· calculus, history, teaching
Introducing The Calculus Chronicles
Why I built an interactive history of calculus, and how I use it in lessons.
Students usually meet calculus as a finished machine: rules to apply, notation to copy. What they rarely see is that it took four thousand years, and some of the best minds in history, to make it work.
The Calculus Chronicles follows one question across that whole story: how do we calculate with infinitely many, infinitely small things?
What’s in it
- A true timeline of 61 moments, from Babylonian clay tablets to Abraham Robinson’s infinitesimals in 1961.
- 25 hands-on labs: squeeze a circle between polygons with Archimedes, measure wine barrels with Kepler, find \(e\) three different ways.
- Step-by-step proofs and worked examples, shown the way the people on each card made them, with modern versions where they help.
- The original texts: Newton on vanishing quantities, Berkeley’s “ghosts of departed quantities”, Cauchy’s mistake and Abel’s reply.
How I use it
Open a card on the board and step through it together. A favourite: Newton’s argument for the derivative of \(x^n\), followed straight away by Berkeley’s objection. Students spot the problem, that \(o\) is not zero when you divide and zero when you discard it, and suddenly limits are the answer to a real question rather than a definition to memorise.
It’s free to use and adapt for teaching (CC BY-NC-SA), and the code is on GitHub. If you spot an error, I’d love to hear about it.