Short Answer 
Pi is an irrational number with an infinite, non-repeating decimal representation, making its digit calculation complex. Specialized algorithms like the Bailey-Borwein-Plouffe and Gauss-Legendre methods are used to calculate pi’s digits, requiring substantial computational power to generate large sequences for various applications.
Step 1: Understanding Pi as an Irrational Number
The first requirement is to recognize that pi (π) is an irrational number. This means that its decimal representation is infinite and non-repeating. Thus, calculating its digits is inherently complex because there is no terminating point or predictable pattern in its sequence.
Step 2: Employing Specialized Algorithms
Mathematicians and computer scientists use specific algorithms to compute pi’s digits. Two commonly used methods are the Bailey-Borwein-Plouffe (BBP) algorithm and the Gauss-Legendre algorithm. These algorithms allow for precise calculations by incrementally refining the total figures through a combination of modular arithmetic and series expansions.
Step 3: Digit Calculation Process
The calculation of the first million digits of pi begins with an initial integer part followed by the fractional part. Using the aforementioned algorithms, each digit is computed one after another. This process requires significant computational power, usually performed by supercomputers or specialized software, resulting in an extensive sequence of digits useful for scientific and mathematical applications.