Everything cited
Resources
Every claim on this site should be checkable. Here's where the claims come from — primary sources first, then trustworthy popularizations, then the best videos.
Draft in progress. Sources will be added as we add material. If something's missing or you know a better source for a claim, please flag it.
Start here
Accessible overviews that'll ground the rest of the list.
- A History of PiBook
Petr Beckmann (1971)
The classic popular history. Opinionated, sometimes cranky, but the narrative sweep from Babylon to the computer age is unmatched. Still in print.
- Pi UnleashedBook
Jörg Arndt & Christoph Haenel (2001)
Springer-published. More technical than Beckmann — goes into the actual algorithms. The reference if you want to go deep without a research-math background.
- Wikipedia: PiReference
Unusually well-cited for a Wikipedia article. Use it as an index into the primary sources in its reference list, not as the final word.
Methods & algorithms
Deeper on the specific techniques the methods pages walk through.
- Archimedes’ Measurement of a CircleReference
Heath's 1897 English translation of Archimedes, scanned and hosted by the Internet Archive. This is the primary source for the polygon method.
- Wikipedia: Leibniz formula for πReference
Solid overview of the 1/1 − 1/3 + 1/5 − … series, including the Madhava–Gregory–Leibniz history and why the series converges so painfully slowly.
- Wikipedia: Nilakantha SomayajiReference
Context on the Kerala school of mathematics and why Nilakantha’s series predates Leibniz by 150+ years.
- Buffon’s needle problemReference
Statement, proof, and historical context. The derivation is short enough to read in one sitting and is genuinely beautiful.
- Monte Carlo methodReference
Broader than π — covers the whole family of "solve it by sampling" techniques that came out of the Manhattan Project.
- Machin-like formulaReference
The arctan identities that powered every π record from 1706 to 1973. Includes the original Machin formula and its many cousins.
- Chudnovsky algorithmReference
The engine behind every current record. Adds ~14 correct digits per term. Traces cleanly back to Ramanujan 1914.
- Bailey–Borwein–Plouffe formulaReference
The 1995 formula that computes the n-th hex digit of π without computing the digits before it. Still surprises people.
Primary sources (papers)
The original papers when they're available online. Dense, but definitive.
G. W. Reitwiesner (1950)
The first-ever computer calculation of π, published in Mathematics of Computation. Free full text from the AMS.
Bailey, Borwein, Plouffe (1997)
The BBP paper. Hosted on David H. Bailey’s Stanford-affiliated personal page.
- The Quest for PiPaper
Bailey, Borwein, Borwein, Plouffe (1997)
A survey paper from four of the field's leading figures. Less technical than their research work; great bridge from the popular side.
Modern records & tools
Where the actual large-scale calculations get done today.
- y-cruncherTool
Alexander Yee
The open-source program behind every modern digit record. Source, documentation, and a verified list of records.
Emma Haruka Iwao (2022)
First-person writeup by the engineer who's set multiple records. Good practical detail on storage, compute, and verification.
Current record (2024), on a single server rather than a cloud cluster. Detailed hardware writeup.
- Chronology of computation of πReference
The master record list. Every entry cited. If you only bookmark one π page on Wikipedia, it should be this one.
How few digits you actually need
For the "why π matters" side of the site.
Marc Rayman, JPL Education (2016)
NASA's own director of the Dawn mission explains why 15 digits suffices for interplanetary navigation. The source for those numbers everywhere on the internet.
Long-form journalism
The two best magazine pieces ever written about π.
- The Mountains of PiArticle
Richard Preston, The New Yorker (1992)
Preston's profile of the Chudnovsky brothers and the supercomputer they built in a Manhattan apartment. One of the great pieces of science journalism.
Watch
Video explanations from people who know what they’re talking about.
3Blue1Brown
Grant Sanderson’s visual proof of Euler’s result. The π surprise payoff is deserved.
3Blue1Brown
A walkthrough of Ivan Niven's 1947 proof that π is irrational. Short, complete, beautiful.
Matt Parker (standupmaths)
Matt Parker spends an entire day computing π by hand for π day. Exactly as chaotic as it sounds.
- Pi is BeautifulVideo
Numberphile
Numberphile’s channel has dozens of π videos with working mathematicians; this is a good entry point.
A note on what we cite
Not every source is equal. The site tries to stick to, in rough order of preference:
- Peer-reviewed papers or the primary historical document.
- Institutional writeups (NASA, Google Cloud, university pages) where an engineer or scientist is explaining their own work.
- Books by working mathematicians or historians of math.
- Magazine journalism with an editorial process (The New Yorker, Quanta).
- Wikipedia — but only as an index into the references in its bibliography, not as the end of the trail.
- Long-form video from specialists (3Blue1Brown, Numberphile, standupmaths).
If something on the site isn't backed by at least one source from the top three tiers, that's a bug. Say so.