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: And here are links to a few beautiful interactive animations of the circle stacking marvels that I talk about in this video (on the Cuttheknot site):