Vedic Science

# Apastamba: India’s most complicated Mathematician

It is hard to write much of Apastamba since researchers are unable to discover a great deal about him  except that he was the author of a Sulbasutra which is certainly later than the Sulbasutra of Baudhayana.

It would also be fair to say that Apastamba’s Sulbasutra is the most interesting from a mathematical point of view.  Apastamba’s exact birth dates and death dates are currently unknown. Since he is known to have lived around 600 BC, scholars will typically list this as both his birth and death year.

Apastamba was neither a mathematician in the sense that we would understand it today, nor a scribe who simply copied manuscripts like Ahmes. He would certainly have been a man of very considerable learning but probably not interested in mathematics for its own sake, merely interested in using it for religious purposes. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites and to improve and expand on the rules which had been given by his predecessors. Apastamba would have been a Vedic priest instructing the people in the ways of conducting the religious rites he describes.

The mathematics given in the Sulbasutras is there to enable the accurate construction of altars needed for sacrifices. It is clear from the writing that Apastamba, as well as being a priest and a teacher of religious practices, would have been a skilled craftsman. He must have been himself skilled in the practical use of the mathematics he described as a craftsman who himself constructed sacrificial altars of the highest quality.

Apastamba’s main work in his extended version of the Sulbastura was to give the estimation of the square root of two. The general linear equation was solved in the Apastamba’s Sulbasutra. He also gives a remarkably accurate value for √2 namely:

### 1 + 1/3 + 1/(3×4) – 1/(3×4×34) = 1.4142156861.

which gives an answer correct to five decimal places.

Other contributions by Apastamba that were not fully explained included squaring the circle and dividing a segment into seven equal parts. Further explanations of his work can be found in translated versions of the Sulbastura.

Various critics have tried to reconstruct these processes but they have proved unsuccessful, leaving Apastamba’s to be the most well known Mathematician in modern day.

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• Balasubramanian says:

interesting

• On the day of my initiation as a young Brahmin I was taught a self-introduction in Sanskrit, wherein I begin mentioning three Rishis to be followed by the statement that my ancestors were followers of Apastambha Sutra. After decades and decades,, at last I come to know who he was.
Thank you for the information.

From Germany.

• Sri Aiyer Raju Sreenivasan says:

Well. Same thing with me too. I have been mechanically saying that I belong to such and such Gotra, that I follow Aapasthampa sutra. and that I chant the Yajur Veda. Only today I realize the mathematical calculations involved in the very many rituals we have been observing from the time preceding our birth till death and beyond. How much have we lost! Can they ever be retrieved? The irony is we lost them all only in the past 100 years or so.

• Raghunathan Srinivasan says:

More than his Mathematics, his Yogic powers were high; when somebody,as a matter of routine was offering Arkyam- water- chanting Kala Atheatha – Apasthamba noticed that that individual was doing the Sandhya Vandhanam in the right time only and so the statement ‘ Kala Atheatha ‘ and the Arkyam was irrelevant; so he simply told the Arkyam water not to flow down- Aapaha means water; sthamba means stop- and so he got the name Apasthamba! Lord Vishnu is said to be in Yoga Nidra-ie. HE is not sleeping; he appears to be sleeping- and is continuously creating- yathra Yogesvara Krishno…..- we the Hindus, particularly the Brahmins should know at least a miniscule of that Yoga Vidhya or Brahma Vidhya, said to have been passed on to Brahma by Vishnu @ Narayana through the Gayathri!

• श्रीनिवास says:

Thank you sir brilliant commentary !

• Sri Aiyer Raju Sreenivasan says:

And Gayathri is the fusion of Siva & Sakthi, Purusha & Prakriti, Mahadeva & Mahavishnu. There is no Siva without Sakthi, there is no Purusha without Prakriti, there is no Mahadeva without Mahavishnu. That’s the reason why Gayathri has been given such an exalted position in our lives. And yet, 99.99% of us Brahmins without realizing the unbound treasure we have been bequeathed from generation to generation, have given up on our Sandhyavandanam. Who is to be blamed: The Kali-Yuga and the Kali’s manifestations in the form of anti-Sanatana Dharma forces from the deserts of the Middle East? Or we>our own selves? Who?

• Krishna says:

I have been chanting his name daily from the past 10 yrs or so. Never knew his background.
I chant his name in pravara. apasthamba surtraha ..along with rishi names n my gothra.

• Reuben says:

very interesting! and also Raghu’s comment… fascinating!

• charan says:

A small correction, if I may:
Apastamba was a Mathematician par excellence; and a great Philosopher.And hence the statement that “Apastamba was neither a Mathematician…..” is not factual.It is better if one comes out of the unfortunate tendency to connect everything that is Indian to “Religious practices”; which is NOT true.
To just quote C.K.Raju, a well-known historian and Mathematician,from paper titled “Planetary theory Newton and Buddhism” (just as an example….)—
QUOTE In India,Mathematics was seen as purely utilitarian and practical.Although some incompetent historians have tried to suggest that Sulbasutra was linked to “ritual geometry” there no similar connection between geometry and religious beliefs in India, as there was among the Greeks.The Sulbasutra were only used for the practical purposes of constructing brick structures.The empirical was not regarded as inferior; mathematical proofs employed empirical techniques .UNQUOTE
And also, just to add, all the “sacrifices” in Ancient India were of metaphorical in nature, symbolizing the spiritual aspect of Human Existence.There were NO animal sacrifices as such, during that time.
However, a good article; describing the genius.
Thank You.

• Chandrasekar says:

He was the Rishi who included mother side while doing tharpanam

• Many great sages(rishis) are still living in india some are known and some are unknown.

• during daily SandhyaIAN Vandam time I recite APASTMBHA SUTHRA AND MY GOTHRA. tO DAY i AM FORTUNATE TO KNOW ABOUT THIS GREAT APASTHMBHA SUTHRA. Thanks.

• Laxman Ramachandran says:

. I am very very much thanks to sanskruthi, team for their hardworking about sanathana dharma. And also good information of about Rishis and sages