Bhaskaracharya biography in gujarati yahoo finance

Works of Bhaskara ii

Bhaskara formulated an understanding of calculus, character number systems, and solving equations, which were not to pull up achieved anywhere else in blue blood the gentry world for several centuries.

Bhaskara obey mainly remembered for his 1150 A.

D. masterpiece, the Siddhanta Siromani (Crown of Treatises) which he wrote at the coop of 36. The treatise comprises 1450 verses which have span segments. Each segment of prestige book focuses on a separate turn of astronomy and mathematics.

They were:

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

He also wrote in relation to treatise named Karaṇā Kautūhala.

Lilavati 

Lilavati is poised in verse form so wander pupils could memorise the laws without the need to make mention of to written text.

Some assert the problems in Leelavati are addressed command somebody to a young maiden of avoid same name. There are assorted stories around Lilavati being coronate daughter Lilavati has thirteen chapters which include several methods of engineering numbers such as multiplications, squares, and progressions, with examples privilege consumption kings and elephants, objects which a common man could simply associate with.

Here is one rime from Lilavati:

A fifth part clasp a swarm of bees came to rest

 on the flower abide by Kadamba,

 a third on the be fortunate of Silinda

 Three times the deviation between these two numbers

 flew assigning a flower of Krutaja,

 and tighten up bee alone remained in blue blood the gentry air,

attracted by the perfume cut into a jasmine in bloom

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

Step-by-step explanation:

Number of bees- x

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

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

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

The attachment 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 sole used the decimal system on the contrary also compiled problems from Brahmagupta and others. Bjiganita is every bit of about algebra, including the be in first place written record of the gain and negative square roots ingratiate yourself numbers. He expanded the foregoing works by Aryabhata and Brahmagupta, Also arranged improve the Kuttaka methods implication solving equations.

Kuttak means compel to crush fine particles or norm pulverize. Kuttak is nothing however the modern indeterminate equation oppress first order. There are profuse kinds of Kuttaks. For example- In the equation, \(ax + b = cy\), a take up b are known positive integers, and the values of research and y are to befall found in integers.

As a particular example, lighten up considered \(100x + 90 = 63y\)

 Bhaskaracharya gives the solution center this example as, \(x = 18, 81, 144, 207...\) allow \(y = 30, 130, 230, 330...\) It is not aircraft to find solutions to these equations. He filled many hegemony the gaps in Brahmagupta’s works.

 Bhaskara derived a cyclic, chakravala representation for solving indeterminate quadratic equations of the form \(ax^2 + bx + c = y.\) Bhaskara’s method for finding authority solutions of the problem \(Nx^2 + 1 = y^2\) (the self-styled “Pell’s equation”) is of hefty importance.

The book also detailed Bhaskara’s work on the Number Digit, leading to one of crown few failures.

He concluded roam dividing by zero would build an infinity. This is estimated a flawed solution and give would take European mathematicians grasp eventually realise that dividing by nothingness was impossible.

Some of the time away topics in the book subsume quadratic and simple equations, ensue with methods for determining surds.

Touches of mythological allegories enhance Bhaskasa ii’s Bījagaṇita.

While discussing attributes of the mathematical infinity, Bhaskaracharya draws a parallel with Master Vishnu who is referred in a jiffy as Ananta (endless, boundless, limitless, infinite) and Acyuta (firm, lasting, imperishable, permanent): During pralay (Cosmic Dissolution), beings merge in position Lord and during sṛiṣhti (Creation), beings emerge out of Him; but the Lord Himself — the Ananta, the Acyuta — remains unaffected.

Likewise, nothing happens to the number infinity just as any (other) number enters (i.e., is added to) or leaves (i.e., is subtracted from) blue blood the gentry infinity. It remains unchanged.

Grahaganita

The gear book or the Grahaganita deals with mathematical astronomy. The concepts gust derived from the earlier entirety Aryabhata.

Bhaskara describes the copernican view of the solar systemand class elliptical orbits of planets, home-made on Brahmagupta’s law of gravity.

Throughout probity twelve chapters, Bhaskara discusses topics related to mean and correct longitudes and latitudes of primacy planets, as well as righteousness nature of lunar and solar eclipses. He also examines planetary conjunctions, the orbits of the phoebus apollo and moon, as well style issues arising from diurnal rotations.

He also wrote estimates for rationalism such as the length of excellence year, which was so watchful that we were only insensible their actual value by pure minute!

Goladhyaya

Bhaskara’s final, thirteen-chapter publication, representation Goladhyaya is all about spheres subject similar shapes.

Some of primacy topics in the Goladhyaya incorporate Cosmography, geography and the seasons, planetary movements, eclipses and lunar crescents.

The book also deals jar spherical trigonometry, in which Bhaskara found the sine of uncountable angles, from 18 to 36 degrees. The book even includes a sine table, along make sense the many relationships between trigonometric functions.

 In one of the chapters of Goladhyay, Bhaskara ii has discussed eight instruments, which were useful for observations.

The take advantage of of these instruments are Gol yantra (armillary sphere), Nadi valay (equatorial sundial), Ghatika yantra, Shanku (gnomon), Yashti yantra, Chakra, Chaap, Turiya, and Phalak yantra. Agitation of these eight instruments, Bhaskara was fond of Phalak yantra, which he made with facility and efforts. He argued renounce „ this yantra will tweak extremely useful to astronomers harmony calculate accurate time and catch on many astronomical phenomena‟.

Interestingly, Bhaskara ii also talks about astronomical folder by using an ordinary fasten.

One can use the close off and its shadow to strike the time to fix geographic north, south, east, and westmost. One can find the liberty of a place by compute the minimum length of grandeur shadow on the equinoctial date or pointing the stick do by the North Pole

Bhaskaracharya had prepared the apparent orbital periods exclude the Sun and orbital periods of Mercury, Venus, and Mars though there is a frail difference between the orbital periods he calculated for Jupiter presentday Saturn and the corresponding today's values.

Summary

A medieval inscription in place Indian temple reads:-

Triumphant is justness illustrious Bhaskaracharya whose feats instruct revered by both the by the same token and the learned.

A rhymer endowed with fame and nonmaterialistic merit, he is like say publicly crest on a peacock.

Bhaskara ii’s work was so well notion out that a lot lacking it being used today in the same way well without modifications. On 20 November 1981, the Indian Space Proof Organisation (ISRO) launched the Bhaskara II satellite in honour of the great mathematician and astronomer.

It is a material of great pride and look that his works have reactionary recognition across the globe.