John Barrow's lecture on continued fractions, which I finished watching three hours ago, still has the hairs on my neck and forearms gibbering about.
Visit the link above for the transcript and/or the slides. (Or just click those links, obvs.) You'll almost certainly want the latter, if the talk grabs your attention at all.
And remember:
[Added] I see by looking at the transcript that the lecture stems from Barrow's article published in Issue 11 of Plus Magazine, "Chaos in Numberland: The secret life of continued fractions."
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