Exploration in π Calculation Using Various Methods Implemented in Python

The mathematical constant π, found ubiquitously in many applications, has been a subject of interest for mathematicians ever since the beginning of recorded history. In order to seek out better understanding of its nature, calculation of the its decimal digits has been a perennial favored activity of many mathematicians throughout history. The length of digit of π capable of being obtained has always been commensurate with the technological advance in mathematics at the time. First, the ancients Egyptians and Hebrew su ced with the estimate of roughly 3 based on their intuition. Later, discoveries by Archimedes in Greece and Liu Hui in China led to more precise estimation of π using calculations based on regular polygons inscribed and circumscribed in a circle. However, it was not until the discovery of the in nite series that mathematicians began to make major strides in the calculating the digits of π. As we enter the modern era, the advent of digital computers allows us to obtain precision of π of astronomical proportions. Even though it is said that 39 digits of π is su cient to calculate the circumference of the entire measurable universe accurate to the width of one hydrogen atom, π calculation is still beloved by hobbyists and computer benchmarkers. In this project, we will explore three π algorithms based on various types of in nite series and iterative techniques, in order to calculate π to as many digits as possible while optimizing for speed of calculation. In addition, we will make some observations about the distribution of digits in π using the results we calculate.