Vedic Mathematics

Sulba Sutras

The Sulba Sutras or Sulva Sutras are texts of the Hindu canon dealing with the geometry of altar construction. They are parts of larger works called Dharma Sutras which are appendices to the Vedas elaborating sacrificial rituals, the conduct of marriage, the sacred law and such. The Sulba Sutras are our only source of knowledge of Indian mathematics of the Vedic period.

The name "Sulba Sutra" means rule of chords, which is another name for geometry. Of the Sulvas so far 'uncovered', the four major and most mathematically significant are those composed by Baudhayana, Manava, Apastamba and Katyayana. These Sulba Sutras have been dated from around 800-500 BC and include first 'use' of irrational numbers, quadratic equations of the form ax2 = c and ax2 + bx = c, unarguable evidence of the use of the Pythagorean theorem and Pythagorean triples, predating Pythagoras (c 572 - 497 BC), and evidence of a number of geometrical proofs.

Pythagoras's theorem is first found in the Baudhayana sutra—so was hence known from around 800 BC. It is also implied in the later work of Apastamba, and Pythagorean triples are found in his rules for altar construction. One of the Sulba Sutras estimates the value of pi as 3.16049. Altar construction also led to the discovery of irrational numbers—a remarkable estimation of the square root of 2 is found in three of the sutras. The method for approximating the value of this number gives the following result:


The result is correct to 5 decimal places. Elsewhere in Indian works however it is stated that various square root values cannot be exactly determined, which strongly suggests an initial knowledge of irrationality.

Indeed an early method for calculating square roots can be found in some Sutras, the method involves repeated application of the formula:


Before the period of the Sulbasutras was at an end, the Brahmi numerals had definitely begun to appear (c. 300BC) and the similarity with modern day numerals is clear to see. More importantly even still was the development of the concept of decimal place value. Certain rules given by the famous Indian grammarian Panini (c. 500 BC) imply the concept of the mathematical zero.

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Vedic mathematics is a system of mental calculation developed by Shri Bharati Krishna Tirthaji in the middle 20th century which he claimed he had based on a lost appendix of Atharvaveda, an ancient text of the Indian teachings called Veda. It has some similarities to the Trachtenberg system in that it speeds up some arithmetic calculations. It claims to have applications to more advanced mathematics, such as calculus and linear algebra. The system was first published in the book Vedic Mathematics ISBN 8120801644 in 1965. The system has since been developed further and there have been several other books released.