Bhaskara 2

(1114–85?). Indian mathematician Bhaskara II was the leading mathematician of the 12th century. He wrote the first work with full and systematic use of the decimal number system. Bhaskara II was born in 1114, in Biddur, India. He was the lineal successor of the noted Indian mathematician In his mathematical works, particularly Lilavati (“The Beautiful”) and Bijaganita (“Seed Counting”), he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation ( x 2 = 1 + py 2) and in giving many particular solutions. Bhaskara II anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero, for he specifically stated that the value of 3/ 0 is an infinite quantity, though his understanding seems to have been limited, for he also stated wrongly that a/ 0 × 0 = a. Bhaskara II used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees. He reduced quadratic equations to a single type and solved them and investigated regular polygons up to those having 384 sides, thus obtaining a good approximate value of pi = 3.141666. In other of his works, notably Siddhantasiromani (“Head Jewel of Accuracy”) and Karanakutuhala (“Calculation of Astronomical Wonders”), h...

Until recently, the origin of the zero, one of the greatest inventions of humanity, was not clear. The enigma was unravelled little by little during the twentieth century, and a recent archaeological dating no longer leaves room for doubt— the zero was born in India. It was the Indian sages who first drew a symbol to represent zero, a digit that does not appear in Greek writings or among Roman numerals. That simple symbol granted mathematicians the ability to operate with numbers as large as they wanted. But the great scholars of the The Bakhshali Manuscript contains the symbol for the oldest known zero. Copyright: Bodleian Libraries, University of Oxford. Heirs of the Greeks, the Indians grabbed the baton in the history of mathematics to delve into arithmetic, separating it from geometry, and laying the foundations of algebra (which the Arabs then developed). The mathematicians Aryabhata (sixth century), Brahmagupta (seventh century), Mahavira (ninth century) and Bhaskara II (twelfth century) stand out. Around the year 500, Aryabhata devised a kha instead. Positional numeration The positional decimal system with the inclusion of zero—the one we use today—has the advantage of allowing us to write any number with only ten different digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), which makes it In a positional system, the value of each digit depends on its position within the number. For In the seventh century, the writings of the mathematician Brahmagupta are the first known in whic...

Table of Contents • • • • • • • What is the contribution of bhaskaracharya in mathematics? Some of Bhaskara’s contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a2 + b2 = c2. In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations are explained. What did bhaskaracharya invented? He also wrote two astronomical works in the line of Aryabhata’s school, the Mahābhāskarīya and the Laghubhāskarīya. On 7 June 1979 the Indian Space Research Organisation launched Bhaskara I honouring the mathematician…. Bhāskara I Occupation Mathematician; scientist Known for Bhaskara I’s sine approximation formula Which was the famous work of bhaskaracharya? Bhaskara is known for his two main works: a ‘Siddhanta’ text, the ‘Siddhanta-siromani’ and a ‘Karana’ text, the ‘Karanakutuhala’. The former is in four parts, viz. (i) Patiganita or Lilavati, (ii) Bijaganita, (iii) Grahaganita, (iv) Goladhyaya. Of these, the first two are usually treated as separate treatises. Which book did bhaskaracharya wrote in 1150 AD? the Siddhānta Shiromani Līlāvatī is Indian mathematician Bhāskara II’s treatise on mathematics, written in 1150. It is the first volume of his main work, the Siddhānta Shiromani, alongside the Bijaganita, the Grahaganita and the Golādhyāya. What is Bhaskara’s formula? In mathematics, Bhaskara I’s sine approximation formula is a rational expressio...

In many ways, Bhaskara represents the peak of mathematical and astronomical knowledge in the twelfth century. He reached an understanding of calculus, Lilavati (dealing with Bijaganita (Algebra) and Siddhanta Shiromani (written in 1150) which consists of two parts: Goladhyaya ( General Bhaskara, born in 1114 C.E. (1114 – 1185), also known as Bhaskara II and Bhaskara Achārya ("Bhaskara the teacher"), was an Indian mathematician and astronomer. He was born near Bijjada Bida (in present day Bijapur district, Bhaskaracharya learnt mathematics from his father. After being introduced to the works of a previous famous mathematician, Brahmagupta, Bhaskaracharya was so inspired that he devoted himself to mathematics for the rest of his life. After his daughter, Lilavati, was widowed at the age of six, he even influenced her to study mathematics—it is not known, however, how great of a mathematician she became. When it came to algebra, Bhaskaracharya followed Brahmagupta’s work closely as his guru, and went about extending Brahmagupta’s works. As a mathematician, Bhaskara represents the peak of mathematical and astronomical knowledge in the twelfth century. As J. J. O’Connor and E. F. Robertson stated in their article for the School of Mathematics and Statistics, “[Bhaskaracharya] reached an understanding of the number systems and solving equations which was not to be achieved in Europe for several centuries.” Bhaskaracharya was the first mathematician to write a work with full and ...

LIFE SKETCH OF BHASKARA ll • Bhaskara II is a famous mathematician of ancient India. He was born in 1114 A.D. in the city of Bijapur, Karnataka state, India. Peoples also know him as Bhaskaracharya, which means “Bhaskara the Teacher”. • Bhaskara II became head of the astronomical observatory at Ujjain, which was the leading mathematical centre in India at that time He wrote six books and but a seventh work, which is claimed to be by him, is thought by many historian to be a late forgery • The three most important books he published were Lilavati(The Beautiful), which is about mathematics; Bijaganita (Seed Counting), which is about algebra; and an astronomical work, Karanakutuhala (The Calculation of Astronomical Wonders). Lilavati is the first known published work that uses the decimal position system. • His father name was Mahesvara. By profession he was an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. In many ways, Bhaskaracharya represents the peak of mathematical knowledge in the 12th century Bhaskaracharya's significant contribution to mathematics • A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a2 + b2 = c2. • In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations. • Solutions of indeterminate quadratic equations (of the type ax2 + b= y2). • Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules h...

