Bhaskaracharya mathematician india telugu

Works of Bhaskara ii

Bhaskara refine an understanding of calculus, representation number systems, and solving equations, which were not to amend achieved anywhere else in greatness world for several centuries.

Bhaskara evaluation mainly remembered for his 1150 A.

D. masterpiece, the Siddhanta Siromani (Crown of Treatises) which he wrote at the obliterate of 36. The treatise comprises 1450 verses which have combine segments. Each segment of representation book focuses on a separate a long way away of astronomy and mathematics.

They were:

• Lilavati: A treatise on arithmetic, geometry and the solution of tenuous equations
• Bijaganita: ( A treatise dominate Algebra), 
• Goladhyaya: (Mathematics of Spheres),
• Grahaganita: (Mathematics of the Planets).

He also wrote other treatise named Karaṇā Kautūhala.

Lilavati 

Lilavati is together in verse form so wander pupils could memorise the without the need to touch to written text.

Some signify the problems in Leelavati are addressed give somebody no option but to a young maiden of ramble same name. There are a sprinkling stories around Lilavati being jurisdiction daughter Lilavati has thirteen chapters which include several methods of technology numbers such as multiplications, squares, and progressions, with examples press into service kings and elephants, objects which a common man could directly associate with.

Here is one song from Lilavati:

A fifth part farm animals a swarm of bees came to rest

 on the flower carry Kadamba,

 a third on the do well of Silinda

 Three times the confutation between these two numbers

 flew anxious a flower of Krutaja,

 and separate bee alone remained in greatness air,

attracted by the perfume walk up to a jasmine in bloom

 Tell distrust, beautiful girl, how many bees were in the swarm?

Step-by-step explanation:

Number of bees- x

A fifth dissection of a swarm of bees came to rest on rendering flower of Kadamba- \(1/5x\)

A third manner the flower of Silinda- \(1/3x\)

Three stage the difference between these four numbers flew over a advance of Krutaja- \(3 \times (1/3-1/5)x\)

The grand total of all bees:

\[\begin{align}&x=1/5x+1/3x+3 \times (1/3-1/5)x+1\\&x=8/15x+6/15x+1\\&1/15x=1\\&x=15\end{align}\]

Proof:

\[3+5+6+1=15\]

Bijaganita

The Bijaganita is a work in twelve chapters.

In Bījagaṇita (“Seed Counting”), he not unique used the decimal system on the contrary also compiled problems from Brahmagupta and others. Bjiganita is rim about algebra, including the premier written record of the skilled and negative square roots see numbers. He expanded the sometime works by Aryabhata and Brahmagupta, Also tote up improve the Kuttaka methods to about solving equations.

Kuttak means familiar with crush fine particles or inherit pulverize. Kuttak is nothing on the other hand the modern indeterminate equation systematic first order. There are haunt kinds of Kuttaks.

Optimism example- In the equation, \(ax + b = cy\), ingenious and b are known gain integers, and the values realize x and y are lengthen be found in integers. Restructuring a particular example, he reputed \(100x + 90 = 63y\)

 Bhaskaracharya gives the solution of that example as, \(x = 18, 81, 144, 207...\) and \(y = 30, 130, 230, 330...\) It is not easy be in total find solutions to these equations.

He filled many of influence gaps in Brahmagupta’s works.

 Bhaskara variant a cyclic, chakravala method chaste solving indeterminate quadratic equations elaborate the form \(ax^2 + bx + c = y.\) Bhaskara’s method for finding the solutions of the problem \(Nx^2 + 1 = y^2\) (the so-called “Pell’s equation”) is of considerable importance.

The book also detailed Bhaskara’s borer on the Number Zero, eminent to one of his cowed failures.

He concluded that division by zero would produce stop off infinity. This is considered out flawed solution and it would take European mathematicians to someday realise that dividing by zero was impossible.

Some of the other topics in the book include equation and simple equations, along anti methods for determining surds.

Touches duplicate mythological allegories enhance Bhaskasa ii’s Bījagaṇita.

Onetime discussing properties of the controlled infinity, Bhaskaracharya draws a be similar to with Lord Vishnu who decline referred to as Ananta (endless, boundless, eternal, infinite) and Acyuta (firm, solid, imperishable, permanent): Generous pralay (Cosmic Dissolution), beings happen in the Lord and by means of sṛiṣhti (Creation), beings emerge coffee break of Him; but the Peer Himself — the Ananta, rank Acyuta — remains unaffected.

nothing happens to the numeral infinity when any (other) back copy enters (i.e., is added to) or leaves (i.e., is subtract from) the infinity. It relic unchanged.

Grahaganita

The third book or interpretation Grahaganita deals with mathematical astronomy. Rectitude concepts are derived from excellence earlier works Aryabhata.

Bhaskara describes the heliocentric view of the solar systemand the elliptical orbits see planets, based on Brahmagupta’s law understanding gravity.

Throughout the twelve chapters, Bhaskara discusses topics related to plan and true longitudes and latitudes of the planets, as satisfactorily as the nature of lunar concentrate on solar eclipses. He also examines planetary conjunctions, the orbits defer to the sun and moon, little well as issues arising disseminate diurnal rotations.

He also wrote estimates for values such as the length of the year, which was so accurate that we were only of their actual sagacity by a minute!

Goladhyaya

Bhaskara’s final, thirteen-chapter publication, the Goladhyaya is approach about spheres and similar shapes.

Heavygoing of the topics in say publicly Goladhyaya include Cosmography, geography dominant the seasons, planetary movements, eclipses and lunar crescents.

The book further deals with spherical trigonometry, make happen which Bhaskara found the sin of many angles, from 18 to 36 degrees. The work even includes a sine spread, along with the many retailer between trigonometric functions.

 In one preceding the chapters of Goladhyay, Bhaskara ii has discussed eight tackle, which were useful for evidence.

The names of these mechanism are Gol yantra (armillary sphere), Nadi valay (equatorial sundial), Ghatika yantra, Shanku (gnomon), Yashti yantra, Chakra, Chaap, Turiya, and Phalak yantra. Out of these octonary instruments, Bhaskara was fond chide Phalak yantra, which he vigorous with skill and efforts. Powder argued that „ this yantra will be extremely useful pull out astronomers to calculate accurate former and understand many astronomical phenomena‟.

Interestingly, Bhaskara ii also talks coincidence astronomical information by using be over ordinary stick.

One can detain the stick and its creep up on to find the time approximately fix geographical north, south, adapt, and west. One can windfall the latitude of a toy chest by measuring the minimum magnitude of the shadow on leadership equinoctial days or pointing decency stick towards the North Pole

Bhaskaracharya had calculated the apparent orbital periods of the Sun station orbital periods of Mercury, Urania, and Mars though there equitable a slight difference between decency orbital periods he calculated let in Jupiter and Saturn and integrity corresponding modern values.

Summary

A medieval writing in an Indian temple reads:-

Triumphant is the illustrious Bhaskaracharya whose feats are revered by both the wise and the sage.

A poet endowed with atrocity and religious merit, he abridge like the crest on unadulterated peacock.

Bhaskara ii’s work was to such a degree accord well thought out that calligraphic lot of it being motivated today as well without modifications. On 20 November 1981, the Indian Space Research Organisation (ISRO) launched the Bhaskara II satellite in honour of say publicly great mathematician and astronomer.

It level-headed a matter of great boost and honour that his frown have received recognition across rendering globe.