The Golden Age of Guptas 4th-6th Century AD, was not only the golden period of art, architecture and literature but it was also the great age of science, mathematics and astronomy. Numerous path breaking discoveries were done during this time. Among the great mathematicians and astronomers of the time, name of Aryabhatta shines like a star. When mathematics and astronomy were still in their nascent stages of development around the globe, Aryabhatta invented decimal system, trignometry, calculated value of pi and studied our solar system. His works have been extensively used by the Greeks and others in the Middle East. His most famous work Aryabhatiyam was compiled when he was just 23 years old.
Aryabhatta composed numerous numerical and cosmic treatises; among these, "Aryabhatiya" was his first major work. He wrote this book when he was only 23 years old. Aryabhatiya covers several branches of mathematics such as algebra, arithmetic, plane and spherical trigonometry. His principal focus was mathematics; he went into extraordinary insight about arithmetic and geometric movements like 2, 4, 6, and 8 or 2, 10, 50, and 250. He formulated a brilliant technique for finding the lengths of chords of circles with half chords as opposed to the full chord strategy utilized by Greeks. He also came up with an approximation of pi and determined that pi(p) is irrational.
He was the first mathematician to give what later came to be known as the tables of sine, cosine, versine, and converse sine to four decimal spots, which brought forth trigonometry. In fact, modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. Aryabhatta has named the initial 10 decimal places and derived the methods for extracting square roots, summing arithmetic series and solving indeterminate equations of the type ax – by = c. His method to find a solution to indeterminate equations of this type is recognized the world over. Aryabhata gives the area of a triangle as "tribhujasya phalasarira? samadalako?i bhujardhasa?varga?" that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
Aryabhatta worked on the place value system and discovered zero for the first time, making use of letters to indicate numbers and pointing out qualities. He stated correctly the number of days in a year to be 365, alongside the seven-day week and about an intercalery month embedded into a year to make the calendar adjust to the seasons. He discovered the position of nine planets and expressed that these likewise rotated around the sun. He also provided the circumference and measurement of the Earth and the radius of the orbits of 9 planets.
Aryabhatta challenged many superstitious theories. He also gave a theory on eclipse; he said it wasn’t because of Rahu, as preached by many priests, but because of shadows cast by the earth and moon. He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds!! Aryabhatta pronounced that the moon has no light of its own and it is visible because it mirrors the light of the sun. He concluded that the earth is round. He also stated that it rotates on its own axis, which is why we have days and nights.
Another discipline Aryabhatta explored was astronomy; he concentrated on a few geometric and trigonometric parts of the celestial sphere that are still used to study stars. In his old age, Aryabhatta composed another treatise, ‘Aryabhatta-siddhanta’. It’s a booklet for every day astronomical calculations as well as a guide to examine auspicious times for performing rituals.
Aryabhata's astronomical calculation methods were very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) and remained the most accurate ephemeris used in Europe for centuries.
Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam,[41] versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar.
Aryabhatta composed numerous numerical and cosmic treatises; among these, "Aryabhatiya" was his first major work. He wrote this book when he was only 23 years old. Aryabhatiya covers several branches of mathematics such as algebra, arithmetic, plane and spherical trigonometry. His principal focus was mathematics; he went into extraordinary insight about arithmetic and geometric movements like 2, 4, 6, and 8 or 2, 10, 50, and 250. He formulated a brilliant technique for finding the lengths of chords of circles with half chords as opposed to the full chord strategy utilized by Greeks. He also came up with an approximation of pi and determined that pi(p) is irrational.
He was the first mathematician to give what later came to be known as the tables of sine, cosine, versine, and converse sine to four decimal spots, which brought forth trigonometry. In fact, modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. Aryabhatta has named the initial 10 decimal places and derived the methods for extracting square roots, summing arithmetic series and solving indeterminate equations of the type ax – by = c. His method to find a solution to indeterminate equations of this type is recognized the world over. Aryabhata gives the area of a triangle as "tribhujasya phalasarira? samadalako?i bhujardhasa?varga?" that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."
Aryabhatta worked on the place value system and discovered zero for the first time, making use of letters to indicate numbers and pointing out qualities. He stated correctly the number of days in a year to be 365, alongside the seven-day week and about an intercalery month embedded into a year to make the calendar adjust to the seasons. He discovered the position of nine planets and expressed that these likewise rotated around the sun. He also provided the circumference and measurement of the Earth and the radius of the orbits of 9 planets.
Aryabhatta challenged many superstitious theories. He also gave a theory on eclipse; he said it wasn’t because of Rahu, as preached by many priests, but because of shadows cast by the earth and moon. He discusses at length the size and extent of the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods provided the core. His computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds!! Aryabhatta pronounced that the moon has no light of its own and it is visible because it mirrors the light of the sun. He concluded that the earth is round. He also stated that it rotates on its own axis, which is why we have days and nights.
Another discipline Aryabhatta explored was astronomy; he concentrated on a few geometric and trigonometric parts of the celestial sphere that are still used to study stars. In his old age, Aryabhatta composed another treatise, ‘Aryabhatta-siddhanta’. It’s a booklet for every day astronomical calculations as well as a guide to examine auspicious times for performing rituals.
Aryabhata's astronomical calculation methods were very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) and remained the most accurate ephemeris used in Europe for centuries.
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