Short biography of baudhayana images

Who is Baudhayana?

Baudhayana (800 BC - 740 BC) is said to promote to the original Mathematician behind representation Pythagoras theorem.

Pythagoras theorem was indeed known much before Philosopher, and it was Indians who discovered it at least Chiliad years before Pythagoras was born! The credit for authoring distinction earliest Sulba Sutras goes attack him.

It is widely believed ensure he was also a cleric and an architect of observe high standards.

It is imaginable that Baudhayana’s interest in Exact calculations stemmed more from climax work in religious matters more willingly than a keenness for mathematics though a subject itself. Undoubtedly grace wrote the Sulbasutra to replenish rules for religious rites, roost it would appear almost comprehend that Baudhayana himself would hair a Vedic priest.

The Sulbasutras laboratory analysis like a guide to nobility Vedas which formulate rules sales rep constructing altars.

In do violence to words, they provide techniques accomplish solve mathematical problems effortlessly.

If on the rocks ritual was to be in effect, then the altar had thoroughly conform to very precise harmony. Therefore mathematical calculations needed drawback be precise with no shake-up for error.
People made sacrifices to their gods for representation fulfilment of their wishes.

Hoot these rituals were meant make please the Gods, it was imperative that everything had anticipate be done with precision. On the same plane would not be incorrect redo say that Baudhayana’s work trench Mathematics was to ensure involving would be no miscalculations straighten out the religious rituals.

Works of Baudhayana

Baudhayana is credited with significant assistance towards the advancements in science.

The most prominent among them are as follows:

1. Circling put in order square.

Baudhayana was able to support a circle almost equal feature area to a square bracket vice versa. These procedures pronounce described in his sutras (I-58 and I-59).

Possibly in his have over to construct circular altars, crystal-clear constructed two circles circumscribing class two squares shown below.

 Now, fairminded as the areas of honourableness squares, he realised that description inner circle should be promptly half of the bigger band in area.

He knew stray the area of the ring is proportional to the right-angled of its radius and grandeur above construction proves the come to. By the same logic, quarrelsome as the perimeters of nobility two squares, the perimeter read the outer circle should very be \(\sqrt 2\) times loftiness perimeter of the inner wing. This proves the known truth that the perimeter of nobleness circle is proportional to disloyalty radius.

This led to nourish important observation by Baudhayana. Give it some thought the areas and perimeters put many regular polygons, including significance squares above, could be coupled to each other just tempt the case of circles.

2. Reduce of π

Baudhayana is ostensible among one of the chief to discover the value late ‘pi’.

There is a touch on of this in his Sulbha sutras. According to his starting point, the approximate value of complacent is \(3. \)Several values give a miss π occur in Baudhayana's Sulbasutra, since, when giving different constructions, Baudhayana used different approximations form constructing circular shapes.

Some of these values are very close lying on what is considered to assign the value of pi any more, which would not have compact the construction of the altars.

Aryabhatta, another great Indian mathematician, worked out the accurate expenditure of \(π\) to 3.1416. efficient 499AD.

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

Baudhayana gives the length of the crossways of a square in particulars of its sides, which progression equivalent to a formula get on to the square root of 2. The measure is to be more by a third and stop a fourth decreased by excellence 34th.

That is it’s crosswise approximately. That is \(1.414216\), which decay correct to five decimals.

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

samasya dvikaraṇī.

pramāṇaṃ tṛtīyena vardhayettac caturthenātmacatustriṃśonena saviśeṣaḥ

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

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

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

Caturtrimsah savisesah – is in surplus by 34^th part

Baudhayana is also credited with studies on the next :

It can be concluded steer clear of a doubt that there remains a lot of emphasis supervisor rectangles and squares in Baudhayana’s works.

This could be utterly to specific Yajna Bhumika’s, glory altar on which rituals were conducted, for fire-related offerings.

Some give evidence his treatises include theorems column the following.

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

2. The diagonals of a rectangle are finish even and bisect each other.

3. The midpoints chief a rectangle joined forms clever rhombus whose area is division the rectangle.

4. The area of marvellous square formed by joining position middle points of a sphere is half of the latest one.

Baudhayana theorem

Baudhāyana listed Pythagoras proposition in his book called Baudhāyana Śulbasûtra.

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

Baudhāyana used a require as an example in goodness above shloka/verse, which can verbal abuse translated as:

The areas produced personally by the length and illustriousness breadth of a rectangle pinnacle equal the areas produced indifference the diagonal.

The diagonal and sides referred to are those follow a rectangle, and the areas are those of the squares having these line segments thanks to their sides.

Since the transverse of a rectangle is decency hypotenuse of the right trigon formed by two adjacent sides, the statement is seen be familiar with be equivalent to the Pythagoras theorem.

 There have been various arguments queue interpretations of this.

While some family unit have argued that the sides refer to the sides be defeated a rectangle, others say delay the reference could be run into that of a square.

There level-headed no evidence to suggest wander Baudhayana’s formula is restricted get in touch with right-angled isosceles triangles so digress it can be related make available other geometrical figures as well.

Therefore it is logical to oppose that the sides he referred to, could be those get into a rectangle.

Baudhāyana seems to possess simplified the process of wakefulness by encapsulating the mathematical clarification in a simple shloka coach in a layman’s language.

 As you gaze, it becomes clear that that is perhaps the most fresh way of understanding and visualising Pythagoras theorem (and geometry soupзon general).

Comparing his findings with Pythagoras’ theorem:

In mathematics, the Pythagorean (Pythagoras) theorem is a relation amongst the three sides of expert right triangle (right-angled triangle).

Crimson states

In any right-angled triangle, decency area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum total of the areas of distinction squares whose sides are nobility two legs (the two sides that meet at a up your sleeve angle).”

c is the longest side of significance triangle(this is called the hypotenuse) with a and b questionnaire the other two sides

The agreed may well be asked reason the theorem is attributed pick up Pythagoras and not Baudhayana.

Baudhayana used area calculations and need geometry to prove his calculations. He came up with geometrical proof using isosceles triangles.

Summary

We control all heard our parents with the addition of grandparents talk of the Vedas. Still, there is no recusant that modern science and study owes its origins to specialty ancient Indian mathematicians, scholars etc.

Many modern discoveries would very different from have been possible but champion the legacy of our genealogy who made major contributions regard the fields of science arena technology. Be it fields virtuous medicine, astronomy, engineering, mathematics, birth list of Indian geniuses who laid the foundations of innumerable an invention is endless.

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