collisionPI

Compute PI with specified number of digit from elastic collisions
Reference: YouTube video: https://www.youtube.com/watch?v=HEfHFsfGXjs&list=PLZHQObOWTQDMalCO_AXOC5GWsuY8bOC_Y&index=2&t=0s

How it works

1. First download this repository, or using command line:

   git clone https://github.com/newTypeGeek/collisionPI.git
   

2. Compile the source codes:

   g++ *.cpp -c
   g++ *.o
   

3. Run the program ./a.out

   You will see the console output, asking the user to enter the number of digit of PI to compute

   ****************************************************************
   ****                                                        ****
   ****    Welcome to PI calculation using physics engine !    ****
   ****                                                        ****
   ****************************************************************
   
   Please enter the number of digit of PI you want to compute
   

   Let say we want to do 10 digits and we input 10 and press enter

   Then we have

   [INFO] computePi function is called
   [INFO] Pi is computed via a counting collisions from a physics engine
   [INFO] Number of digit for Pi = 10
   [INFO] countCollisions function is called
   [INFO] Simulation begins ... 
   [INFO] Time Elapsed (seconds) = 15.7324
   [INFO] Total number of collisions = 3141592653
   [INFO] Simulation finished
   [INFO] countCollisions function is completed
   [INFO] Computed Pi: 3.141592653
   

   The Pi is computed to be 3.141592653 (10 digits in total)

Limitations

We compute Pi by counting the total number of collisions (an integer). In this program, written in C++, unsigned long long variable is used to count the number of collision. The maximum value is ULLONG_MAX = 18446744073709551615 (64 bits, 20 digits). As a result this program at this date can only compute Pi with a maximum of 19 digits only.