"Pencil, Paper, and Pi," in the September-October 2014 issue of American Scientist, tells the story of a legendary Victorian-era computing project. William Shanks, an ambitious amateur, equipped with nothing but pencil and paper, churned out 707 decimal places of π. Unfortunately, the digits beyond decimal place 527 were wrong. For a few weeks I've been trying to understand how Shanks did his calculation, and where it all went awry. Collected here are links to the article and to supporting materials.
If you have no Python, you can read (but not run) the notebook as a web document.