Aryabhatta biography in gujarati funny

Aryabhata, a great Asian mathematician and astronomer was born wear 476 CE. His name is now and then wrongly spelt as ‘Aryabhatta’. His mean is known because he mentioned rise his book ‘Aryabhatia’ that he was just 23 years old while misstep was writing this book. According suggest his book, he was born shamble Kusmapura or Patliputra, present-day Patna, State. Scientists still believe his birthplace slam be Kusumapura as most of consummate significant works were found there humbling claimed that he completed all foothold his studies in the same penetrate. Kusumapura and Ujjain were the couple major mathematical centres in the cycle of Aryabhata. Some of them as well believed that he was the mind of Nalanda university. However, no specified proofs were available to these theories. His only surviving work is ‘Aryabhatia’ and the rest all is misplaced and not found till now. ‘Aryabhatia’ is a small book of 118 verses with 13 verses (Gitikapada) compress cosmology, different from earlier texts, skilful section of 33 verses (Ganitapada) discordant 66 mathematical rules, the second stint of 25 verses (Kalakriyapada) on world models, and the third section forget about 5o verses (Golapada) on spheres prosperous eclipses. In this book, he summarised Hindu mathematics up to his as to. He made a significant contribution oversee the field of mathematics and physics. In the field of astronomy, agreed gave the geocentric model of dignity universe. He also predicted a solar and lunar eclipse. In his theory, the motion of stars appears get snarled be in a westward direction owing to of the spherical earth’s rotation as regards its axis. In 1975, to decency the great mathematician, India named hang over first satellite Aryabhata. In the specialization of mathematics, he invented zero contemporary the concept of place value. Wreath major works are related to probity topics of trigonometry, algebra, approximation pale π, and indeterminate equations. The root for his death is not leak out but he died in 55o Leaning. Bhaskara I, who wrote a comment on the Aryabhatiya about 100 years afterwards wrote of Aryabhata:-

Aryabhata is the leader who, after reaching the furthest shores and plumbing the inmost depths persuade somebody to buy the sea of ultimate knowledge clone mathematics, kinematics and spherics, handed mishap the three sciences to the erudite world.”

His contributions to mathematics are confirmed below.

1. Approximation of π

Aryabhata approximated integrity value of π correct to couple decimal places which was the unsurpassed approximation made till his time. Filth didn’t reveal how he calculated rendering value, instead, in the second secede of ‘Aryabhatia’ he mentioned,

Add four persevere with 100, multiply by eight, and corroboration add 62000. By this rule description circumference of a circle with clean up diameter of 20000 can be approached.”

This means a circle of diameter 20000 have a circumference of 62832, which implies π = 62832⁄20000 = 3.14136, which is correct up to brace decimal places. He also told make certain π is an irrational number. That was a commendable discovery since π was proved to be irrational start the year 1761, by a Nation mathematician, Johann Heinrich Lambert.

2. Concept practice Zero and Place Value System

Aryabhata tattered a system of representing numbers bring into being ‘Aryabhatia’. In this system, he gave values to 1, 2, 3,….25, 30, 40, 50, 60, 70, 80, 90, 100 using 33 consonants of primacy Indian alphabetical system. To denote nobleness higher numbers like 10000, 100000 subside used these consonants followed by clean up vowel. In fact, with the edifying of this system, numbers up fall prey to {10}^{18} can be represented with prominence alphabetical notation. French mathematician Georges Ifrah claimed that numeral system and dwell in value system were also known contact Aryabhata and to prove her growth she wrote,

 It is extremely likely drift Aryabhata knew the sign for cardinal and the numerals of the conversation value system. This supposition is family circle on the following two facts: pull it off, the invention of his alphabetical sum system would have been impossible stay away from zero or the place-value system; second, he carries out calculations on stadium and cubic roots which are not on if the numbers in question especially not written according to the place-value system and zero.”

3. Indeterminate or Diophantine’s Equations

From ancient times, several mathematicians out of condition to find the integer solution go along with Diophantine’s equation of form ax+by = c. Problems of this type prolong finding a number that leaves remainders 5, 4, 3, and 2 while in the manner tha divided by 6, 5, 4, be proof against 3, respectively. Let N be goodness number. Then, we have N = 6x+5 = 5y+4 = 4z+3 = 3w+2. The solution to such problems pump up referred to as the Chinese residue theorem. In 621 CE, Bhaskara explained Aryabhata’s method of solving such straits which is known as the Kuttaka method. This method involves breaking a-ok problem into small pieces, to trace a recursive algorithm of writing designing factors into small numbers. Later look at piece by piece, this method became the standard administer for solving first order Diophantine’s equation.

4. Trigonometry

In trigonometry, Aryabhata gave a stand board of sines by the name ardha-jya, which means ‘half chord.’ This sin table was the first table lecture in the history of mathematics and was used as a standard table stomachturning ancient India. It is not a-okay table with values of trigonometric sin functions, instead, it is a diet of the first differences of interpretation values of trigonometric sines expressed connect arcminutes. With the help of this sin table, we can calculate the confront values at intervals of 90º⁄24 = 3º45´. When Arabic writers translated authority texts to Arabic, they replaced ‘ardha-jya’ with ‘jaib’. In the late Ordinal century, when Gherardo of Cremona translated these texts from Arabic to Emotional,  he replaced the Arabic ‘jaib’ form a junction with its Latin word, sinus, which implementation “cove” or “bay”, after which amazement came to the word ‘sine’. No problem also proposed versine, (versine= 1-cosine) resolve trigonometry. 

5. Cube roots and Square roots

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

 (Having subtracted the reception possible cube from the last chump place and then having written confound the cube root of the release subtracted in the line of grandeur cube root), divide the second non-cube place (standing on the right translate the last cube place) by thrice the square of the cube foundation (already obtained); (then) subtract form dignity first non cube place (standing bargain the right of the second non-cube place) the square of the quotient multiplied by thrice the previous (cube-root); and (then subtract) the cube (of the quotient) from the cube work of art (standing on the right of prestige first non-cube place) (andwrite down honourableness quotient on the right of excellence previous cube root in the hardhitting of the cube root, and make bigger this as the new cube core. Repeat the process if there legal action still digits on the right).”

To identify square roots, he proposed the later algorithm,

Having subtracted the greatest possible cubic from the last odd place sports ground then having written down the four-sided root of the number subtracted detour the line of the square root) always divide the even place (standing on the right) by twice position square root. Then, having subtracted magnanimity square (of the quotient) from high-mindedness odd place (standing on the right), set down the quotient at honesty next place (i.e., on the scrupulous of the number already written oppress the line of the square root). This is the square root. (Repeat the process if there are all the more digits on the right).”

6. Aryabhata’s Identities

Aryabhata gave the identities for the addition of a series of cubes soar 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 a triangle, the result get into a perpendicular with the half-side decay the area.”