Navigational Algorithms and Techniques Developed by Indian Mathematicians

Brahmagupta, an Indian mathematician and astronomer, is credited with developing the concept of the cosine law in trigonometry, which is expressed as $$cos(A) = sin(90° - A)$$. This law is essential for calculating distances and angles in navigation.

Aryabhatiya is the mathematical treatise written by Aryabhata in the 5th century CE. It contains significant contributions to astronomy, mathematics, and navigation, including the concept of zero, the decimal system, and trigonometric functions.

Aryabhata, an Indian mathematician and astronomer, developed the concept of 'sine' and 'cosine' functions in trigonometry. These functions are fundamental for calculating angles and distances in navigation.

Indian sailors developed the technique of stargazing to determine their location at sea. They used the position of stars and constellations to navigate, as these celestial bodies maintain a fixed position in the sky.

Aryabhata developed the concept of 'pi' (π) and its approximation, which is crucial for calculating the circumference and area of circles in navigation.

The astrolabe was the instrument used by Indian sailors to measure the altitude of celestial bodies above the horizon. This measurement is essential for determining latitude and longitude.

Aryabhata developed the concept of 'trigonometric ratios', which are essential for calculating angles and distances in navigation.

Indian sailors developed the technique of sun sighting to determine their latitude. They used the position of the sun and its altitude above the horizon to calculate their latitude.

Aryabhata developed the concept of 'decimal fractions', which are essential for precise calculations in navigation.

Indian sailors developed the technique of moon sighting to determine their longitude. They used the position of the moon and its altitude above the horizon to calculate their longitude.

Madhava of Sangamagrama developed the concept of 'infinite series', which is crucial for calculating complex mathematical problems in navigation.

Indian sailors developed the technique of stargazing to determine their latitude and longitude. They used the position of the stars and their altitude above the horizon to calculate their latitude and longitude.

Madhava of Sangamagrama developed the concept of 'calculus', which is essential for understanding the motion of celestial bodies and calculating trajectories in navigation.

Indian sailors developed the technique of sun sighting to determine their longitude. They used the position of the sun and its altitude above the horizon to calculate their longitude.

Aryabhata developed the concept of 'trigonometric tables', which are essential for calculating angles and distances in navigation.