Re:High-dimensional spheres are "spikey"
by xyzzyz on Sunday May 20, 2012 @05:44AM
(#3998397)
A nearly flat cap from the 3D sphere with big radius will also have small volume. I think the word "spikey" is bad for getting your idea across.
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Re:High-dimensional spheres are "spikey"
by ColinWright on Sunday May 20, 2012 @05:53AM
(#3998406)
But in the 3D sphere the volume of the cap grows rapidly with the height. That's not true in higher dimensions, which is why in higher dimensions it behaves more like a spike than a sphere. It's the apparent contradiction of that image that helps prevent the usual mistake in visualization.
That's why I use the term, for that shock value.