The concept of zero, which originated in India, was essential for the development of positional notation and the accurate representation of numbers in European navigation.

The concept of zero revolutionized European mathematics and navigation by enabling place value notation, facilitating the development of algorithms for arithmetic operations, and allowing for the representation of negative numbers.

Aryabhata's work, particularly his treatise 'Aryabhatiya,' had a profound impact on European navigation. His contributions included the development of trigonometric functions and tables, as well as methods for calculating astronomical positions.

Indian mathematics was extensively used in European navigation for various purposes, including calculating distances, determining latitude and longitude, and navigating through unfamiliar waters.

The sine rule, also known as the law of sines, was a valuable tool for determining the latitude of a ship by measuring the angle between the horizon and a celestial body.

Indian mathematics played a crucial role in the development of various navigational instruments, including astrolabes, compasses, and quadrants, which were essential for accurate navigation.

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, was used to calculate the distance between two points on a map.

Indian mathematics contributed to the development of more accurate maps, the use of latitude and longitude lines, and the development of the Mercator projection, which is still widely used in modern navigation.

The method of lunar distances, which involved measuring the angular distance between the moon and a star, was used to determine the longitude of a ship.

Indian mathematics played a crucial role in the development of more accurate navigation tables, the use of trigonometric functions, and the development of logarithmic tables, which were essential for efficient navigation.

The sine rule was used to calculate the time of sunrise and sunset by determining the angle between the horizon and the sun.

Indian mathematics contributed to the development of more efficient navigational algorithms, the use of mathematical models, and the development of computer-based navigation systems, which revolutionized the field of navigation.

The cosine rule was used to calculate the speed of a ship by determining the distance traveled and the time taken.

Indian mathematics played a crucial role in the development of various navigational instruments, including astrolabes, compasses, and quadrants, which were essential for accurate navigation.

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, was used to calculate the distance between two points on a map.