Yathaa Shikha Mayuranaam, Naaganammanayoyatha Tadvadvedaangasaastranaam Ganitammoordhanistitham’
This sloka, as mentioned in the Vedaanga Jyotisham, the irst known work in astronomy, means
‘Like the crests on the head of peacocks and the gems on the heads of the cobras, Mathematics is adorned at the top of the Vedanga Sciences.’
The Vedas are full of mathematical concepts, the Indian prowess in the ield of mathematics is immense. The work by scholars like Aapastamba, Baudhayana, Bhaskaracharya, Brahmagupta and Arya Bhatta (among others) in the ield of Mathematics remains unparalleled.
Be it the invention of zero, geometry, trigonometry, the number system, the value of pi or the irst power series; Indians have deined and reined almost all mathematical concepts. Let us dwell a little deeper into various concepts that were prevalent in India during the vedic era.
The Sulva Sutras composed by Baudhayana, Manava, Aapastamba and Katyayana are considered the most signiicant.
Pythagorean Theorem and Pythagorean Triplets
The sutras contain discussion and non-axiomatic demonstrations of cases of the Pythagorean Theorem and Pythagorean triplets.
‘The areas (of the squares) produced separately by the length and breadth of a rectangle, together equals to the area of the square produced by the diagonal.’
‘Multiply the length of a right-angled triangle by the same length and breadth by the same breadth; the square-root of the sum of these two results gives the hypotenuse’ ie,
AB2+ BC2= AC2
Aapastamba’s rules for building right angles in altars use the following Pythagorean triplets
(3, 4, 5)
(5, 12, 13) (8, 15, 17) (12, 35, 37)
Square Root of 2
Baudhayana in his Sulva Sutras computed the value of â ˆš 2 correct to seven decimal places;
√2 = 1.4142156….
‘The measure is to be increased by its third and this [third] again by its own fourth less the thirty-fourth part [of that fourth]; this is [the value of ] the diagonal of a square [whose side is the measure].’
Whereas the modern scientiic calculator puts the value as; √2= 1.4142135…
The value of π
Today, we simply know that the ratio of the circumference of a circle to its diameter is constant, denoted by π. Arya Bhattagives the value of this constant in the following fashion:
‘Add 4 to 100, multiply by 8 and add to 62,000. This approximately (aasanna) is the circumference of the circle, whose diameter is 20,000.’ (Arya Bhattiyam, Ganita Paadam, 10)
This means a circle whose diameter is 20,000 units has its circumference approximately equal to:
(100+4) x 8 + 62000 = 62, 832 units
Since, the ratio of circumference of a circle to its diameter is a constant, it follows that:
62832 ÷ 20000 = 3.1416
The Unit of Angle Measure
The angle around a point is measured as 360 degrees. Let us look at how it comes into force.
It is actually connected to astronomical descriptions. The solar system, rotation of earth around the sun, revolution of earth on its own axis as well as the seasonal changes are all calculated using this unit.
In the Rigveda (I-164-48) there is the picturesque description of this, compared to a potter’s wheel,
Dvadasapradhayascakramekam Trininabhyanika u tacciketa Tasminsakamtrimsatanasankavo f arpitah Sastirnacalacalasa
A wheel with 12 spokes, revolves making 360 degrees but not tied to any nails. These 12 spokes represent 12 months or rasis of 30 degrees each and 360 degrees means 360 days in a year. The 3 nabhyas may be the northern, equatorial and southern solstices. Another vedic mantra states,
‘He moves in a circular like path making four divisions and each division consisted of ninety days. His path is vast and has different four stages, he is young but not ixed. Let that heavenly body come to our prayer spot.’
Four quadrants each of 90 = 4A —90 = 360. So the angle around point is 360 degrees.
As the thread that supports the pearls is invisible, likewise, the sustaining and integrating string of underlying Mathematics is also invisible beneath the pearls of various disciplines of Science. This particular aspect of Mathematics was ably recognised by the ancient Indians, who hailed it to be the ‘Crest Jewel’ among all the decorous divisions of Science.
Grant Duff, British Indological Historian, very aptly noted,
‘Many of the advances in the sciences that we consider today to have been made in Europe were in fact made in India centuries ago.’