Mathematical developments in ancient India: Mathematics in India and literary works of Kalidasa, Sudraka and other writers flourished almost at the same time. Aryabhata led the development of Mathematics in India. After Aryabhata, mathematics in India was developed by Brahmagupt and Bhaskaracharya.
Contributions of mathematical developments in India to world:
Mathematical developments in India contributed to the progress of mathematics in other areas of the world. Mathematical understanding in India reached to Greece and Rome. Gautama became the head of the official Chinese Board of Astronomy in the 8th century. He was an Indian mathematician. Mathematical developments in India also spread to Arabs. From Arabs, mathematical developments in India reached Europe and contributed to mathematical progress between the 8th and 11th centuries. Arabs transmitted the decimal system to Europe. Decimal system was developed in India.
Trigonometry in ancient India and external influence: In the first century BC, trigonometry was applied to astronomy in the Surya Siddhanta, a Sanskrit text in Indian astronomy. Greek mathematicians like Euclid and Archimedes worked on trigonometry in the 3rd century BC. Hipparchus in Asia Minor worked on trigonometry in 4th century. Trigonometry in the Surya Siddhanta was more advanced than the influences brought by Alexander and Greek settlers.
Development of modern trigonometric word sine from Aryabhata’s jya: In the 5th century, Aryabhata used the word jya-ardha for the concept of sine. Short form of jya-ardha was jya. In Arabic translations, jya was replaced by Arabic word jaib. In Latin translation, the Arabic word jaib was translated into Latin word sinus. So, Aryabhata’s concept of jya led to modern trigonometric word sine through Arabic and Latin translations.
Comment on mathematical developments in ancient India and their spread to other areas of the world. How Aryabhata’s jya got converted to modern trigonometric word sine?