Brahmagupta, a 7th-century Indian mathematician, is widely recognized for introducing the concept of zero and its use in mathematical operations.

The Ujjain Observatory, located in the city of Ujjain, Madhya Pradesh, is considered the oldest astronomical observatory in India, dating back to the 5th century BCE.

Aryabhata, a 5th-century Indian mathematician and astronomer, made significant contributions to trigonometry, including the development of the sine function and the concept of half-angles.

The Tata Institute of Fundamental Research (TIFR) is a premier Indian research institute dedicated to fundamental research in mathematics, astronomy, and other basic sciences.

Bhaskara II, an 11th-century Indian mathematician, made significant contributions to number theory, including the development of the Pell equation and the Chakravala method for solving indeterminate quadratic equations.

The gnomon is a simple astronomical instrument used to measure the altitude of celestial objects, such as the Sun and stars. It consists of a vertical rod or pillar with a horizontal crossbar.

Bhaskara II made significant contributions to calculus, including the development of the concept of infinitesimals and the idea of a limit. He also developed a method for finding the area of a circle using infinitesimals.

The sundial is an ancient astronomical instrument used to measure the time of day by the position of the Sun. It consists of a flat plate with a pointer that casts a shadow.

Brahmagupta made significant contributions to algebra, including the development of the concept of negative numbers and the idea of a zero coefficient. He also developed methods for solving quadratic and indeterminate equations.

Parallax is a method used in astronomy to measure the distance to celestial objects by observing their position from two different locations.

Baudhayana, an ancient Indian mathematician, is credited with developing the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The astrolabe is an ancient astronomical instrument used to measure the angular distance between celestial objects, such as the Sun, Moon, and stars.

Pingala, an ancient Indian mathematician, is credited with developing the Fibonacci sequence, a series of numbers in which each number is the sum of the two preceding ones.

The eclipse predictor is an astronomical instrument used to predict the time and duration of eclipses.