700 years of secrets of the Sum of Sums (paradoxical harmonic series)
Today s video is about the harmonic series . Apart from all the usual bits (done right and animated :) I ve included a lot of the amazing properties of this prototypical infinite series that hardly anybody knows about. Enjoy, and if you are teaching this stuff, I hope you ll find something interesting to add to your repertoire 00:00 Intro 01:00 Chapter 1: Balanced warmup 03:26 Chapter 2: The leaning tower of maths 12:03 Chapter 3: Finite or infinite 15:33 Chapter 4: Terrible aim 20:44 Chapter 5: It gets better and better 29:43 Chapter 6: Thinner and thinner 42:54 Kempner s proof animation 44:22 Credits Here are some references to get you started if you d like to dig deeper into any of the stuff that I covered in this video. Most of these articles you can read for free on JSTOR. Chapter 2: Leaning tower of lire and crazy maximal overhang stacks Leaning Tower of Lire. Paul B. Johnson American Journal of Physics 23 (195
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