A corollary of one of the facts listed there is that the ratio between the volumes of unit sphere and of the unit cube converges to 0 with d. Meaning, in high dimensions, the unit cube is all corners and no interior.
Another one is to consider the n-dimensional standard Gaussian distribution. In dimensions 1, 2 and 3 these look like a fuzzy ball around the origin. But in high dimensions, it is more like a thin shell of radius sqrt(n). You can see this as the (squared) length of a random vector from that distribution is from the Chi^2 distribution which becomes more and more concentrated in higher dimensions.
A corollary of one of the facts listed there is that the ratio between the volumes of unit sphere and of the unit cube converges to 0 with d. Meaning, in high dimensions, the unit cube is all corners and no interior.
Another one is to consider the n-dimensional standard Gaussian distribution. In dimensions 1, 2 and 3 these look like a fuzzy ball around the origin. But in high dimensions, it is more like a thin shell of radius sqrt(n). You can see this as the (squared) length of a random vector from that distribution is from the Chi^2 distribution which becomes more and more concentrated in higher dimensions.