The famous polymath Archimedes showed in his "Circvli Dimensio" how the circle number Pi can be calculated. His inequalities are very unfriendly, when it comes to implementing them in a computer algorithm.
In a first step, I analyzed his work, drew my conclusions from it and then developed possible algorithms from his inequalities. This is an interesting experience.
I will gradually publish the results on Archimedes and others here. There will be well-known and less well-known things. Later, I will present my more modern findings on Pi here and make them available to the interested public.
Algorithms for calculating pi that are based on sine and cosine expressions are generally not permitted, as they assume that pi is already known. Modern software products always use RAD instead of DEG internally. I am not aware of any product that uses DEG internally.
To get things right in terms of pi, you need to know whether a Taylor series is used internally for sine and cosine, for example, and what accuracy can be achieved after the decimal point.
Once SageMath is installed, interested visitors can try out the Jupyter notebooks for themselves. Prerequisite is the installation of SageMath and basic knowledge of Python.
The english translation "The Works of Archimedes" [1] is available in different forms and as PDF-File.
[1] T. L. HEATH, Sc.D., The Works of Archimedes, EDITED IN MODERN NOTATION, WITH INTRODUCTORY CHAPTERS, CAMBRIDGE: AT THE UNIVERSITY PRESS, 1897
[2] SageMath, the Sage Mathematics Software System (Version 10.1), The Sage Developers, 2019, https://www.sagemath.org