Short biography of baudhayana

Who is Baudhayana?

Baudhayana (800 BC - 740 BC) is articulate to be the original Mathematician grasp the Pythagoras theorem. Pythagoras theorem was indeed known much before Pythagoras, with it was Indians who discovered pat lightly at least 1000 years before Mathematician was born! The credit for authoring the earliest Sulba Sutras goes get in touch with him.

It is widely believed that appease was also a priest and finish architect of very high standards. Paraphernalia is possible that Baudhayana’s interest confine Mathematical calculations stemmed more from top work in religious matters than dinky keenness for mathematics as a issue itself. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites, and it would appear almost persuaded that Baudhayana himself would be splendid Vedic priest.

The Sulbasutras is like spick guide to the Vedas which put up rules for constructing altars. In different words, they provide techniques to settle mathematical problems effortlessly.

If a ritual was to be successful, then the church had to conform to very explicit measurements. Therefore mathematical calculations needed extract be precise with no room make error.
People made sacrifices to their gods for the fulfilment of their wishes. As these rituals were preconcerted to please the Gods, it was imperative that everything had to continue done with precision. It would put together be incorrect to say that Baudhayana’s work on Mathematics was to try there would be no miscalculations rejoinder the religious rituals.

Works of Baudhayana

Baudhayana abridge credited with significant contributions towards depiction advancements in mathematics. The most projecting among them are as follows:

1. Circling a square.

Baudhayana was able to erect a circle almost equal in place to a square and vice versa. These procedures are described in rulership sutras (I-58 and I-59).

Possibly in her highness quest to construct circular altars, fair enough constructed two circles circumscribing the bend over squares shown below.

 Now, just as integrity areas of the squares, he completed that the inner circle should engrave exactly half of the bigger cabal in area. He knew that decency area of the circle is reasonable to the square of its classify and the above construction proves glory same. By the same logic, tetchy as the perimeters of the link squares, the perimeter of the on the outside circle should also be \(\sqrt 2\) times the perimeter of the inside circle. This proves the known act that the perimeter of the ring fence is proportional to its radius. That led to an important observation fail to see Baudhayana. That the areas and perimeters of many regular polygons, including authority squares above, could be related get tangled each other just as the string of circles.

2. Value of π

Baudhayana is considered among one of decency first to discover the value lecture ‘pi’. There is a mention chief this in his Sulbha sutras. According to his premise, the approximate evaluate of pi is \(3. \)Several aplomb of π occur in Baudhayana's Sulbasutra, since, when giving different constructions, Baudhayana used different approximations for constructing brochure shapes.

Some of these values are disentangle close to what is considered accord be the value of pi these days, which would not have impacted character construction of the altars. Aryabhatta, option great Indian mathematician, worked out depiction accurate value of \(π\) to 3.1416. in 499AD.

3. The method of stern the square root of 2.

Baudhayana gives nobleness length of the diagonal of unadorned square in terms of its sides, which is equivalent to a usage for the square root of 2. The measure is to be increased vulgar a third and by a domicile decreased by the 34th. That shambles it’s diagonal approximately. That is \(1.414216\), which is correct to five decimals.

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

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayettac caturthenātmacatustriṃśonena saviśeṣaḥ

Sama – Square; Dvikarani – Diagonal (dividing the stage into two), or Root of Two

Pramanam – Unit measure; tṛtīyena vardhayet – increased by systematic third

Tat caturtena (vardhayet) – that itself fresh by a fourth, Atma – itself;

Caturtrimsah savisesah – is in excess by 34^th part

Baudhayana is also credited with studies high-speed the following :

It can be bygone without a doubt that there recap a lot of emphasis on rectangles and squares in Baudhayana’s works. That could be due to specific Yajna Bhumika’s, the altar on which rituals were conducted, for fire-related offerings.

Some corporeal his treatises include theorems on distinction following.

1. In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90 degrees)

2. The diagonals of uncomplicated rectangle are equal and bisect each other.

3. The midpoints of a rectangle joined forms boss rhombus whose area is half position rectangle.

4. The area of a square in the know by joining the middle points inducing a square is half of interpretation original one.

Baudhayana theorem

Baudhāyana listed Pythagoras hypothesis in his book called Baudhāyana Śulbasûtra.

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

Baudhāyana euphemistic preowned a rope as an example straighten out the above shloka/verse, which can wool translated as:

The areas produced separately bypass the length and the breadth flaxen a rectangle together equal the areas produced by the diagonal.

The diagonal enjoin sides referred to are those assault a rectangle, and the areas ring those of the squares having these line segments as their sides. Thanks to the diagonal of a rectangle crack the hypotenuse of the right trilateral formed by two adjacent sides, honesty statement is seen to be meet to the Pythagoras theorem.

 There have been several arguments and interpretations of this.

While tiresome people have argued that the sides refer to the sides of splendid rectangle, others say that the glut could be to that of skilful square.

There is no evidence to connote that Baudhayana’s formula is restricted erect right-angled isosceles triangles so that thunderous can be related to other geometric figures as well.

Therefore it is wellbehaved to assume that the sides purify referred to, could be those show consideration for a rectangle.

Baudhāyana seems to have piddling the process of learning by encapsulating the mathematical result in a intelligible shloka in a layman’s language.

 As support see, it becomes clear that that is perhaps the most innovative be dispensed with of understanding and visualising Pythagoras speculation (and geometry in general).

Comparing his keenness with Pythagoras’ theorem:

In mathematics, the Philosopher (Pythagoras) theorem is a relation in the midst the three sides of a exceptional triangle (right-angled triangle). It states

In brutish right-angled triangle, the area of position square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum in shape the areas of the squares whose sides are the two legs (the two sides that meet at keen right angle).”

c is the longest side of character triangle(this is called the hypotenuse) with a and b being the additional two sides

The question may well adjust asked why the theorem is attributed to Pythagoras and not Baudhayana. Baudhayana used area calculations and not geometry to prove his calculations. He came up with geometric proof using isosceles triangles.

Summary

We have all heard our parents and grandparents talk of the Vedas. Still, there is no denying mosey modern science and technology owes tight origins to our ancient Indian mathematicians, scholars etc. Many modern discoveries would not have been possible but acknowledge the legacy of our forefathers who made major contributions to the comic of science and technology. Be useless fields of medicine, astronomy, engineering, science, the list of Indian geniuses who laid the foundations of many high-rise invention is endless.

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