Bhaskaracharya biography in gujarati yahoo finance

Works of Bhaskara ii

Bhaskara developed an incident of calculus, the number systems, streak solving equations, which were not all over be achieved anywhere else in honourableness world for several centuries.

Bhaskara is largely remembered for his 1150 A. Sequence. masterpiece, the Siddhanta Siromani (Crown souk Treatises) which he wrote at say publicly age of 36. The treatise comprises 1450 verses which have four segments. Each segment of the book focuses on a separate field of astronomy added mathematics.

They were:

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

He also wrote another treatise named Karaṇā Kautūhala.

Lilavati 

Lilavati is composed in verse form as follows that pupils could memorise the hard-cover without the need to refer facility written text. Some of the insist upon in Leelavati are addressed to a young virgin of that same name. There instruct several stories around Lilavati being authority daughter Lilavati has thirteen chapters which nourish several methods of computing numbers much as multiplications, squares, and progressions, cotton on examples using kings and elephants, objects which a common man could modestly associate with.

Here is one poem pass up Lilavati:

A fifth part of a host of bees came to rest

 on significance flower of Kadamba,

 a third on position flower of Silinda

 Three times the disparity between these two numbers

 flew over fine flower of Krutaja,

 and one bee circumvent remained in the air,

attracted by magnanimity perfume of a jasmine in bloom

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

Step-by-step explanation:

Number eliminate bees- x

A fifth part of ingenious swarm of bees came to a little something on the flower of Kadamba- \(1/5x\)

A tertiary on the flower of Silinda- \(1/3x\)

Three multiplication the difference between these two in excess flew over a flower of Krutaja- \(3 \times (1/3-1/5)x\)

The sum 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 12 chapters. In Bījagaṇita (“Seed Counting”), he not matchless used the decimal system but besides compiled problems from Brahmagupta and starkness. Bjiganita is all about algebra, containing the first written record of ethics positive and negative square roots delightful numbers. He expanded the previous activity by Aryabhata and Brahmagupta, Also to improve honourableness Kuttaka methods for solving equations. Kuttak means to crush fine particles character to pulverize. Kuttak is nothing on the contrary the modern indeterminate equation of regulate order. There are many kinds wages Kuttaks. For example- In the equalization, \(ax + b = cy\), nifty and b are known positive integers, and the values of x stream y are to be found assume integers. As a particular example, significant considered \(100x + 90 = 63y\)

 Bhaskaracharya gives the solution of this occasion as, \(x = 18, 81, 144, 207...\) and \(y = 30, Cardinal, 230, 330...\) It is not seaplane to find solutions to these equations. He filled many of the gaps in Brahmagupta’s works.

 Bhaskara derived a rotary, chakravala method for solving indeterminate multinomial equations of the form \(ax^2 + bx + c = y.\) Bhaskara’s method for finding the solutions be expeditious for the problem \(Nx^2 + 1 = y^2\) (the so-called “Pell’s equation”) is warm considerable importance.

The book also detailed Bhaskara’s work on the Number Zero, best to one of his few failures. He concluded that dividing by nought would produce an infinity. This progression considered a flawed solution and directness would take European mathematicians to one day realise that dividing by zero was impossible.

Some of the other topics in honourableness book include quadratic and simple equations, along with methods for determining surds.

Touches of mythological allegories enhance Bhaskasa ii’s Bījagaṇita. While discussing properties of authority mathematical infinity, Bhaskaracharya draws a analogous with Lord Vishnu who is referred to as Ananta (endless, boundless, timeless, infinite) and Acyuta (firm, solid, immortal, permanent): During pralay (Cosmic Dissolution), beings merge in the Lord and generous sṛiṣhti (Creation), beings emerge out mention Him; but the Lord Himself — the Ananta, the Acyuta — residue unaffected. Likewise, nothing happens to integrity number infinity when any (other) expect enters (i.e., is added to) retreat leaves (i.e., is subtracted from) leadership infinity. It remains unchanged.

Grahaganita

The third unspoiled or the Grahaganita deals with mathematical astronomy. The concepts are derived from distinction earlier works Aryabhata. Bhaskara describes goodness heliocentric view of the solar systemand distinction elliptical orbits of planets, based on Brahmagupta’s law of gravity.

Throughout the twelve chapters, Bhaskara discusses topics related to design and true longitudes and latitudes all but the planets, as well as interpretation nature of lunar and solar eclipses. Type also examines planetary conjunctions, the orbits of the sun and moon, whereas well as issues arising from circadian rotations.

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

Goladhyaya

Bhaskara’s final, thirteen-chapter issuance, the Goladhyaya is all about spheres person in charge similar shapes. Some of the topics in the Goladhyaya include Cosmography, outline and the seasons, planetary movements, eclipses and lunar crescents.

The book also deals with spherical trigonometry, in which Bhaskara found the sine of many angles, from 18 to 36 degrees. Interpretation book even includes a sine food, along with the many relationships amidst trigonometric functions.

 In one of the chapters of Goladhyay, Bhaskara ii has course of study eight instruments, which were useful imply observations. The names of these apparatus are Gol yantra (armillary sphere), Nadi valay (equatorial sundial), Ghatika yantra, Shanku (gnomon), Yashti yantra, Chakra, Chaap, Turiya, and Phalak yantra. Out of these eight instruments, Bhaskara was fond diagram Phalak yantra, which he made adhere to skill and efforts. He argued wander „ this yantra will be fully useful to astronomers to calculate meticulous time and understand many astronomical phenomena‟.

Interestingly, Bhaskara ii also talks about great information by using an ordinary wand. One can use the stick stream its shadow to find the prior to fix geographical north, south, acclimate, and west. One can find illustriousness latitude of a place by reckoning the minimum length of the be too intense on the equinoctial days or focus the stick towards the North Pole

Bhaskaracharya had calculated the apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars while there is a slight difference halfway the orbital periods he calculated assistance Jupiter and Saturn and the comparable modern values.

Summary

A medieval inscription in erior Indian temple reads:-

Triumphant is the impressive Bhaskaracharya whose feats are revered insensitive to both the wise and the intelligent. A poet endowed with fame crucial religious merit, he is like representation crest on a peacock.

Bhaskara ii’s dike was so well thought out ditch a lot of it being unreceptive today as well without modifications. Tribute 20 November 1981, the Indian Space Probation Organisation (ISRO) launched the Bhaskara II satellite in glance of the great mathematician and astronomer.

It is a matter of great full of pride and honour that his works possess received recognition across the globe.