientist, he apparently was the most original astronomy of his time, and I hope that some expert will give us more explanations and possibly some translations of his works. --Alcap 11:56, 26 June 2006 (UTC)

"He states that ... the orbits of the planets are ellipses around the Sun". This is an extraordinary claim! I didn't see it anywhere alse. I think clear references on the source of this claim must be added. Dmitri Klimushkin.

[edit] Earth measurement

The article says: "Aryabhata was the first astronomer to make an attempt at ...", but the article on Erastothenes contradicts this. It states that Posidonius used Erastothenes' method 150 years later. It seems likely that this article is wrong, and that the sentence should be changed. His secondness (first after E.) does not seem that important, anyway. It would also be good if his method could be given. --LarsMarius 11:15, 6 August 2006 (UTC)

[edit] Gravitation?

Amartya Sen writes in "Identity and Violence" that Aryabhata proposed a model of gravitational attraction, but the article makes no mention of this. Is this an omission? If so, it seems like a major omission. --LarsMarius 11:25, 6 August 2006 (UTC)

[edit] value zero

aryabhatta discovered the value zero as null. he itroduced zero to the world. there is no where mention of it. can anybody with more knowledge on this subject please edit the page and add the relevant information

Use of zero predates Aryabhata. Aryabhata extensively used zeros. But He did not discover zero. This is a popular myth. Historically we have not found the inventors name yet. But there are arguments that 200 BC mathematician Pingala uses dot to mean zeros in his work Chandasutra.

70.64.7.251

[edit] relativity

See talk in Aryabhata's relativity principle for more details. MarcAurel 05:16, 22 November 2006 (UTC)

I have removed that from this article again. Why do you want to perpetuate such a crazy claim? I look at the article without that, and I see a genius who was way ahead of his time. With that included, I am forced to wonder what else in the article is an exagerated claim. --EMS | Talk 23:43, 22 November 2006 (UTC)

Pls take your own time for wondering.-Bharatveer 06:33, 23 November 2006 (UTC)

I thought about editing the "relativity" section to present my won viewpoint, but quickly concluded doing so would violate both WP:NPOV and WP:POINT. However, the persistent reinsertion of that piece of garbage makes doing so tempting.

Will you people please get it through your heads that "relativity" means that there is no special rest frame of reference!!!? Aryabhata did not make any such claim. Instead he shifted the special rest frame from being the Earth to being the Sun and stars. I know that other writers have been claiming that Aryabhata's verses constitute a principle of relativity, but that does not make that claim true or even encyclopedic. I strongly counsel you all to let Aryabhata's words speak for themself. They show real genius, but this relativity claim makes those words look silly since thay do not at all support that claim. --EMS | Talk 06:37, 23 November 2006 (UTC)

[edit] the adding of A at the end

Shouldn't it be "Aryabhat"?

If you look at the word written in Hindi, there is no "A" matra at the end of the word.

129.186.51.30 17:42, 5 January 2007 (UTC) Tushar

But in whole of india this name is pronounced as Aryabhatta. And Hindiis not the noly language of India. There are so many other major languages (like telugu, Gujarathi, Bengali, Tamil, Malayalam, Kannada). In all these these this word is pronounced and write as Aryabhatta. —The preceding unsigned comment was added by 203.199.144.132 (talk • contribs) 09:53, 11 January 2007 (UTC)

I understand that Hindi is not the only language in India. But it originates in Sanskrit, and in Sanskrit there is no "A" sound at the end of the word. —The preceding unsigned comment was added by Tdayal (talk • contribs) 22:33, 15 January 2007 (UTC)

[edit] Shouldn't there be one more "t" in his name?

I was given to understand that it is AryabhatTa and not Aryabhata. I notice that both spellings are used in the article, though it appears that the single-t version is preferred. I feel this leads to awkward pronunciation. Perhaps the dot below the 't' in the first line of the article represents the extra emphasis on the 't'? In this case, it should be used everywhere. (Mindthief) —Preceding unsigned comment added by 128.12.187.66 (talk) 22:51, 27 April 2008 (UTC)

[edit] Aryabhata th Indian Mathematician

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[edit] Indian or Sri Lankan ??

The earliest of all the Indian mathematicians, who used the modern arithmetic was Aryabhata. Here it will be shown that Aryabhata, the father of arithmetic could be a Sri Lankan.

Aryabhata wrote two books. After nearly 1,500 years later only one book is in existence today. This book is known as Aryabhatiyam and here I would show that Aryabhata was a Sri Lankan using internal evidence available in Aryabhatiyam.

Here I would use Aryabhatiyam translated by a Harvard University Professor Walter Eugene Clarke.

Aryabhata in lemma 19 says the following:

Lemma 19: "The circle which intersects the east and west points and the two points in the meridian which are above and below the horizon by the amount of the observer’s latitude called the horizon of Lanka, on it the increase and decrease of day and night are measured."

Here Aryabhata uses horizon of Lanka as his reference to measure the apogee and situate himself in the celestial sphere. Now the question is, if Aryabhata is an Indian, why would he use Lanka as the point of measurement?

In Lemma 18, he says the following?

Lemma 18: "As a man in a boat going forward sees a stationary object moving backward so at Lanka, a man sees the stationary asterisms moving backward in a straight line."

WTF????123.255.54.74 12:59, 16 March 2007 (UTC)

Again, the movement of the celestial sphere or in this case the rotation of the earth that causes the diurnal motion is obtained using Lanka as a reference point. Aryabhata has to be stationed in Lanka for this statement to be true.

