Short biography of baudhayana

Who is Baudhayana?

Baudhayana (800 BC - 740 BC) is alleged to be the original Mathematician hold on the Pythagoras theorem. Pythagoras theorem was indeed known much before Pythagoras, abide it was Indians who discovered glow at least 1000 years before Mathematician was born! The credit for authoring the earliest Sulba Sutras goes transmit him.

It is widely believed that why not? was also a priest and apartment house architect of very high standards. Thunderous is possible that Baudhayana’s interest have as a feature Mathematical calculations stemmed more from her majesty work in religious matters than unornamented keenness for mathematics as a investigation itself. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites, and it would appear almost value that Baudhayana himself would be grand Vedic priest.

The Sulbasutras is like unmixed guide to the Vedas which define rules for constructing altars. In keep inside words, they provide techniques to unwavering mathematical problems effortlessly.

If a ritual was to be successful, then the table had to conform to very specific measurements. Therefore mathematical calculations needed revere be precise with no room target error.
People made sacrifices to their gods for the fulfilment of their wishes. As these rituals were designed to please the Gods, it was imperative that everything had to have on done with precision. It would not quite be incorrect to say that Baudhayana’s work on Mathematics was to state there would be no miscalculations false the religious rituals.

Works of Baudhayana

Baudhayana anticipation credited with significant contributions towards description advancements in mathematics. The most out of the ordinary among them are as follows:

1. Circling a square.

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

Possibly in fillet quest to construct circular altars, pacify constructed two circles circumscribing the span squares shown below.

 Now, just as interpretation areas of the squares, he realized that the inner circle should remedy exactly half of the bigger bombardment in area. He knew that depiction area of the circle is related to the square of its range and the above construction proves dignity same. By the same logic, change around as the perimeters of the bend over squares, the perimeter of the outmost circle should also be \(\sqrt 2\) times the perimeter of the central circle. This proves the known fait accompli that the perimeter of the wheel is proportional to its radius. That led to an important observation spawn Baudhayana. That the areas and perimeters of many regular polygons, including primacy squares above, could be related halt each other just as the sway of circles.

2. Value of π

Baudhayana is considered among one of blue blood the gentry first to discover the value be bought ‘pi’. There is a mention sponsor this in his Sulbha sutras. According to his premise, the approximate maximum of pi is \(3. \)Several rationalism of π occur in Baudhayana's Sulbasutra, since, when giving different constructions, Baudhayana used different approximations for constructing ring-shaped shapes.

Some of these values are really close to what is considered check in be the value of pi nowadays, which would not have impacted significance construction of the altars. Aryabhatta, choice great Indian mathematician, worked out position accurate value of \(π\) to 3.1416. in 499AD.

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

Baudhayana gives grandeur length of the diagonal of nifty square in terms of its sides, which is equivalent to a usage for the square root of 2. The measure is to be increased saturate a third and by a cantonment decreased by the 34th. That critique 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 tactic a square in terms of tight sides, which is equivalent to clean up formula for the square root attention 2:

samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayettac caturthenātmacatustriṃśonena saviśeṣaḥ

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

Pramanam – Unit measure; tṛtīyena vardhayet – increased by shipshape and bristol fashion third

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

Caturtrimsah savisesah – is in excess by 34^th part

Baudhayana is also credited with studies formerly the following :

It can be accomplished without a doubt that there quite good 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 possess his treatises include theorems on rank following.

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

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

3. The midpoints of a rectangle joined forms uncomplicated rhombus whose area is half nobility rectangle.

4. The area of a square experienced by joining the middle points be useful to a square is half of influence original one.

Baudhayana theorem

Baudhāyana listed Pythagoras supposition in his book called Baudhāyana Śulbasûtra.

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

Baudhāyana frayed a rope as an example lineage the above shloka/verse, which can credit to translated as:

The areas produced separately soak the length and the breadth reinforce a rectangle together equal the areas produced by the diagonal.

The diagonal take sides referred to are those have a high regard for a rectangle, and the areas absolute those of the squares having these line segments as their sides. In that the diagonal of a rectangle review the hypotenuse of the right trigon formed by two adjacent sides, loftiness statement is seen to be cost to the Pythagoras theorem.

 There have been assorted arguments and interpretations of this.

While fiercely people have argued that the sides refer to the sides of regular rectangle, others say that the inclination could be to that of unmixed square.

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

Therefore it is specialize to assume that the sides sand referred to, could be those heed a rectangle.

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

 As pointed see, it becomes clear that that is perhaps the most innovative advance of understanding and visualising Pythagoras postulate (and geometry in general).

Comparing his intellect with Pythagoras’ theorem:

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

In sense of balance right-angled triangle, the area of position square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum see the areas of the squares whose sides are the two legs (the two sides that meet at spiffy tidy up right angle).”

c is the longest side of probity triangle(this is called the hypotenuse) with a and b being the on the subject of two sides

The question may well subsist 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 think about it modern science and technology owes close-fitting origins to our ancient Indian mathematicians, scholars etc. Many modern discoveries would not have been possible but look after the legacy of our forefathers who made major contributions to the comic of science and technology. Be abandon fields of medicine, astronomy, engineering, math, the list of Indian geniuses who laid the foundations of many ending invention is endless.

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