Computing Pi with Examples

Introduction

In this article, we will explore the pi command, which allows us to compute decimal digits of Archimedes’ constant Pi. We will walk through different use cases of the command with code examples, motivations, explanations, and example outputs.

1: Display 100 decimal digits of Archimedes’ constant Pi

Code:

pi

Motivation:

This use case is helpful when we need to quickly compute and display a certain number of decimal digits of Pi. It is commonly used in mathematical calculations or when we want to inspect the value of Pi to a high precision.

Explanation:

Executing the command pi without any arguments will automatically display 100 decimal digits of Pi. The command calculates the value of Pi using an algorithm known as Archimedes’ method.

Example Output:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

2: Display a specified number of decimal digits of Archimedes’ constant Pi

Code:

pi 50

Motivation:

This use case is useful when we want to customize the number of decimal digits of Pi that we want to display. It allows us to calculate Pi to a specific precision based on our requirements.

Explanation:

By specifying a number as an argument after the pi command, we can request the display of that many decimal digits. In this example, pi 50 will compute and display 50 decimal digits of Pi.

Example Output:

3.14159265358979323846264338327950288419716939937510

3: Display help

Code:

pi --help

Motivation:

This use case is handy when we need information about the command’s usage, options, and arguments. It helps us understand the available functionalities and their syntax.

Explanation:

When we execute the pi --help command, it displays a help message that provides an overview of the command along with a brief explanation of each option and argument that we can use with it.

Example Output:

Usage: pi [OPTION]... [NUMBER]
Compute decimal Archimedes' constant Pi.

  -h, --help         display this help and exit
  -v, --version      output version information and exit
  -b, --bibliography output recommended readings and exit

4: Display version

Code:

pi --version

Motivation:

This use case is beneficial when we need to know the version of the pi command that we are using. It can be helpful for troubleshooting purposes or documenting the specific version of the command used in a project.

Explanation:

Executing the pi --version command will display the version number of the pi command. It allows us to quickly identify the version without going through the documentation or source code.

Example Output:

pi 1.0.0

5: Display recommended readings

Code:

pi --bibliography

Motivation:

This use case is handy when we want to access additional resources or further study materials related to Archimedes’ constant Pi. It provides us with a list of recommended readings to explore the topic more deeply.

Explanation:

When we execute the pi --bibliography command, it displays a list of recommended readings. These readings can include scientific papers, books, or online articles that delve deeper into the mathematical aspects and historical background of Pi.

Example Output:

Further readings on Archimedes' constant Pi:
1. "Pi: A Source Book" by Lennart Berggren, Jonathan Borwein, and Peter Borwein
2. "The Joy of Pi" by David Blatner
3. "Pi: A Biography of the World's Most Mysterious Number" by Alfred S. Posamentier and Ingmar Lehmann 

Conclusion

In this article, we explored various use cases of the pi command. We demonstrated how to display a specific number of decimal digits of Pi, access help messages, retrieve the command’s version, and find recommended readings. These examples showcase the flexibility and versatility of the pi command for computing and exploring Archimedes’ constant Pi.