Lemma 10: "The cause of their rising and setting is due to the fact the circle of the asterisms together with the planets driven by the provector wind, constantly moves westwards at Lanka."

This phrase was shown by some Indian scholars as non-Sri Lankan origin of Aryabhata. Here Aryabhata indicates the wind is flowing towards Lanka due to the setting and rising of asterisms. If he was stationed in Lanka why would he say the wind is moving towards Lanka? This lemma indicates non-Sri Lankan reference of Aryabhata.

Brahmagupta, the staunch critic of Aryabhata who lived nearly 200 years after Aryabhta criticices Aryabhata for using Lanka as his reference. In Panchasiddhantika Brahmagupta says the following.

"Aryabhata maintains that the beginning of the day is to be reckoned from midnight of Lanka. The same teacher says that the day begins at sunrise of Lanka."

It is not clear what Brahmagupta had in mind. But as per Brahmagupta, it is very clear that Aryabhata had two systems for the measurement of the rotation of the celestial sphere. Either way using two systems for the measurements of the celestial sphere is been criticised. Could it be that Aryabhata used one system while he was in Lanka and the other one after he came to India?

See table 1 for numbers of India dated to the 11th century based on Brahmi characters. Brahmi characters came to southern India from Sri Lanka (John Keay, India History).

It could be established that based on internal evidence in Aryabhatiyam, the foremost Indian mathematician who was responsible for developing modern arithmetic was in face a Sri Lankan.

It is established that Aryabhata lived from 476 AD to 520 AD.

King Kassapa ruled in Sri Lanka from 478 to 495 AD, Moggallana from 495 to 515 AD and Kumara Dhatusena from 515 to 523 AD.

This was an interesting time period. Bhuddhagosha arrived in 430 AD from Bodhi Gaya. Aryabhata lived in Pataliputra which was walking distance from Bodhi Gaya. The Mahavamsa says that Kalidasa, the great poet of India came to Sri Lanka and died here during King Kumara Dhatusena’s time. Kalidasa was a great friend of Kumara Dhatusena and as per the Mahavamsa, Kumara Dhatusena jumped into the funeral pyre of Kalidasa.

These events show us that there was much communication between India and Sri Lanka at the time. The above information show us that there is a very great possibility that Aryabhata was a Sri Lankan.

The fact that Aryabhata refers to Lanka tells as little about his origin as would the fact that a modern astronomer defines the longitude and time from Greenwich. We can't infer that the modern astronomer was from London, nor can we infer that Arryabhata was from Sri Lanka. --SteveMcCluskey 15:40, 10 April 2007 (UTC)

And even if he was from the island of Sri Lanka, in a historical context "India" refers to the Indian subcontinent, since this was before there was even the concept of the modern Republic of India.

Other examples of this are:

the United States of America isn't all of the continent of America
the Republic of Guinea isn't the only country in the region of Guinea
the European Union isn't all of Europe
there where united arab republics before, during and after the existance of the United Arab Republic
the Republic of Colombia isn't the only country in the continent of America, which Columbia is another word for

Saimdusan Talk|Contribs 00:35, 9 June 2008 (UTC)

[edit] Pi is irrational section needs work

The Pi is irrational section needs work, but I know nothing of the material. All I know is that it currently doesn't make sense. Ben Hocking ^{(talk|contribs)} 19:02, 20 July 2007 (UTC)

[edit] Article reorganization

I have reorganized the article sectioning into what I feel is a more logical format [1]. Please let me know if there are any objections or suggestions. I will try to expand and reference this article over the next few weeks and any help will be greatly appreciated. Thanks. Abecedare 19:44, 21 July 2007 (UTC)

I reorganized the article a bit more; added some meat to many claims in the legacy and astronomy sections, provided several references, etc. Sorry if I made too many changes.

Ben Hocking: Took a look at the "pi is irrational" section, I am not sure what is unclear, it seems that the meaning "Asanna" as irrational is explained adequately. The book by Balachandra Rao referred to in that section quotes the commentator Nilalkantha.

Some unsigned users made a call to change the article name to "Aryabhat". As it is written in Hindi today, one may or may not pronounce the final "a" (it's a schwa). But surely one does not place a halant to indicate that the final vowel is absent. This ambiguity arises because Devanagari, like most Indo-Aryan writing, is an abugida script. However, this was not so in the Sanskrit tradition, where the last consonant would be pronounced. In Sanskrit, the morpheme "bhaTTa", meaning teacher, is often written with a doubled T. Also, in English, Aryabhata is a far more prevalent spelling. So there seems to be little need or justification for such a change.

I have been looking for claims of heliocentricism in Aryabhata, but haven't found any; possibly the claims here are largely spurious. If someone has some concrete source on this, pls give the reference.

The zero part should be a little clearer now. He used a numeric transcription that did not explicitly call for a zero.

I don't have access to Shukla/Sharma, but it would be good if we could have some more discussion on the fog surrounding his place of birth. Marc Aurel would you like to take a stab? mukerjee (talk) 10:38, 1 August 2007 (UTC)

[edit] Birth date calculation

Is there a source for this lengthy analysis in the article? It seems to be WP:OR and conflicts with claim here. On a related note, there is far too much quoting in sanskrit in the article for an English language mainstream encyclopedia. Professor marginalia (talk) 01:12, 6 December 2007 (UTC)

[edit] Apparent copyvio

I recently reverted an apparent copyright violation added by User:Plmokn951753 which reproduces verbatim a lengthy passage from an online essay on Indian mathematics. SteveMcCluskey (talk) 20:51, 4 May 2008 (UTC)