Shulba Sutras (Vedangas)
SHULBA SŪTRAS (VEDĀNGAS)
SHULBA SŪTRAS (VEDĀNGAS) The Shulba Sūtras belong to the Vedāngas, or supplementary texts of the Vedas. Although they are part of the Kalpa Sūtras, which deal with ritual, their importance stems from the constructions they provide for building geometric altars. Their contents, written in the condensed sūtra style, deal with geometrical propositions and problems related to rectilinear figures and their combinations and transformations, squaring the circle, as well as arithmetical and algebraic solutions to these problems. The root shulb means measurement, and the word shulba means a cord, rope, or string.
The extant Shulba Sūtras belong to the schools of the Yajurveda. The most important Shulba texts are the ones by Baudhāyana, Āpastamba, Kātyāyana, and Mānava. They have been generally assigned to the period 800 to 500 b.c. Baudhāyana's text is the oldest, and he is believed to have belonged to the Andhra region. Baudhāyana begins with units of linear measurement and then presents the geometry of rectilinear figures, triangles, and circles, and their transformations from one type to another using differences and combinations of areas. An approximation to the square root of 2 and to p are next given.
Then follow constructions for various kinds of geometric altars in the shapes of the falcon (both rectilinear and with curved wings and extended tail), kite, isosceles triangle, rhombus, chariot wheel with and without spokes, square and circular trough, and tortoise.
In the methods of constructing squares and rectangles, several examples of Pythagorean triples are provided. It is clear from the constructions that both the algebraic and the geometric aspects of the socalled Pythagorean theorem were known. This knowledge precedes its later discovery in Greece. The other theorems in the Shulba include:
The diagonals of a rectangle bisect each other.
The diagonals of a rhombus bisect each other at right angles.
The area of a square formed by joining the middle points of the sides of a square is half of the area of the original one.
A quadrilateral formed by the lines joining the middle points of the sides of a rectangle is a rhombus whose area is half of that of the rectangle.
A parallelogram and rectangle on the same base and within the same parallels have the same area.
If the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is rightangled.
A variety of constructions are listed. Some of the geometric constructions in these texts are based on algebraic solutions of simultaneous equations, both linear and quadratic. It appears that geometric techniques were often used to solve algebraic problems.
The Shulbas are familiar with fractions. Algebraic equations are implicit in many of their rules and operations. For example, the quadratic equation and the indeterminate equation of the first degree are a basis of the solutions presented in the constructions.
The Shulba geometry was used to represent astronomical facts. The altars that were built according to the Shulba rules demonstrated knowledge of the lunar and the solar years.
Subhash Kak
See alsoScience ; Vedic Aryan India ; Yajur Veda
BIBLIOGRAPHY
Seidenberg, A. "The Origin of Mathematics." Archive for History of Exact Sciences 18 (1978): 301–342.
Sen, S. N., and A. K. Bag. The Sulbasūtras. New Delhi: Indian National Science Academy, 1983.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"Shulba Sutras (Vedangas)." Encyclopedia of India. . Encyclopedia.com. 18 Apr. 2019 <https://www.encyclopedia.com>.
"Shulba Sutras (Vedangas)." Encyclopedia of India. . Encyclopedia.com. (April 18, 2019). https://www.encyclopedia.com/international/encyclopediasalmanacstranscriptsandmaps/shulbasutrasvedangas
"Shulba Sutras (Vedangas)." Encyclopedia of India. . Retrieved April 18, 2019 from Encyclopedia.com: https://www.encyclopedia.com/international/encyclopediasalmanacstranscriptsandmaps/shulbasutrasvedangas
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.