The Yajurveda, one of the four Vedas, contains references to the use of mathematics in agriculture, including the calculation of land area and the distribution of water.

The golden ratio, also known as the divine proportion, was used by ancient Indian farmers to determine the optimal time for planting crops based on the position of the sun and the length of the day.

Brahmagupta, a 7th-century Indian mathematician, developed a formula for calculating the area of a triangle using the lengths of its sides.

Network flow techniques were used by ancient Indian farmers to design irrigation systems that distributed water equitably among their fields, taking into account the elevation and distance of each field from the water source.

Bhaskara II, a 12th-century Indian mathematician, developed a formula for calculating the volume of a pyramid using its height and the area of its base.

The Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones, was used by ancient Indian farmers to determine the optimal size of their fields based on the principle of diminishing returns.

Aryabhata, a 5th-century Indian mathematician, developed a formula for calculating the circumference of a circle using its diameter.

Time series analysis techniques were used by ancient Indian farmers to analyze historical weather data and predict future weather patterns, which helped them plan their agricultural activities accordingly.

Aryabhata, a 5th-century Indian mathematician, developed a formula for calculating the area of a circle using its radius.

The golden ratio, also known as the divine proportion, was used by ancient Indian farmers to determine the optimal spacing between crops based on the principle of maximizing sunlight exposure and minimizing competition for resources.

Bhaskara II, a 12th-century Indian mathematician, developed a formula for calculating the volume of a sphere using its radius.

Integer programming techniques were used by ancient Indian farmers to design irrigation systems that minimized water loss by optimizing the flow of water through the system and taking into account the capacity of the channels and reservoirs.

Bhaskara II, a 12th-century Indian mathematician, developed a formula for calculating the surface area of a sphere using its radius.

The Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones, was used by ancient Indian farmers to determine the optimal time for harvesting crops based on the principle of maximizing yield and minimizing losses.