This is a Lilavati of 151: The square of the pillar is divided by the distance between the snake and its hole; the result is subtracted from the distance between the snake and its hole. The place of meeting of the snake and the peacock is separated from the hole by a number of hastas equal to half that difference. 152: There is a hole at the foot of a pillar nine hastas high, and a pet peacock standing on top of it. Seeing a snake returning to the hole at a distance from the pillar equal to three times its height, the peacock descends upon it slantwise. Say quickly, at how many hastas from the hole does the meeting of their two paths occur? (It is assumed here that the speed of the peacock and the snake are equal.) These verses and much else from the Lilavati may be found in Kim Plofker, "Mathematics in India", in (Princeton: Princeton University Press, 2007), pp. 385-514. Lilavati gives another illustration ofthe Pythagorean Theorem. Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Lilavati of Bhaskara," Convergence (January 2011)

This is a Lilavati of 151: The square of the pillar is divided by the distance between the snake and its hole; the result is subtracted from the distance between the snake and its hole. The place of meeting of the snake and the peacock is separated from the hole by a number of hastas equal to half that difference. 152: There is a hole at the foot of a pillar nine hastas high, and a pet peacock standing on top of it. Seeing a snake returning to the hole at a distance from the pillar equal to three times its height, the peacock descends upon it slantwise. Say quickly, at how many hastas from the hole does the meeting of their two paths occur? (It is assumed here that the speed of the peacock and the snake are equal.) These verses and much else from the Lilavati may be found in Kim Plofker, "Mathematics in India", in (Princeton: Princeton University Press, 2007), pp. 385-514. Lilavati gives another illustration ofthe Pythagorean Theorem. Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Lilavati of Bhaskara," Convergence (January 2011)

In many ways, Bhaskara represents the peak of mathematical and astronomical knowledge in the twelfth century. He reached an understanding of calculus, Lilavati (dealing with Bijaganita (Algebra) and Siddhanta Shiromani (written in 1150) which consists of two parts: Goladhyaya ( General Bhaskara, born in 1114 C.E. (1114 – 1185), also known as Bhaskara II and Bhaskara Achārya ("Bhaskara the teacher"), was an Indian mathematician and astronomer. He was born near Bijjada Bida (in present day Bijapur district, Bhaskaracharya learnt mathematics from his father. After being introduced to the works of a previous famous mathematician, Brahmagupta, Bhaskaracharya was so inspired that he devoted himself to mathematics for the rest of his life. After his daughter, Lilavati, was widowed at the age of six, he even influenced her to study mathematics—it is not known, however, how great of a mathematician she became. When it came to algebra, Bhaskaracharya followed Brahmagupta’s work closely as his guru, and went about extending Brahmagupta’s works. As a mathematician, Bhaskara represents the peak of mathematical and astronomical knowledge in the twelfth century. As J. J. O’Connor and E. F. Robertson stated in their article for the School of Mathematics and Statistics, “[Bhaskaracharya] reached an understanding of the number systems and solving equations which was not to be achieved in Europe for several centuries.” Bhaskaracharya was the first mathematician to write a work with full and ...

LIFE SKETCH OF BHASKARA ll • Bhaskara II is a famous mathematician of ancient India. He was born in 1114 A.D. in the city of Bijapur, Karnataka state, India. Peoples also know him as Bhaskaracharya, which means “Bhaskara the Teacher”. • Bhaskara II became head of the astronomical observatory at Ujjain, which was the leading mathematical centre in India at that time He wrote six books and but a seventh work, which is claimed to be by him, is thought by many historian to be a late forgery • The three most important books he published were Lilavati(The Beautiful), which is about mathematics; Bijaganita (Seed Counting), which is about algebra; and an astronomical work, Karanakutuhala (The Calculation of Astronomical Wonders). Lilavati is the first known published work that uses the decimal position system. • His father name was Mahesvara. By profession he was an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. In many ways, Bhaskaracharya represents the peak of mathematical knowledge in the 12th century Bhaskaracharya's significant contribution to mathematics • A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a2 + b2 = c2. • In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations. • Solutions of indeterminate quadratic equations (of the type ax2 + b= y2). • Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules h...

(1114–85?). Indian mathematician Bhaskara II was the leading mathematician of the 12th century. He wrote the first work with full and systematic use of the decimal number system. Bhaskara II was born in 1114, in Biddur, India. He was the lineal successor of the noted Indian mathematician In his mathematical works, particularly Lilavati (“The Beautiful”) and Bijaganita (“Seed Counting”), he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation ( x 2 = 1 + py 2) and in giving many particular solutions. Bhaskara II anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero, for he specifically stated that the value of 3/ 0 is an infinite quantity, though his understanding seems to have been limited, for he also stated wrongly that a/ 0 × 0 = a. Bhaskara II used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees. He reduced quadratic equations to a single type and solved them and investigated regular polygons up to those having 384 sides, thus obtaining a good approximate value of pi = 3.141666. In other of his works, notably Siddhantasiromani (“Head Jewel of Accuracy”) and Karanakutuhala (“Calculation of Astronomical Wonders”), h...