||VEDAS depicting MATHEMATICS||~Mention of Modern Mathematical Theorems in Vedas!!

It was a very common and well believed dialogue of our elders or folks of previous generations that ” Vedas have it all” or ” One who knows Vedas knows everything! “.

Initially these talks were subjects of ignorance as far as Modern Scientific approach was taken as pivot point but gradually many discoveries and sequential series of decoding activities of prehistoric Vedic quotes, shlokas and mantras has been able to clear many misconceptions and ambiguities and these pre-historic scriptures have proved themselves to be flamboyant enough to attract global interest in their exploration both at scientific and spiritual front.

Just for instance, there are Baudhayana Sutras which are compilation of Vedic Sanskrit texts related to dharma, daily rituals, mathematics etc. and are one of the earliest texts of the ‘sutra’ genre.

The Baudhayana sūtras consist of six texts:

the Śrautasûtra, in 19 Praśnas (questions),

the Dvaidhasûtra in 4 Praśnas,

the Grihyasutra in 4 Praśnas,

the Dharmasûtra in 4 Praśnas

The Baudhāyana Śulbasûtra is noted for containing several early mathematical results, including an approximation of the square root of 2 and the statement of a version of the Pythagorean theorem.

Pythagorean theorem is also referred to as Baudhayana theorem. The most notable of the rules (the Sulbasūtra-s do not contain any proofs for the rules which they describe, since they are sūtra-s, formulae, concise) in the Baudhāyana Sulba Sūtrasays:

दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī,

The lines are to be referring to a rectangle, although some interpretations consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, however, it would constitute a less general claim, but the text seems to be quite open to unequal sides.

If this refers to a rectangle, it is the earliest recorded statement of the Pythagorean theorem.

Baudhāyana also provides a non-axiomatic demonstration using a rope measure of the reduced form of the Pythagorean theorem for an isosceles right triangle.

Circling the square

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

Explanation:

Square root of 2

Baudhāyana i.61-2 (elaborated in Āpastamba Sulbasūtra i.6) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2:

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.

It should be noted that 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). This is an aspect of Vaastu Shastras and Shilpa Shastras. These theroms are derived from those texts.

Since a long time various studies and research works are being conducted on the above mentioned sutras and shastras like the following-

Various such sutras, shlokas and scripts are still to be analysed, decoded and yet to be understood which proclaim the richness and command of mathematicians, scientists and thinkers of Vedic Era, eloquently, over various fields of literature, mathematics, science and arts in a vivid and specialised mode of approach.