The secret of the 7th row - visually explained

In 1995 I published an article in the Mathematical Intelligencer. This article was about giving the ultimate visual explanations for a number of stunning circle stacking phenomena. In today's video I've animated some of these explanations. Here is a copy of a preprint of the Intelligencer article: http://www.qedcat.com/misc/stacks.pdf And here are links to a few beautiful interactive animations of the circle stacking marvels that I talk about in this video (on the Cut-the-knot site): https://www.cut-the-knot.org/Curricul... https://www.cut-the-knot.org/Curricul... (check for more links to related animations at the bottom of these pages) As usual, many thanks go to Marty for all his help in getting this presentation just right and Danil for his Russian subtitles. Also, thank you very much dad for your help with building the stacking machine that features at the end of this video. Enjoy :)