Notes on Pi

All my notes on the Pi number, updated every time I find some interesting information. Some notes may be removed once the information is used in a full article.

Historical

1. The following link, obtained by searching for “pi”, lists historical articles on Pi published in Historia Mathematica: https://www.sciencedirect.com/search?qs=pi&pub=Historia+Mathematica&cid=272588.
2. Searching for “circle” one can find other interesting articles: https://www.sciencedirect.com/search?pub=Historia+Mathematica&cid=272588&qs=circle
3. The document (in French) entitled Quelques textes mathématiques de la mission de Suse, by E. M. Bruins, contains a summary of the mathematics content of the Babylonian tablets found in 1936 near Susa. E.M. Bruins was Evert Marie Bruins (1909 – 1990), a specialist of ancient mathematics (see https://www.persee.fr/authority/76567). He published in 1850 Aperçu sur les mathématiques babyloniennes.
4. Information about the history of the use of the Greek letter π as the symbol related to circles: https://mathshistory.st-andrews.ac.uk/Miller/mathsym/constants/ . The 2 volumes of the book History of mathematical notations, published in 1928 by Florian Cajori (1859 – 1930) are available here: Vol 1, Vol 2. The 1702 English edition of Clavis Mathematicae, by Oughtred, is available here: https://archive.org/details/bim_eighteenth-century_clavis-mathematicae-en_oughtred-william_1702. The symbol π appears page 99. A latin edition of 1667 is available there: https://archive.org/details/bim_early-english-books-1641-1700_clavis-mathematic-_oughtred-william_1667. The symbol π appears page 66.

Mathematics

1. A simple proof that π is irrational was published by Ivan Niven in Bull. Amer. Math. Soc. 53 (6), 509, (June 1947) and is available online.
2. https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_functions
3. Le nombre Pi est partout is an interesting article (in French) showing unexpected examples where the Pi number appears. From this article I found the following one: Playing Pool with π (the number π from a billiard point of view)

Computing

1. Where does the formula used in http://ajennings.net/blog/a-million-digits-of-pi-in-9-lines-of-javascript.html to compute Pi come from ?
2. https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html shows a 160 bytes C code to compute Pi. What is the smallest possible code to compute Pi ?
3. http://villemin.gerard.free.fr/Wwwgvmm/Geometri/PiFormul.htm contains a very large number of formulas to compute Pi

People

1. Herman C. Schepler wrote around 1950 a long article (or maybe a short book) on the History of Pi. This article is included in Pi: A Source Book and can be downloaded here: The Chronology of Pi | SpringerLink. Can it be this person: Herman C. Schepler (1913-1986) – Mémorial Find a Grave

Others

1. You can download 22.4 trillion digits of pi.
2. There is a website called The Online Encyclopedia of Integer Sequences.
3. https://abakcus.com/longest-pi-article-on-internet-everything-about-pi/ is a very long article on Pi. Is it really the longest ?