For millennia, mathematicians have worked to increase the precision of π, transitioning from manual calculations to the incredible capabilities of modern computers, which can now compute this mathematical constant to trillions of digits.
Leveraging the power of generative artificial intelligence and advanced programming languages, the following calculators were crafted by a large language model (LLM) to aid in the exploration of π. Each calculator includes the complete source code, along with the AI-generated prompts used in their creation. Feel free to use these tools, modify them, or even rewrite them to suit your needs.
These calculators are based on the Gauss-Legendre algorithm. See the history of attempts made to use other algorithms on our journey timeline.
Simple C Calculator
This calculator was written by Chat GPT-4.0 in C and uses the Gauss-Legendre algorithm to accurately calculate π to high levels of precision. Creating this calculator was originally inspired by an early 80’s computer program that ran on an Apple II computer. That calculator could calculate approximately 100 digits of PI every 48 hours. The Simple C Calculator gives its user control over the precision of calculation and the speed at which it runs.
PI Time
The PI Time tool measures the time required to calculate π to a specified number of digits of precision. Written in C and based on the Gauss-Legendre algorithm, this calculation engine was designed to perform. This tool is ideal for benchmarking and comparing the performance of different computer processors and operating systems in handling high precision π calculations.
PI Digits
Based on the Gauss-Legendre algorithm, PI Digits is a versatile calculator designed to generate π outputs that can be easily utilized in tables or integrated into other software programs. It offers a default, reader-friendly output suitable for BASH, as well as options for CSV and JSON formats.
PI Server
The PI Server is a server-based calculator designed to handle REST API calls, calculating π to a specified number of decimal places. Built as an event-driven, multi-threaded server, similar to Nginx, it is highly scalable—functioning as a stand-alone server or pooled for virtually limitless scale-out capability. AI successfully generated the code on the first pass based on the initial requirements. Once testing is complete and basic in-memory caching is implemented, the source code will be made available on this site.
Phi Calculator
This calculator was written by Chat GPT-4.0 in C and features two formulas, one series, and one method for calculating Φ to high levels of precision. This calculator was created with a retired architect conducted a 1970 graduate studies presentation on The Golden Ratio in Architecture. It is the only calculator on this site not related to Pi (π).