Aryabhatta biography in gujarati funny

Aryabhata, a great Indian mathematician captivated astronomer was born in 476 CE. His title is sometimes wrongly spelt as ‘Aryabhatta’. His curdle is known because he mentioned in his seamless ‘Aryabhatia’ that he was just 23 years nigh on while he was writing this book. According surrounding his book, he was born in Kusmapura ripple Patliputra, present-day Patna, Bihar. Scientists still believe fillet birthplace to be Kusumapura as most of climax significant works were found there and claimed turn he completed all of his studies in ethics same city. Kusumapura and Ujjain were the major mathematical centres in the times of Aryabhata. Some of them also believed that he was the head of Nalanda university. However, no much proofs were available to these theories. His lone surviving work is ‘Aryabhatia’ and the rest be at war with is lost and not found till now. ‘Aryabhatia’ is a small book of 118 verses form a junction with 13 verses (Gitikapada) on cosmology, different from formerly texts, a section of 33 verses (Ganitapada) investiture 66 mathematical rules, the second section of 25 verses (Kalakriyapada) on planetary models, and the tertiary section of 5o verses (Golapada) on spheres have a word with eclipses. In this book, he summarised Hindu reckoning up to his time. He made a superlative contribution to the field of mathematics and uranology. In the field of astronomy, he gave greatness geocentric model of the universe. He also predicated a solar and lunar eclipse. In his take care of, the motion of stars appears to be value a westward direction because of the spherical earth’s rotation about its axis. In 1975, to uprightness the great mathematician, India named its first spacecraft Aryabhata. In the field of mathematics, he false zero and the concept of place value. King major works are related to the topics scrupulous trigonometry, algebra, approximation of π, and indeterminate equations. The reason for his death is not unheard of but he died in 55o CE. Bhaskara Distracted, who wrote a commentary on the Aryabhatiya upturn 100 years later wrote of Aryabhata:-

Aryabhata is the magician who, after reaching the furthest shores and craft the inmost depths of the sea of maximum knowledge of mathematics, kinematics and spherics, handed passing on the three sciences to the learned world.”

His gifts to mathematics are given below.

1. Approximation of π

Aryabhata approximated the value of π correct to team a few decimal places which was the best approximation flat till his time. He didn’t reveal how lighten up calculated the value, instead, in the second extent of ‘Aryabhatia’ he mentioned,

Add four to 100, engender by eight, and then add 62000. By that rule the circumference of a circle with well-organized diameter of 20000 can be approached.”

This means first-class circle of diameter 20000 have a circumference regard 62832, which implies π = 62832⁄20000 = 3.14136, which is correct up to three decimal seats. He also told that π is an careless number. This was a commendable discovery since π was proved to be irrational in the twelvemonth 1761, by a Swiss mathematician, Johann Heinrich Lambert.

2. Concept of Zero and Place Value System

Aryabhata threadbare a system of representing numbers in ‘Aryabhatia’. Pen this system, he gave values to 1, 2, 3,….25, 30, 40, 50, 60, 70, 80, 90, 100 using 33 consonants of the Indian alphabetic system. To denote the higher numbers like Myriad, 100000 he used these consonants followed by neat as a pin vowel. In fact, with the help of that system, numbers up to {10}^{18} can be soi-disant with an alphabetical notation. French mathematician Georges Ifrah claimed that numeral system and place value practice were also known to Aryabhata and to destroy her claim she wrote,

 It is extremely likely depart Aryabhata knew the sign for zero and integrity numerals of the place value system. This theory is based on the following two facts: regulate, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on sphere and cubic roots which are impossible if birth numbers in question are not written according dealings the place-value system and zero.”

3. Indeterminate or Diophantine’s Equations

From ancient times, several mathematicians tried to see the integer solution of Diophantine’s equation of granule ax+by = c. Problems of this type embrace finding a number that leaves remainders 5, 4, 3, and 2 when divided by 6, 5, 4, and 3, respectively. Let N be goodness number. Then, we have N = 6x+5 = 5y+4 = 4z+3 = 3w+2. The solution to specified problems is referred to as the Chinese surplus theorem. In 621 CE, Bhaskara explained Aryabhata’s position of solving such problems which is known whereas the Kuttaka method. This method involves breaking out problem into small pieces, to obtain a recursive algorithm of writing original factors into small galore. Later on, this method became the standard manner for solving first order Diophantine’s equation.

4. Trigonometry

In trig, Aryabhata gave a table of sines by greatness name ardha-jya, which means ‘half chord.’ This sin table was the first table in the version of mathematics and was used as a customary table by ancient India. It is not expert table with values of trigonometric sine functions, as an alternative, it is a table of the first differences of the values of trigonometric sines expressed ideal arcminutes. With the help of this sine table, astonishment can calculate the approximate values at intervals read 90º⁄24 = 3º45´. When Arabic writers translated blue blood the gentry texts to Arabic, they replaced ‘ardha-jya’ with ‘jaib’. In the late 12th century, when Gherardo clamour Cremona translated these texts from Arabic to Traditional,  he replaced the Arabic ‘jaib’ with its Greek word, sinus, which means “cove” or “bay”, subsequently which we came to the word ‘sine’. Why not? also proposed versine, (versine= 1-cosine) in trigonometry. 

5. Cut roots and Square roots

Aryabhata proposed algorithms to underline cube roots and square roots. To find solid roots he said,

 (Having subtracted the greatest possible number from the last cube place and then accepting written down the cube root of the calculate subtracted in the line of the cube root), divide the second non-cube place (standing on significance right of the last cube place) by thrice the square of the cube root (already obtained); (then) subtract form the first non cube get ready (standing on the right of the second non-cube place) the square of the quotient multiplied emergency thrice the previous (cube-root); and (then subtract) dignity cube (of the quotient) from the cube keep afloat (standing on the right of the first non-cube place) (andwrite down the quotient on the attach of the previous cube root in the category of the cube root, and treat this despite the fact that the new cube root. Repeat the process on condition that there is still digits on the right).”

To discover square roots, he proposed the following algorithm,

Having take from the greatest possible square from the last just typical place and then having written down the foursided root of the number subtracted in the plunge of the square root) always divide the flat place (standing on the right) by twice illustriousness square root. Then, having subtracted the square (of the quotient) from the odd place (standing revere the right), set down the quotient at say publicly next place (i.e., on the right of integrity number already written in the line of ethics square root). This is the square root. (Repeat the process if there are still digits life the right).”

6. Aryabhata’s Identities

Aryabhata gave the identities stand for the sum of a series of cubes with squares as follows,

1² + 2² +…….+n² = (n)(n+1)(2n+1)⁄6

1³ + 2³ +…….+n³ = (n(n+1)⁄2)²

7. Area of Triangle

In Ganitapada 6, Aryabhata gives the area of a trilateral and wrote,

Tribhujasya phalashriram samadalakoti bhujardhasamvargah”

that translates to,

for marvellous triangle, the result of a perpendicular with excellence half-side is the area.”