Pi is a mathematical constant that represents the ratio of a circle’s circumference to its diameter. According to Dominic Olivastro, the author of the 1997 article, In Pursuit of Pi1, for nearly a thousand years from its origin, pi was used a rough tool for measuring circular plots of land. He writes:

“The earliest known estimate of pi is contained in an Egyptian scroll dating back to 1650 B.c. The Rhind mathematical papyrus sets forth eighty-four problems and their solutions. Problem number fifty assumes that the area of a circle with a diameter of nine units is the same as that of a square with sides of eight units. The assumption is incorrect, but it was probably meant only as an approximation, and it is a very good approximation at that. By setting the Egyptian formula equal to the correct formula (pi times the radius squared), you will find that the papyrus implicitly set pi equal to about 3.1605. (About the same time, the Babylonians estimated pi to be 3.125, a value only slightly superior.)”

The Egyptians may have used their estimate of pi to construct a granary courtyard. The Tell Edfu Project, begun by the University of Cambridge in 2001, is an archeological study of an ancient town, Edfu, located on the West Bank of the Nile River in Egypt. Here you can find pictures of grain silos from the Second Intermediate Period. The choice to eat foods that store well and to invest in storage infrastructure are points of advancement in human history. Today, pi is being used to do more than calculate the volume of a cylinder. The orbit of the NASA–ISRO Synthetic Aperture Radar (NISAR) satellite mission can be calculated with pi. One offering of NISAR is the provision of timely soil moisture data. This information may support best water management practices in the context of a drought and the growing demand for food. For Pi Day 2024, NASA challenged us to calculate how much data NISAR would produce a day. Here is the problem below:

NISAR will produce more than 85 terabytes of data products every day, orbit the earth twice every 12 days, and has an imaging swath of 240 kilometers, but the ground track spacing is 231 km to allow overlap between swaths. Given that Earth’s radius is 6,371 km, how many orbits are executed in one day? How much data is produced per orbit on average?

We use the formula for the circumference of a sphere to determine the length of one orbit around the Earth.

\[2\pi(6,731 km) = 40,030 km\]

To calculate the number of imaging swaths needed to cover the rotating Earth divide 40,030 km by double the length ground track to account for the fact that the satellite crosses the equator twice in one orbit:

\[\frac{40,030 km}{2*231 km} = 86.65 swaths\]

Now letʻs add the variable of time. If it takes 86.65 swaths to cover the Earth and this is accomplished in 6 days, then

\[\frac{86.65 swaths}{6 days} = 14.4 \frac{orbits}{day}\]

To finally find how much data is produced by NISA divide 85 TB/day by 14.4 orbits/day to equal 

\[85 TB * \frac{1 day}{14.4 orbits} = 5.9 \frac{TB}{orbit}\]

Here is a link to 2024 Pi Day questions and the answer key. Humanity has taken our understanding of circles to build systems to help us understand Earth from space and this has changed agriculture. Satellites also play a role in GPS-controlled tractors, so not only are we observing farms from space, but we are running farm operations using real-time satellite data. 

Reflecting on how pi is used in agriculture (regionally, globally, yesterday, today) is an exercise in imagining a mathematical relationship as a gear in a system. Mathematical relationships existed before and exist without human discovery. Our ability to communicate these relationships is amazing. As my understanding of pi becomes more tangible in my mind, I expect it will become easier to build with. 

  1. Olivastro, D. (1985). In Pursuit of Pi. Sciences, 25(3), 58. https://doi.org/10.1002/j.2326-1951.1985.tb02922.x ↩