The "Birth" of Pi


     The discovery of pi is an interesting topic as there is no definite answer. Pi was discovered and used thousands of years ago, from the ancient Greeks and Babylonians to the Egyptians. Several cultures knew of the existence of pi to differing degrees and uses.





     The Egyptians are generally considered to be the creators of geometry. They created it out of necessity due to the limited amounts of fertile land and the constant rise and fall of the Nile. Land was a precious commodity. It was important to be able to calculate the areas of plots of land. On the famous Rhind Papyrus there are several problems dealing with geometry. Problem 50 in particular talks about the area of a circular area and gives this formula to calculate it: Area = (8d/9)^2. When we compare this to our current formula we derive that there approximation of pi 3(1/7).
     There is further evidence of the Egyptians knowledge of pi in the Great Pyramid of Giza. The ratio of the perimeter and the height is approximately 6.2857, which is very close to 2*pi. While this may be just a coincidence, this pyramid was constructed around 2580 BC., so it's possible that the Egyptians had knowledge of pi thousands of years earlier than many other civilizations.





     During the Old Babylonian Period which lasted from about 1800 BC. to 1600 BC., the Babylonians had derived their own value for pi. To find the circumference of a circle they would multiply the diameter by three. This means that they would be using 3 as the value for pi, which was close, but not quite as accurate as the Egyptians had discovered. There was also a Babylonian tablet discovered from the same time period that implies that they used 28/5 as pi. This is much more accurate than three and makes the Egyptian and the Babylonian approximations correct to within one percent.




     The Greek, namely Archimedes', approximation of pi came much later, around 250 BC., was also more accurate than any of the previous approximations. In fact, it was much closer to the actual value of pi. Archimedes' method was so close to using calculus that, had it not been rediscovered so late, would have started the development of calculus many years before Leibniz and Newton. Archimedes used an ingenious method to do this, by using polygons inscribed inside and outside of the circle to calculate an approximate area for the circle itself. He started with a polygon with a small number of sides, then would use more sides each time and calculate the areas of the outer and inner polygons and compare them to the area of the circle. He did this all the way up 98 sided polygons, and each time the areas got closer and closer to the actual area of the circle. His approximation came out to be 22/7, which is within 0.2 percent of the actual value of pi. I constructed an applet to illustrate his method. CLick the link below to use it.

Approximation of Pi Applet

     I have scratched the surface of the history of pi and the influence it has had on the world. Many books can and have been written on the subject and many more are sure to written as well. While these three civilizations were among the first most accurate to derive pi and use it in their culture, there are others as well. It is interesting that so many people that were separated and had no communication could all come up with the same ratio and by differing methods. That is the magic of pi.