Vedic period is a period in which oldest scripts of world, in Sanskrit, called as Vedas were made which were based on Hinduism. Initially for many years these Vedic scripts, texts, hymes were transferred orally. The Vedic period starts around in 1700 BC and ends in the year 500 BC. People initially were present in north-west part of ancient India but slowly moved towards eastern India and also towards south (Deccan).
People from the Vedic period cannot be termed as mathematicians by professions; they were priests/ pandits/ rishis who made use of mathematics for carrying out their religious rituals. Thus emphasis was not given on the proofs but used as properties/sutras. Vast knowledge of mathematics was also used in fields of astronomical and astrological topics like calculation of year duration, eclipses, zodiac signs etc.
Vedic period can be divided in 2 periods (approx dates):
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[wptabtitle] Early Vedic Period[/wptabtitle]
Early Vedic Period
(1700 – 1000 BC):
No mathematical texts are found from this period as in those days each information was transferred orally and was recited number of times so that they are well remembered. But still they used mathematics on large basis and used mathematical knowledge for carrying out their rituals.
- As stated in Rigveda, like Babylonians, they were able to independently predict the date of solar eclipse.
- Vedic people did name very large numbers (upto till 1062) and surprisingly they used all these big numbers just for their rituals.For one of the ritual, one of the Rishi counts till 1012.
He after preparing bricks for a Vedic ritual, prays to the Lord of fire (Agni).
Imā me Agna istakā dhenava
Santvekā ća desa ća satam ća
Sahasram ćāyutam ća niyutam ća
Prayutam ćārbudam ća nyarbudam ća
Samudrasća madhyam ćāntasća
Parārdhasćaita me agna ishtakā
Oh Agni! Let these bricks be milk giving cows to me
Please give me one and ten and hundred and thousand
Ten thousand and lakh and ten lakh and
One crore and ten crore and hundred crore,
A thousand crore and one lakh crore in this world
and other worlds too.
Eka 1 100 Dasa 10 101 Satam 100 102 Sahasram 1000 103 Ayutam 10000 104 Niyutam 100000 105 Prayutam 1000000 106 Arbudam 10000000 107 Nyaburdam 100000000 108 Samudram 1000000000 109 Madhyam 10000000000 1010 Antam 100000000000 1011 Paradham 1000000000000 1012
As stated in Yajurveda, Vedic people were able to calculate (almost accurate) duration of year, month, day and also the 4 cosmic periods which were based on Sun. They were able to calculate the duration of year as > 365 but < 366 days.
They knew a circle is made up of 360 degrees. Based on this knowledge they were able to calculate the zodiac signs. Also while fixing spokes in the wheels of chariots they used the concept of 360 degrees circle. More geometrical work was seen in Sulbhsutras.
Altar is shape of structure which was built using large number of bricks categorized as special & ordinary in a various shapes and various layers to perform their rituals like sacrifice.
One of the altar in the shape of a bird called as Falcom is shown below (1st Layer).
[wptabtitle] Late Vedic Period[/wptabtitle] [wptabcontent]
Late Vedic Period
(1000 – 500 BC):
1st ever Indian texts on mathematics were prepared in this period and they are called as SulbaSutras.
It is considered as only source of ancient Indian Mathematics from Vedic Period and was written in the period 800 BC – 200 BC. But again it was used for carrying out rituals. Sulbasutras is a list of rules for carrying out fire altars. These Sulbasutras had good amount of Geometry which was required as altars were needed to be in specific shapes and dimensions like length, height, area, etc. and also were required to convert 1 shape of altar to another to maintain similar properties like area.
Sulbasutras were written by
- Baudhayana (arnd 800BC)
- Manava (arnd 750BC)
- Apastamba (arnd 600BC)
- Katyayana (arnd 200BC)
Mathematics involved in Sulbasutras as follows:
Geometric figures and their inter conversions:
Many geometrical figures (probably 1st time) were seen in Sulbasutras for carrying out their rituals in the form of Altars. These included circle, square, rectangle, trapezium, isosceles trapezium, isosceles triangle, rhombus, etc. Also their conversion, keeping the areas same, like square to circle, rectangle to square, square to circle, circle to square, etc. were seen.
And hence in these conversions, value of pi was also calculated.
Example: Conversion of circle to square keeping area constant.
Constructing a square of side 13/15 times the diameter of the given circle
This corresponds to taking π = 4 × (13/15)2 = 676/225 = 3.00444.
More correct value of pi was calculated as 3.125 by Manava.
Baudhayana clearly knew the Pythagorus theorem and the Pythagorus Triples and he commented as
“The rope which is stretched across the diagonal of a square produces an area double the size of the original square”.
Katyayana gave more general version of Pythagorus theorem:
“The rope which is stretched along the length of the diagonal of a rectangle produces an area which the vertical and horizontal sides make together”.
In Sulbasutras frequent usage of Pythagorean triples were observed like (3, 4, 5), (5, 12, 13), (12, 16, 20), (8, 15, 17), etcAlthough this property(theorem) was known to many like Baudhayana and Babylonians, still it is credited to Greek mathematician Pythagoras, who was born arnd 800 years after Baudhayana, as it is believed that Pythagoras and his pupils were first to prove this property.
Calculation of Irrational numbers was also seen in Sulbasutras.
Eg: Squareroot of 2(irrational number).
It was stated as “Increase a unit length by its third and this third by its own fourth less the thirty-fourth part of that fourth”.
√2 = 1 + 1/3 + 1/(3 × 4) – 1/(3 × 4 × 34) = 577/408 = 1.4142