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1 The sutras of Baudhayana
- 1.1 The Shrautasutra
- 1.2 The Dharmasutra
2 The mathematics in Shulbasutra
3 Notes
4 References
5 See also

Baudhāyana, (fl. ca. 800 BCE)[1] was an Indian mathematician, who was most likely also a priest. He is noted as the author of the earliest Sulba Sutra — appendices to the Vedas giving rules for the construction of altars — called the Baudhāyana Śulbasûtra, which contained several important mathematical results. He is older than other famous mathematician Apastambha. He belongs to Yajurveda school.

The sutras of Baudhayana

The Sûtras of Baudhāyana are associated with the Taittiriya Śākhā (branch) of Krishna (black) Yajurveda. The sutras of Baudhāyana have six sections, 1. the Śrautasûtra, probably in 19 Praśnas (chapters), 2. the Karmāntasûtra in 20 Adhyāyas (chapters), 3. the Dvaidhasûtra in 4 Praśnas, 4. the Grihyasutra in 4 Praśnas, 5. the Dharmasûtra in 4 Praśnas and 6. the Śulbasûtra in 3 Adhyāyas[2].

The Shrautasutra

Main article: Baudhayana Shrauta Sutra

His shrauta sutras related to performing to Vedic sacrifices has followers in some Smartha brahmins (Iyers)And some Iyengars of Tamil Nadu, Yajurvedis or Namboothiris of Kerala, Gurukkal brahmins, among others. The followers of this sutra follow a different method and do 24 Tilatarpana, as Lord Krishna had done tarpana on the day before Amavasaya; they call themselves Baudhayana Amavasya.

The Dharmasutra

The Vivarana of Govindasvami is an important commentary on the Dharmasûtra.

The mathematics in Shulbasutra

Pythagorean theorem

The now known Pythagorean theorem is believed to have been invented by Baudhayana. This theorem is used to calculate the sides of a right angle triangle. There is evidence to this fact exists all over India.^{[citation needed]}

Circling the Square

Another problem tackled by Baudhayana is that of finding a circle whose area is the same as that of a square (the reverse of squaring the circle). His sutra i.58 gives this construction:

Draw half its diagonal about the centre towards the East-West line; then describe a circle together with a third part of that which lies outside the square.

Explanation:

Draw the half-diagonal of the square, which is larger than the half-side by $x = {a \over 2}\sqrt{2}- {a \over 2}$ .
Then draw a circle with radius ${a \over 2} + {x \over 3}$ , or ${a \over 2} + {a \over 6}(\sqrt{2}-1)$ , which equals ${a \over 6}(2 + \sqrt{2})$ .
Now $(2+\sqrt{2})^2 \approx 11.66 \approx {36.6\over \pi}$ , so the area ${\pi}r^2 \approx \pi \times {a^2 \over 6^2} \times {36.6\over \pi} \approx a^2$ .

Square root of 2

Baudhayana i.61-2 (elaborated in Apastamba Sulbasutra i.6) gives this formula for square root of two:

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayet
tachchaturthānātma chatusastriṃshenena savisheShaḥ.

Translation Requested

$\sqrt{2} = 1 + \frac{1}{3} + \frac{1}{3 \cdot 4} - \frac{1}{3 \cdot4 \cdot 34} = \frac{577}{408} \approx 1.414216$

which is correct to five decimals.

Other theorems include: diagonals of rectangle bisect each other, diagonals of rhombus bisect at right angles, area of a square formed by joining the middle points of a square is half of original, the midpoints of a rectangle joined forms a rhombus whose area is half the rectangle, etc.

Note the emphasis on rectangles and squares; this arises from the need to specify yajña bhūmikās—i.e. the altar on which a rituals were conducted, including fire offerings (yajña).

Apastamba (c. 600 BC) and Katyayana (c. 200 BC), authors of other sulba sutras, extend some of Baudhayana's ideas. Apastamba provides a more general proof^{[citation needed]} of the Pythagorean theorem.

Notes

^ O'Connor, J J; E F Robertson (November 2000). "Baudhayana". School of Mathematics and Statistics, University of St Andrews, Scotland. http://www-history.mcs.st-and.ac.uk/~history/Biographies/Baudhayana.html. Retrieved 2007-06-09.
^ Sacred Books of the East, vol.14 – Introduction to Baudhayana

References

George Gheverghese Joseph. The Crest of the Peacock: Non-European Roots of Mathematics, 2nd Edition. Penguin Books, 2000. ISBN 0-14-027778-1.
Vincent J. Katz. A History of Mathematics: An Introduction, 2nd Edition. Addison-Wesley, 1998. ISBN 0-321-01618-1
S. Balachandra Rao, Indian Mathematics and Astronomy: Some Landmarks. Jnana Deep Publications, Bangalore, 1998. ISBN 8190096206
O'Connor, John J.; Robertson, Edmund F., "Baudhayana", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Baudhayana.html . St Andrews University, 2000.
J. J. O'Connor and E. F. Robertson. The Indian Sulbasutras at the MacTutor archive. St Andrews University, 2000.
Ian G. Pearce. Sulba Sutras at the MacTutor archive. St Andrews University, 2002.

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