Summary: Khoury explores counterintuitive properties of high dimensional space, such as spheres within cubes. As dimensions increase, inner spheres start poking outside, with volume decreasing to nearly nothing after dimension six. The band width needed to capture surface area around the equator decreases in higher dimensions. The kissing number of circles touching a central circle varies by dimension, with details provided up to 24 dimensions. The unique properties of high dimensional space challenge our geometric intuition, revealing surprising and fascinating characteristics of higher dimensions.
https://people.eecs.berkeley.edu/~jrs/highd/