Indian mathematical knowledge in navigation was preserved and transmitted through a combination of oral tradition, written texts, and inscriptions.

The Sulbasutras are a collection of ancient Indian texts that contain mathematical knowledge related to geometry, astronomy, and navigation.

The primary purpose of the Sulbasutras was to provide instructions for constructing altars for religious rituals.

The Pythagorean theorem was developed in the Sulbasutras to aid in the construction of altars.

The Arthashastra, written by Kautilya, contains mathematical knowledge related to navigation.

The Arthashastra contains a system for measuring distances at sea using a device called a 'yojana'.

Aryabhata developed a formula for calculating the circumference of the Earth in his work 'Aryabhatiya'.

Aryabhata calculated the Earth's circumference to be 24,000 miles.

Varahamihira developed a method for determining the direction of the wind in his work 'Brihat Samhita'.

Varahamihira used a weather vane to determine the direction of the wind.

Brahmagupta developed a system for calculating the positions of stars and planets in his work 'Brahmasphutasiddhanta'.

Brahmagupta used an armillary sphere to calculate the positions of stars and planets.

Bhaskara II developed a method for calculating the distance between two points on the Earth's surface in his work 'Lilavati'.

Bhaskara II developed the Great-circle distance formula for calculating the distance between two points on the Earth's surface.

Indian mathematical knowledge in navigation influenced the development of navigation in other parts of the world by leading to the development of new navigational instruments, helping in the discovery of new trade routes, and contributing to the development of accurate maps and charts.