Who among the following was an ancient Indian mathematician-astronomer?

Varahamihira

The correct answer is Option 3- Varahamihira

Varahamihira was an ancient Indian mathematician-astronomer. The other options are not:

• Amalananda was a 9th-century Indian philosopher and logician.
• Nagarjuna was a 2nd-century Indian Buddhist philosopher and scholar.
• Banabhatta was a 7th-century Indian poet and playwright.

Varahamihira was born in 505 CE in a Brahmin family at Kapittha, a village near Ujjain. He was a prolific writer and produced several important works on astronomy, mathematics, and astrology. His most famous work is the Pancha Siddhantika (Treatise on the Five Astronomical Canons), which is a synthesis of five earlier Indian astronomical texts. The Pancha Siddhantika contains information on a wide range of astronomical topics, including planetary motions, eclipses, and comets.

Varahamihira also made significant contributions to mathematics. He discovered several trigonometric formulas and developed new methods for calculating the areas and volumes of geometric shapes. He was also one of the first mathematicians to use the decimal system of numbers.

Varahamihira's work had a profound influence on the development of astronomy and mathematics in India and the Islamic world. He is considered to be one of the greatest astronomers and mathematicians of ancient India.